Research seminar "Geometric and Harmonic Analysis"
This joint research seminar of the Universities of Aarhus and Paderborn is devoted to current research questions in the field of geometric and harmonic analysis.
The seminar takes place every Tuesday 2:153:30pm in room D 2 314 in hybrid form. If you are interested in participating online please contact Tobias Weich or Benjamin Delarue in order to receive the login details.
Organizers:
 Jan Frahm (Aarhus)
 Joachim Hilgert (Paderborn)
 Margit Rösler (Paderborn)
 Tobias Weich (Paderborn)
Program
16.04.2024  N.N. 
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23.04.2024  N.N. 
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30.04.2024  no seminar due to hiring committee talks 
07.05.2024  no seminar due to hiring committee talks 
14.05.2023  no seminar due to hiring committee talks 
21.05.2024  N.N. 
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28.05.2024  N.N. 
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04.06.2024  N.N. 
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11.06.2024  N.N. 
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18.06.2024  N.N. 
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25.06.2024  N.N. 
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02.07.2024  N.N. 
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09.07.2024  N.N. 
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16.07.2024  N.N. 
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Supported by Deutsche Forschungsgemeinschaft via CRCTRR 358 "Integral Strucutres in Geometry and Representation Theory"
Seminar Program (Past)
17.10.2023  Carsten Peterson (Paderborn) 
Titel:  Quantum ergodicity on the BruhatTits building for PGL(3, F) in the BenjaminiSchramm limit 
Abstract:  Originally, quantum ergodicity concerned equidistribution properties of Laplacian eigenfunctions with large eigenvalue on manifolds for which the geodesic flow is ergodic. More recently, several authors have investigated quantum ergodicity for sequences of spaces which ``converge'' to their common universal cover and when one restricts to eigenfunctions with eigenvalues in a fixed range. Previous authors have considered this type of quantum ergodicity in the settings of regular graphs, rank one symmetric spaces, and some higher rank symmetric spaces. We prove analogous results in the case when the underlying common universal cover is the BruhatTits building associated to PGL(3, F) where F is a nonarchimedean local field. This may be seen as both a higher rank analogue of the regular graphs setting as well as a nonarchimedean analogue of the symmetric space setting. The proof uses tools from padic representation theory, polytopal geometry, and the geometry of affine buildings. 


24.10.2023  Shi Wang (Shanghai)  zoom talk 
Titel:  Kleinian groups of small critical exponent 
Abstract:  Given a finitely generated discrete subgroup G which acts isometrically on the hyperbolic space, the critical exponent of G measures the exponential growth rate of the Gorbits. In joint work with Beibei Liu, we show that if the critical exponent is small, then G must be convex cocompact and virtually free. This partly answers a conjecture of Kapovich. 


31.10.2023  N.N. 
Titel:  tba 
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07.11.2023  Simon Becker (Zürich)  joint with Complex Quantum Systems seminar 
Titel:  Mathematics of magic angles 
Abstract:  Magic angles are a hot topic in condensed matter physics: when two sheets of graphene are twisted by those angles the resulting material is superconducting. I will present a very simple operator whose spectral properties are thought to determine which angles are magical. It comes from a 2019 PR Letter by TarnopolskyKruchkovVishwanath. The mathematics behind this is an elementary blend of representation theory (of the Heisenberg group in characteristic three), Jacobi theta functions and spectral instability of nonselfadjoint operators (involving Hörmander's bracket condition in a very simple setting). Recent mathematical progress also includes the proof of existence of generalized magicangles and computer assisted proofs of existence of real ones (LuskinWatson, 2021). The results will be illustrated by colourful numerics which suggest many open problems (joint work with M Embree, J Wittsten, M Zworski 2020 and T Humbert, M Zworski 2022). 


14.11.2023  Martin Hallnäs (Gothenburg) 
Title:  Integral equations for HeckmanOpdam hypergeometric functions and a quantum CalogeroMoser system 
Abstract:  Motivated by spherical functions theory, Heckman and Opdam introduced in the late 1980s hypergeometric functions associated with root systems as joint eigenfunctions of a commutative algebra of Weyl group invariant PDOs, which are related by conjugation to quantum integrals of the hyperbolic CalogeroMoser system. In this talk, I will consider the type A case and show that the corresponding hypergeometric functions satisfy a oneparameter family of explicit integral equations. I will also discuss an interpretation of the result in terms of a socalled Qoperator for the hyperbolic CalogeroMoser system. 


21.11.2023  Xiaocheng Li (Shandong University)  zoom talk 
Titel:  An estimate for spherical functions on SL(3,R) 
Abstract:  We prove an estimate for spherical functions $\varphi_\lambda(a)$ on SL(3,R), establishing uniform decay in the spectral parameter $\lambda$ when the group variable $a$ is restricted to a compact subset of the abelian subgroup $A$. In the case of SL(3,R), it improves a result by J.J. Duistermaat, J.A.C. Kolk and V.S. Varadarajan by removing the limitation that $a$ should remain regular. As in their work, we estimate the oscillatory integral that appears in the integral formula for spherical functions by the method of stationary phase. However, the major difference is that we investigate the stability of the singularities arising from the linearized phase function by classifying their local normal forms when $\lambda$ and $a$ vary. 


28.11.2023  Paul Nelson (Aarhus)  zoom talk 
Titel:  Microlocal lifts and quantum unique ergodicity for GL(2,Qp) 
Abstract:  We will present the paper named in the title, which available at https://arxiv.org/abs/1601.02528. The paper constructs a representationtheoretic microlocal lift for principal series representations of GL(2,Qp), and uses this to prove a form of QUE for Hecke eigenfunctions on certain path spaces over finite arithmetic graphs. This provides an analogue at nonarchimedean places of some results of Zelditch, Wolpert and Lindenstrauss at the archimedean place. 


05.12.2023  Andrew Sanders (Cambridge, Masschusetts)  zoom talk 
Titel:  Uniformization of Locally Flag Manifolds 
Abstract:  By the PoincareKoebe uniformization theorem, every closed Riemann surface of negative Euler characteristic can be realized as a quotient of the upper half plane by a discrete subgroup of Mobius transformations. Moving from the Riemann sphere to other complex homogeneous flag varieties F, the theory of Anosov subgroups gives rise to a vast array of compact complex manifolds uniformized by open domains in F. In this talk, we aim to give an introduction through examples to the basic objects of the theory, discuss the (lack of a robust) function theory, and explain some results concerning the deformation theory of these objects. No prior knowledge of Anosov subgroups will be assumed. This is joint work with David Dumas (UIC). 


12.12.2023  Quentin Labriet (Aarhus)  zoom talk 
Title:  Convolution formulas for Jacobi polynomials and representation theory of sl(2). 
Abstract:  The goal of the talk is to present some convolutions formulas for Jacobi polynomials and how to obtain them using the representation theory of the Lie algebra sl(2). Doing so I will present some realizations of the socalled Hahn and Racah algebras. We will apply these formulas to prove identities involving the symmetry breaking operators involved in this problem called the RankinCohen brackets. This is a joint work with L. Poulain d'Andecy from the university of Reims. 


09.01.2024  Christian Arends (Aarhus)  zoom talk 
Titel:  Poisson transforms and a pairing formula for graphs 
Abstract:  In this talk I will present key ideas from two recent papers (https://arxiv.org/abs/2312.09101, arxiv.org/abs/2312.10509). In doing so, I will focus on the case of regular graphs resp. its universal covering trees and show how to construct generalizations of scalar Poisson transforms using the automorphism group of the tree. We state some results on associated operator valued Hecke algebras and discuss how this construction gives rise to a spectral correspondence between eigenspaces of a Laplace operator acting on functions on the edges and eigendistributions (socalled resonances) of a transfer operator associated to the shift on onesided infinite nonbacktracking paths. Moreover, we discuss a pairing formula of resonant states and their negative time analogues, the coresonant states. This is joint work with Jan Frahm and Joachim Hilgert. 


16.01.2024  Mostafa Sabri (NYU Abu Dhabi)  zoom talk 
Titel:  Ergodic Theorems for Continuoustime Quantum Walks on Crystal Lattices and the Torus 
Abstract:  We give several quantum dynamical analogs of the classical KroneckerWeyl theorem, which says that the trajectory of free motion on the torus along almost every direction tends to equidistribute. As a quantum analog, we study the quantum walk exp(−itΔ)ψ starting from a localized initial state ψ. Then the flow will be ergodic if this evolved state becomes equidistributed as time goes on. We prove that this is indeed the case for evolutions on the flat torus, provided we start from a point mass, and we prove discrete analogs of this result for crystal lattices. On some periodic graphs, the mass spreads out nonuniformly, on others it stays localized. Finally, we give examples of quantum evolutions on the sphere which do not equidistribute. 
23.01.2024  JeanPhilippe Anker (Orleans) 
Titel:  Spectral projections on hyperbolic surfaces 
Abstract:  In an ongoing collaboration with Pierre Germain (Imperial College) and Tristan Léger (NYU and Princeton University), we study $L^2 \to L^p$ estimates (p>2) for spectral projections in a small window on (locally) symmetric spaces. For hyperbolic surfaces of infinite area and with no cusps, we have recently obtained almost optimal results [arXiv:2306.12827]. In this talk, I will give a brief survey of the problem, which goes back to the restriction theorem of SteinTomas in the Euclidean setting, comment on our result for hyperbolic surfaces and present the main steps of its proof. 


30.01.2024  Daniele Galli (Universität Zürich) 
Titel:  A cohomological approach to RuellePollicott resonances of Anosov diffeomorphisms 
Abstract:  Given a transitive Anosov diffeomorphism on a closed connected manifold, it is known that, for enough smooth observables, the system is mixing w.r.t. the measure of maximal entropy. Accordingly, it makes sense to investigate the speed of decay of correlations and to look for the socalled RuellePollicott resonances, in order to determine an asymptotic for the correlation limit. In this talk I will describe some recent ideas to tackle these questions. In particular, I will point out some surprising connections between the spectrum of a particular transfer operator acting on suitable Anisotropic Banach spaces of currents and the spectrum of the action induced by the Anosov map on the De Rham cohomology. As a corollary, we obtain an upper bound for the speed of mixing, w.r.t. the measure of maximal entropy. This talk is based on my PhD thesis that I defended last June at the University of Bologna. 
04.04.2023  Joachim Hilgert (Paderborn University) 
Titel:  Quantization in fibering polarizations, Mabuchi rays and geometric Peter–Weyl theorem 
Abstract:  For Lie groups and symmetric spaces one has Fourier transformations between spaces on which the symmetry group acts. The Fourier transforms are intertwining the (highly reducible) representations, thus showing their equivalence. We analyze the question whether the intertwining operator can be obtained from a change of polarization in the sense of geometric quantization and give a positive answer fro the case of compact groups. In this case the change of polarization yields at the same time the PeterWeyl decomposition of L^2(G) and the BorelWeil theorem for the irreducible components.
The key tool is a connection on the space of Kähler polarizations on the cotangent bundle whose parallel transport provides the intertwiner.
This is joint work with T. Baier, O. Kaya, J. Mourao and J. Nunes. 
11.04.2023  No seminar due to CIRM Workshop 
18.04.2023  N.N. 
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25.04.2023  Hongwei Zhang (Ghent) 
Titel:  Dispersive equations on noncompact Riemannian symmetric spaces 
Abstract:  In this presentation, we provide an overview of spacetime mixed norm estimates for dispersive equations on noncompact symmetric spaces. We focus on two key estimates: the Strichart inequality and the Smoothing property. The former is based on the pointwise kernel estimate, while the latter relies on the SteinWeiss inequality, also known as the HardyLittlewoodSobolev inequality with double weights. These results differ from the classical ones in the Euclidean setting due to the particular geometry at infinity. Additionally, we discuss how the geometric properties of the discrete group affect these results on locally symmetric spaces. 
02.05.2023  no seminar due to parallel Complex Quantum systems seminar 
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09.05.2023  KarlHermann Neeb (Uni Erlangen) 
Titel:  Causal symmetric spaces and nets of operator algebras 
Abstract:  In the theory of local observables in Algebraic Quantum Field Theory (AQFT) modular theory creates a oneparameter group of modular automorphisms from a single state and this group often has a geometric implementation. If modular groups are contained in finitedimensional Lie groups, they naturally lead to 3gradings of the Lie algebra and further to causal symmetric spaces. Conversely, we explain how nets of local observables (resp. of standard subspaces) on causal symmetric spaces can be constructed for all irreducible unitary representations of simple Lie groups which are either linear or locally isomorphic to SL(2,R). 
16.05.2023  no seminar due to parallel Complex Quantum systems seminar 
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23.05.2023  Thibault Lefeuvre (Paris Jussieu) 
Titel:  Marked length spectrum rigidity for Anosov surfaces 
Abstract:  I will show that on a closed Anosov surface (e.g. surface with negative sectional curvature), the marked length spectrum, that is the length of closed geodesics marked by the free homotopy of the surface, determines the metric up to isometry. The proof combines microlocal analysis with the geometry of complex curves. If time permits, I will also discuss the case of surfaces with boundary. Joint works with A. Erchenko, C. Guillarmou and G. Paternain. 
30.05.2023  Zhicheng Han (Uni Göttingen) 
Titel:  Various spectra of the universal cover of SL2(R) 
Abstract:  In this talk we will discuss the universal cover of SL_2(R), treating them as Riemannian manifolds, and study its associated differential form spectrum and Dirac operator spectrum. We will also discuss its application to computing certain topological invariants (NovikovShubin invariants) If time permits, we will discuss some of the ongoing attempts to generalize this to more general semisimple Lie groups (due to HerbWolf) such as the universal cover of Sp(2n, R). 
06.06.2023  Nikhil Savale (Uni Köln) 
Titel:  Spectral Theory of the SubRiemannian Laplacian 
Abstract:  SubRiemannian (sR) geometry is the geometry of bracketgenerating metric distributions on a manifold. Peculiar phenomena in sR geometry include the exotic Hausdorff dimension describing the growth rate of the volumes of geodesic balls. As well as abnormal geodesics that do not satisfy any variational equation. In this talk I will survey my results which show how both these phenomena are reflected in the spectral theory of the hypoelliptic Laplacian in sR geometry. 
13.06.2023  Effie Papageorgiou (Uni Paderborn) 
Titel:  Asymptotic behaviour of solutions to the heat equation on noncompact symmetric spaces 
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20.06.2023  Sebastien Gouezel (University Rennes) (zoom) 
Titel:  Ruelle Resonances for Geodesic Flows on Noncompact Manifolds 
Abstract:  Ruelle resonances are complex numbers associated to a dynamical system that describe the precise asymptotics of the correlations for large times. It is well known that this notion makes sense for smooth uniformly hyperbolic dynamics on compact manifolds. In this talk, I will consider the case of the geodesic flow on some noncompact manifolds. In a class of such manifolds (called SPR), I will explain that one can define Ruelle resonances in a halfplane delimited by a critical exponent at infinity. Joint work with Barbara Schapira and Samuel Tapie. 
27.06.2023  Giovanni Forni (University of Maryland) 
Titel:  Weakly mixing billiards in polygons 
Abstract:  According to numerical simulations (Artuso,Casati, Guarneri, Prosen, Wang, ...) the billiard in the random polygon is ergodic and mixing. The mathematical theory of billiards in polygons is rather welldeveloped for billiards in *rational* polygons (with limitations that will be explained), but there are few results on the ergodic theory of *typical* polygons. KerckhoffMasurSmillie proved in 1986 that ergodic polygons are dense (in the space of polygons), by fast approximation based on their ergodicity result for rational polygons. In this talk we will present a joint result with Jon Chaika that weakly mixing polygons are also dense. 
04.07.2023  Yann Chaubet (Cambridge) (zoom) 
Titel:  Dynamical zeta functions counting triangles and Betti numbers 
Abstract:  In this talk, I will present recent results concerning special values of certain combinatorial zeta functions counting geodesic paths in triangulations. I will show that those values are related to some topological invariants. As such, we recover the first Betti number or L^{^2}Betti number of a compact manifold, as well as the linking number of knots in a 3manifold. This is a joint work with Léo Bénard, Viet Dang and Thomas Schick. 
11.07.2023  Chris Lutsko (Ruttgers University) 
Titel:  An abstract spectral approach to orbit counting 
Abstract:  One of Selberg's many contributions to hyperbolic geometry is an effective count for the number of (hyperbolic) lattice points lying in a ball of radius T. To do this he used the pretrace formula and estimates on the different spectral components. If, instead of a lattice, one considers a thin group, there is no spectral decomposition, and so one must use softer methods to approach the same problem. In this talk I will present this soft approach, and discuss an application to counting circles in Apollonian packings. I will present joint work with Alex Kontorovich and Dubi Kelmer. 
11.10.2022 20:30 zoom  Zhongkai Tao (UC Berkeley) 
Titel:  Spectral asymptotics for kinetic Brownian motion on locally symmetric spaces 
Abstract:  We prove the strong convergence of the spectrum of the kinetic Brownian motion to the spectrum of base Laplacian for locally symmetric spaces. This generalizes recent work of KolbWeichWolf on constant curvature surfaces in two aspects. First we give a construction of Casimir operators for a large family of locally homogeneous spaces, including all locally symmetric spaces. Second, we analyze the spectrum carefully using the Schur complement formula and prove a strong convergence by studying projections to the spherical harmonics. This is joint work with Qiuyu Ren. 
18.10.2022  Allan Merino (University of Ottawa, Canada)  online 
Titel:  Classification and double commutant property for dual pairs in an orthosymplectic Lie supergroup 
Abstract:  In his wonderful paper “Remarks on classical invariant theory”, Roger Howe suggested that his classical duality should be extendable to superalgebras/ supergroups. Roughly speaking, by restricting the spinoroscillator representation (w, H) of the complex orthosymplectic Lie superalgebra spo(V) to some particular super dual pairs (g, g’) (or (G, g’)), he proved that the action of g’ on every Gisotypic components is irreducible. Some results have been obtained for other dual pairs (Howe, Nishiyama, Sergeev, ChengWang, HoweLu, DavidsonKujawaMuth ...) but a general theory for a real or complex orthosymplectic Lie superalgebra (or supergroup) is not known yet. In a recent work with Hadi Salmasian, we obtained a classification of irreducible reductive dual pairs in a real or complex orthosymplectic Lie supergroup SpO(V). Moreover, we proved a “double commutant theorem” for all dual pairs in a real or complex orthosymplectic Lie supergroup. Time permitting, I will explain other questions we are currently working on related to the extension of Howe duality to super dual pairs. 
25.10.2022  Clemens Weiske  online 
Titel:  Heisenberg parabolically induced representations of Hermitian Lie groups 
Abstract:  Let G be a hermitian Lie group. Then G naturally contains a maximal parabolic subgroup MAN whose unipotent radical is a Heisenberg group. Consider the corresponding spherical principal series representations of G, realised on functions on the radical opposite to N, which is also a Heisenberg group. Under the Heisenberg group Fourier transform, this space transforms into operators on Fock spaces. We show that these Fock spaces decompose into a multiplicity free direct sum under the action of M, which is in general noncompact. We find an explicit expression for the KnappStein intertwining operator on the Fourier transformed side, generalising classical results by Cowling for the case G=SU(1,n), where M is compact. This gives a new construction of the complementary series and of certain interesting unitarizable subrepresentatio. The presented results are joint work with Jan Frahm and Genkai Zhang. 
08.11.2022  no seminar due to parallel Complex Quantum Systems seminar 
15.11.2022  no seminar due to parallel Complex Quantum Systems seminar 
22.11.2022  no seminar due to parallel Complex Quantum Systems seminar 
29.11.2022  Hamid Al Saqban (Universität Paderborn)  hybrid 
Titel:  Limit theorems and the KontsevichZorich cocycle 
Abstract:  The KontsevichZorich (KZ) cocycle is a dynamical system that is closely related to the derivative cocycle of the Teichmuller geodesic flow. While these dynamical systems are interesting in and of themselves, they also act as renormalizing dynamical systems for straightline flows on translation surfaces. The main goal of these two talks is to introduce and motivate translation surfaces and their moduli spaces, and to state and sketch the proofs of recent results, parts of which are joint with G. Forni, that establish the existence of large fluctuations for the asymptotic growth of the norm of the KZ cocycle. 
06.12.2022  Hamid Al Saqban(Universität Paderborn)  hybrid 
Titel:  Limit theorems and the KontsevichZorich cocycle 
Abstract:  The KontsevichZorich (KZ) cocycle is a dynamical system that is closely related to the derivative cocycle of the Teichmuller geodesic flow. While these dynamical systems are interesting in and of themselves, they also act as renormalizing dynamical systems for straightline flows on translation surfaces. The main goal of these two talks is to introduce and motivate translation surfaces and their moduli spaces, and to state and sketch the proofs of recent results, parts of which are joint with G. Forni, that establish the existence of large fluctuations for the asymptotic growth of the norm of the KZ cocycle. 
13.12.2022  Ali Suri (Universität Paderborn)  hybrid 
Titel:  Curvature and stability of quasigeostrophic motion 
Abstract:  In this talk, first we restate the necessary background about quantomorphism group and central extension of the corresponding Lie algebra. Then we derive the quasigeostrophic equation as an EulerArnold equation of the L^2 metric on this central extension. Afterwards, using the Lie algebra structure constants, we study the curvature and its impact on the stability of geodesics which are solutions of the quasigeostrophic equation. 
20.12.2022  Pritam Ganguly (Universität Paderborn)  hybrid 
Titel:  An uncertainty principle and its connection with quasianalyticity 
Abstract:  An Uncertainty principle due to Ingham provides the best possible decay of the Fourier transform of a function on \mathbb{R} which vanishes on a nonempty open set. To prove this result Ingham used the classical DenjoyCarleman theorem for quasianalytic functions on the real line. In this talk, we plan to discuss similar results in a more general context. To be precise, we will discuss an $L^2$version of the DenjoyCarelman theorem (due to Chernoff) and use this to prove the Inghamtype uncertainty principle for the (generalized) spectral projections associated with the Laplacian. To life less complicated, we will limit ourselves mainly to Euclidean spaces. 
17.01.2023  Frédéric Naud (Sorbonne Université, France)  online 
Titel:  GOE and GUE statistics on random hyperbolic surfaces. 
Abstract:  We will describe some models of Random compact hyperbolic surfaces on which it is possible to study, in a large genus regime, the smooth linear spectral statistics for the (twisted) Laplace spectrum. We will show that the variance converges, after taking adhoc limits, to the one given by the random matrix models of GOE and GUE. This is, in a fairly weak sense, a rigourous justification of some popular conjectures of quantum chaos from the 80s. 
31.01.2023  William Hide  hybrid 
Titel:  Short geodesics and small eigenvalues on random hyperbolic punctured spheres 
Abstract:  We study the geometry and spectral theory of random genus 0 hyperbolic surfaces with n cusps as n tends to infinity. In particular, we are interested in the number of "short" closed geodesics and "small" Laplacian eigenvalues for surfaces sampled with WeilPetersson probablity. Inspired by the work of Mirzakhani and Petri (in the case of large genus compact surfaces), we demonstrate Poisson statistics for the number of closed geodesics on surfaces with n cusps whose lengths are on scales 1/sqrt(n). Using similar ideas we show that with high probability, a random genus 0 surface with n cusps has polynomially (in n) many small eigenvalues as n tends to infinity. This is joint work with Joe Thomas (Durham). 
07.02.2023  Henrik Gustafsson (Umeå University, Sweden)  online 
Titel:  Automorphic forms and their Fourier coefficients 
Abstract:  I will give a basic introduction to automorphic forms on reductive groups and their Fourier coefficients with respect to different unipotent subgroups. I will review a series of papers joint with Dmitry Gourevitch, Axel Kleinschmidt, Daniel Persson and Siddhartha Sahi for how these Fourier coefficients can be computed by a reduction principle. In particular, we have shown that they simplify drastically for automorphic forms in small automorphic representations, and I will give a brief overview of the applications of these results to scattering amplitudes in string theory. 
12.04.2022  Moritz Doll (Bremen) 
Titel:  Divisor of the Selberg Zeta Function for Hyperbolic Surfaces with Twists 
Abstract:  We consider a finitely generated cocompact Fuchsian group $\Gamma$. The quotient $X = \mathbb{H} / \Gamma$ is a geometrically finite hyperbolic surface with infinite area that might have conical singularities. Given a unitary representation $\chi$ of $\Gamma$, we show that the associated Selberg zeta function admits a factorization, which gives a spectral interpretation of its zeros in terms of the resonances of a suitable Laplacian. This generalizes a theorem by BorthwickJudgePerry, where a similar factorization was shown for untwisted hyperbolic surfaces without conical singularities. This is based on joint work with Ksenia Fedosova and Anke Pohl. 
19.04.2022  Benjamin Hinrichs (Jena) 
Titel:  InfraredCriticality and the Qubit 
Abstract:  In models from quantum physics describing the interaction of a quantum mechanical particle with a quantum field of bosons, one observes the phenomenon of infraredcriticality if the bosons are massless. From the physical perspective, this is attributed to the fact that even tiny energy fluctuations can lead to the creation of an infinite cloud of lowenergy bosons. Mathematically, infraredcriticality means that the selfadjoint Hamilton operator describing the system does not have a ground state, i.e., the infimum of its spectrum is not an eigenvalue. In this talk, we will first demonstrate this phenomenon on a toy quantum field theory. After that, we consider the spin boson model, in which the particle interacting with the massless bosonic field is a qubit. We discuss a recent proof that the spin boson model does have a ground state, even in the infraredcritical situation, if the coupling of qubit and field is below a critical value. Heuristically, this is explained by the fact that symmetries of the model can lead to cancellations of infrareddivergences. Our proof combines three ingredients: a compactness argument, a FeynmanKacNelson type formula and a correlation bound for onedimensional Ising models. The talk is based on joint work with David Hasler and Oliver Siebert. 
10.05.2022  Renato Renner (ETH Zürich) 
Titel:  From Quantum Cryptography to Quantum Gravity 
Abstract:  What statements can we make about information that is inaccessible to us? This question arises both in quantum cryptography and in quantum gravity. In the former, we would like to put bounds on the information that an eavesdropper may possess. In the latter, we are interested, for instance, in the information content of a black hole. In this talk I will show how quantum information theory allows us to characterise such inaccessible information. As applications, I will discuss some implications to quantum cryptography and quantum gravity. 
17.05.2022  Josh Maglione (Uni Bielefeld) 
Titel:  Igusa zeta functions and flag HilbertPoincaré series of hyperplane arrangements 
Abstract:  We define a class of multivariate rational functions associated with hyperplane arrangements called flag HilbertPoincaré series. We show how these rational functions are connected to local Igusa zeta functions and class counting zeta functions for certain graphical group schemes studied by Rossmann and Voll. We report on a general selfreciprocity result and explore other connections within algebraic combinatorics. This is joint work with Christopher Voll and with Lukas Kühne. 
24.05.2022  Javier Echevarria Cuesta (Ecole Polytechnique, Paris) 
Titel:  An algorithm to compute the spectrum of the LaplaceBeltrami operator on hyperbolic surfaces 
Abstract:  The eigenvalues and eigenfunctions of the LaplaceBeltrami operator on a given manifold encode a wealth of information; they help us solve inverse problems, the heat equation, the wave equation, and the Schrödinger equation, to name a few applications. It is hence a classical problem to compute them. Without having to look any further, the case of twodimensional oriented surfaces of constant curvature is already very rich. Indeed, while we fully understand the spectral theory for these manifolds when the curvature is nonnegative, the hyperbolic case eludes explicit computations. Here we propose a new algorithm for their rigorous approximation. This is joint work with Alexander Strohmaier. 
31.05.2022  NN 
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07.06.2022  Krystal Guo (University of Amsterdam)  Hörsaal D1 
Titel:  Quantum walks on graphs 
Abstract:  The interplay between the properties of graphs and the eigenvalues of their adjacency matrices is wellstudied. Important graph invariants, such as diameter and chromatic number, can be understood using these eigenvalue techniques. In this talk, we use classical techniques in algebraic graph theory to study quantum walks. A system of interacting quantum qubits can be modelled by a graph. The evolution of the quantum system can be completely encoded as a quantum walk in a graph, which can be seen, in some sense, as a quantum analogue of random walk. This gives rise to a rich connection between algebraic graph theory, linear algebra and quantum computing. In this talk, I will present recent results on the average mixing matrix of a graph; a quantum walk has a transition matrix which is a unitary matrix with complex values and thus will not converge, but we may speak of an average distribution over time, which is modelled by the average mixing matrix. 
14.06.2022  NN 
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21.06.2022  Samuel Edwards (University of Bristol)  Hörsaal D1 
Titel:  Spectral theory and dynamics on infinitevolume quotients Γ\G 
Abstract:  Connections between representation and spectral theory, and dynamical systems on homogeneous spaces related to semisimple Lie groups G have a long history of study, going back to GelfandFomin. In the most classical setting, one considers dynamics on quotient spaces Γ\G, where Γ is a lattice in G. The other main setting that has been studied are infinitevolume quotients of rankone Lie groups by geometrically finite discrete subgroups Γ. Results in this setting (initiated by Patterson and Sullivan) relate the critical exponent of the group Γ, the spectrum of the Laplace operator on the locally symmetric space Γ\G/K (K being a maximal compact subgroup of G), and dynamics of the geodesic flow on the unit tangent bundle of Γ\G/K. Recently, there has been some interest in extending these results to infinite volume quotients Γ\G, where G is a higherrank group, and Γ is an Anosov subgroup of G. I will discuss join work with Hee Oh in this setting, where we study relations between the eigenfunctions of the invariant differential operators on Γ\G/K, the growth indicator function of Γ (which is the higherrank analogue of the critical exponent), and the conformal measures that govern dynamics on Γ\G. 
28.06.2022  Guenda Palmirotta (Luxembourg)  now ONLINE! 
Titel:  Solvability of invariant systems of differential equations on the hyperbolic plane 
Abstract:  In the Euclidean case, it is wellknown, by Malgrange and Ehrenpreis, that linear differential operators with constant coefficients are solvable. However, what happens, if we genuinely extend this situation and consider systems of linear invariant differential operators, is still solvable? In case of $\mathbb{R}^n$ (for some positive integer $n$), the question has been proved mainly by Hörmander. We will show that this remains still true for Riemannian symmetric spaces of noncompact type $X=G/K$. More precisely, we will present a possible strategy to solve this problem by using the Fourier transform and its PaleyWiener(Schwartz) theorem for (distributional) sections of vector bundles over $X$. We will get complete solvability for the hyperbolic plane $\mathbb{H}^2=SL(2, \mathbb{R})/SO(2)$ and beyond. This work was part of my doctoral dissertation supervised by Martin Olbrich. 
05.07.2022  Viet Dang (Institut Math. Jussieu)  zoom 
Titel:  Length Orthospectrum between convex bodies on flat tori. 
Abstract:  I will describe joint work with Gabriel Rivière and Matthieu Léautaud where we construct new anisotropic Sobolev spaces on cotangent of tori. These spaces are adapted to the study of the transport by the geodesic flow. As an application, we show a new summation formula of MeyerGuinand type relating the orthogeodesic spectrum between two convex bodies and the spectrum of the magnetic Laplacian on the torus. 
06.07.2022 11:1512:45  Job Kuit (Paderborn)  Raum J3.330 
Titel:  The most continuous part of the Plancherel decomposition for a real spherical space 
Abstract:  Let Z be a homogeneous space of a real reductive group G. The Plancherel decomposition of Z is the decomposition of the space L^2(Z) of square integrable functions into a direct integral of irreducible unitary representations of G. In general this decomposition has a mixed discrete and continuous nature. 
12.07.2022  Norio Konno (Yokohama National University)  zoom 
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19.10.2021  Kein Seminar 
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26.10.2021  Lasse Wolf (Universität Paderborn) 
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02.11.2021  Mohammad Talebi (Universität Oldenburg) 
Titel:  Analytic Torsion for manifolds with fibred boundary metrics

Abstract:  The Analytic Torsion was introduced by Daniel Burrill Ray and Isadore M.

09.11.2021  N.n. 
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16.11.2021  Simon Roby (Tsinghua University) 
Titel:  Resonances of the Laplace operator on homogeneous vector bundles over the real hyperbolic space 
Abstract:  We study the resonances of the Laplacian acting on the compactly supported sections of the homogeneous vector bundle over the real hyperbolic space $H^n(\mathbb{R})=G/K$ determined by a representation $\tau$ of the maximal compact $K$ of $G$. We will see how to determine the resonances. Under the additional assumption that $\tau$ occurs in the spherical principal series, we determine the resonance representations. They are all irreducible. We will see how to find their Langlands parameters and their wave front sets. If additional time is available, we will see what are the differences if we replace the real hyperbolic space by others hyperbolic spaces. 
23.11.2021  Christian Arends (Universität Paderborn) 
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30.11.2021  Damian Osajda (University of Wroclaw) 
Titel:  Helly graphs and their automorphism groups 
Abstract:  A graph is Helly if each family of pairwise intersecting (combinatorial) balls has nonempty intersection. Groups acting geometrically on such graphs are themselves called Helly. The family of such groups is vast, it contains: Gromov hyperbolic groups, CAT(0) cubical groups, Garside groups, FC type Artin groups, and others. On the other hand, being Helly implies many important algorithmic and geometric features of the group. In particular, such groups act geometrically on spaces with convex geodesic bicombing, equipping them with a kind of CAT(0)like structure. I will present basic properties and examples of Helly groups. The talk is based on joint works with Jeremie Chalopin, Victor Chepoi, Anthony Genevois, Hiroshi Hirai, Jingyin Huang, Motiejus Valiunas, Thomas Haettel. 
07.12.2021  Kein Seminar wegen Oberwolfach Workshop 
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14.12.2021  Andreas Juhl (HumboldtUniversität Berlin) 
Titel:  Singular Yamabe Problems and extrinsic conformal Laplacians 
Abstract:  For any evendimensional Riemannian manifold (M^{n}, g), there is a distin guished sequence P_{2N} (g) (2N ≤n) of geometric differential operators of the form ∆_{g}^{N} + ··· which are conformally invariant (GJMSoperators). Here P_{2}(g) is the Yamabe operator (or conformal Laplacian) and P_{4}(g) is the Paneitz operator (discovered 1983). The definition and analysis of these operators rest on the ambient metric or the PoincaréEinstein metric in the sense of Fefferman and Graham. In recent years, it was found that there is a farreaching generalization of these constructions for hypersurfaces M ↪ X in any Riemannian manifold X. The resulting conformally invariant operators still live on M but their definition depends on the embedding. I will describe the basic ideas of this theory which among other things leads to higherorder analogs of the Willmore functional. The talk rests on work of GoverWaldron and JuhlOrsted. 
21.12.2021  Antoine Meddane (Université de Nantes) 
Titel:  Morse complex and resonances for Axiom A flows. 
Abstract:  Axiom A flows were flows introduced by Smale in the 70' to generalize the Morse gradient flows and the geodesic flows on negatively curved manifolds. I will explain how tools from microlocal analysis and from the theory of semiclassical resonances of HelfferSjöstrand can be used to construct a Morse complex for Axiom A flows. In particular, it implies a generalization of Morseinequalities in this context which was something not known yet. 
11.01.2022  Dominik Brennecken (Universität Paderborn) 
Titel:  Dunkl theory in line with the analysis on symmetric cones 
Abstract:  Radial analysis on symmetric cones is closely related to the Dunkl theory associated to root systems of type A. Spherical functions, Laplace transform and hypergeometric series have analogues in Dunkl theory which allow to extend many concepts and results to this setting. 
18.01.2022  Philipp Schütte (Universität Paderborn) 
Titel:  Weighted Zeta Functions and Invariant Ruelle Distributions on Open Hyperbolic Systems 
Abstract:  Ruelle resonances constitute important invariants for chaotic (hyperbolic) dynamical systems and their theory has progressed greatly in the last couple of decades. Building on the work of Dyatlov/Guillarmou (2016) in this subject area we define and discuss a notion of weighted zeta function for open hyperbolic systems. First we sketch a proof of their meromorphic continuation and the fact that their poles encode the resonances. Then we show how their residues can be identified with socalled invariant Ruelle distributions. On the one hand this yields a residue interpretation of PattersonSullivan distributions, on the other hand this enables their numerical calculation for example systems like geodesic flows on Schottky surfaces and 3disk obstacle scattering. 
25.01.2022  Anders Karlsson (University of Geneva) 
Titel:  Spectral zeta functions of graphs and analytic number theory 
Abstract:  From the spectrum of a Laplace operator one can form a zeta function. In the case of the circle it gives Riemann’s zeta function. We study such functions for certain finite and infinite graphs. These functions appear (incognito) in several areas of mathematics and physics. In particular we study rather precise asymptotic of discrete tori as is done in statistical physics, and recover spectral zeta functions of real tori which are of interest in number theory. As it turns out, the Riemann hypothesis is equivalent to an approximate functional equation of the spectral zeta functions of cyclic graphs (whose special values incidentally appear in the Verlinde formulas in algebraic geometry / mathematical physics). Joint work with F. Friedli, G. Chinta and J. Jorgenson. 
01.02.2022  Khalid Koufany (Université de Lorraine) 
Titel:  Symmetry breaking differential operators for tensor products of spinorial representations 
Abstract:  Joint work with JeanLouis Clerc. 
13.04.2021  NN 
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20.04.2021  Corina Ciobotaru (IHÉS) 
Titel:  Chabauty limits of subgroups of SL(n,Q_p) 
Abstract:  For a locally compact group G (e.g. G=SL(n,Q_p)) the set S(G) of all closed subgroups of G is a compact topological space with respect to the Chabauty topology. Given a subset X of S(G) it is natural to ask what is the closure of X in S(G) with respect to the Chabauty topology. In a joint work with Arielle Leitner and Alain Valette we study such closure when X is the set of all SL(n,Q_p)conjugates of the diagonal Cartan subgroup C of SL(n,Q_p). By using the action of SL(n,Q_p) on its associated Bruhat—Tits building and an explicit, wellbehaved, replacement of a Lie functor on the closure of our set X, we are able to give a classification of all the limits of X and to compute all of them (up to conjugacy) when n < 5. 
27.04.2021  Yann Chaubet (Université ParisSaclay) 
Titel:  Closed geodesics with prescribed intersection numbers 
Abstract:  On a closed negatively curved surface, Margulis gave the asymptotic growth of the number of closed geodesics of bounded length, when the bound goes to infinity. In this talk, we will investigate such a counting result for closed geodesics of which certain intersection numbers (with a given family of pairwise disjoint simple closed geodesics) are prescribed. 
04.05.2021  Léo Bénard (Universität Göttingen) 
Titel:  Asymptotics of twisted Alexander polynomials and hyperbolic volume 
Abstract:  Given a hyperbolic 3manifold of finite volume M, we compute the asymptotics of the family of twisted Alexander polynomials on the unit circle. We show it grows exponentially as the volume times the square of the dimension of the representation. Joint work with J. Dubois, M. Heusener and J. Porti. The proof goes through the study of the analytic torsion of some compact hyperbolic manifolds obtained by Dehn surgery on M. 
11.05.2021  Quentin Labriet (Université de Reims ChampagneArdenne) 
Titel:  Symmetry breaking operators and orthogonal polynomials 
Abstract:  Symmetry breaking operators are intertwinning operators for the restriction of an irreducible representation. In some cases, these are given by differential operators whose symbol is related some classical orthogonal polynomials. First, I will describe the example of the RankinCohen brackets which are symmetry breaking operators for the tensor product of two representation of the holomorphic discrete series of SL2(R). I will explain how they are related to Jacobi polynomials, and to the classical Jacobi transform. In a second part, I will discuss some ongoing work on the restriction for representation of the holomorphic discrete series for the conformal group of a tube domain. 
18.05.2021  NN 
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01.06.2021  NN 
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08.06.2021  Benjamin Küster (Universität Paderborn) 
Titel:  Oscillatory integrals in equivariant cohomology 
Abstract:  When a symplectic manifold carries a Hamiltonian action of a compact Lie group, it is an elementary question how the topology of the symplectic quotient can be described in terms of the original Hamiltonian group action. Some tools that allow to partially achieve this goal are the Cartan model of equivariant cohomology and the Kirwan map, which I will briefly introduce in my talk. I will then explain how oscillatory integrals arise in that context and what the difficulties and new features are when one considers singular symplectic quotients. 
15.06.2021  JeanPhilippe Anker (Universite d'Orleans) 
Titel:  Bottom of the $L^2$ spectrum of the Laplacian on locally symmetric spaces 
Abstract:  Let $X=G/K$ be a Riemannian symmetric space of noncompact type, let $\Gamma$ be a discrete torsion free subgroup of $G$, let $Y\=\Gamma\backslash G/K$ be the associated locally symmetric space and let $\Delta$ be the LaplaceBeltrami operator on $Y$. In rank one, a celebrated result, due to Elstrodt, Patterson, Sullivan and Corlette, expresses the bottom of the $L^2$ spectrum of $\Delta$ in terms of the critical exponent of the Poincar\'e series of $\Gamma$ on $X$. A less precise result was obtained later on by Leuzinger in higher rank. We shall discuss in this talk higher rank analogs of the rank one result, which are obtained by considering suitable Poincar\'e series. This is joint work with HongWei Zhang [arXiv:2006.06473].

22.06.2021  Gerhard Keller (Universität Erlangen) 
Titel:  Bfree systems and their automorphisms 
Abstract:  I plan to start with a brief introduction to Bfree dynamical systems (derived from Bfree numbers like e.g. the squarefree ones). After a short description of the range of dynamical possibilities of these systems, I will concentrate on the two extreme ends of this range, namely on those Bfree systems which are "as chaotic as possible" (like the squarefree system), and those which are "as close to being periodic as possible" (regular Toeplitz systems). For these two classes of topological dynamical systems I will report about recent and ongoing progress in understanding the automorphism group of the systems. 
29.06.2021  Genkai Zhang (Chalmers University of Technology) 
Titel:  Branching of metaplectic representation of Sp(n, R) under its principal SL(2, R) subgroup 
Abstract:  Any simple split Lie group $G$ has a unique principal S=SL(2, R) subgroup, by the work of Kostant. We study the branching problem for holomorphic representations of G=Sp(n, R) under S. A complete decomposition is found for the metaplectic representation of G=Sp(2, R). We use both some classical method of orthogonal polynomials and the geometric tool of Chern connection. 
06.07.2021  Agnieszka Hejna (University of Wroclaw) 
Titel:  Harmonic analysis in the rational Dunkl setting 
Abstract:  Dunkl theory is a generalization of Fourier analysis and special function This talk is based on the joint articles with JPh. Anker and J. Dziubanski.

13.07.2021  Malte Behr (Universität Oldenburg) 
Titel:  Quasihomogeneous BlowUps and Pseudodifferential Calculus on SL(n,R) 
Abstract:  We consider the quasihomogeneous blowup of a submanifold Y in a surrounding manifold with corners X. It generalizes the concept of radial blowup and revolves around the idea of assigning different weights to functions vanishing at the submanifold Y. In the second part, we consider the hdcompactification of SL(n,R), introduced by Albin, Dimakis, Melrose and Vogan. . We introduce a resolution of this compactification, on which rightinvariant differential operators have simple degeneracies at the boundary. We construct an algebra of pseudodifferential operators on X. It is constructed using a resolution of X^2 by a series of quasihomogeneous blowups. 
20.07.2021  Jorge Vargas (Universidad Nacional de Córdoba) 
Titel:  Restriction of squareintegrable representations 
Abstract:  Let $G$ be a semisimple Lie group, and $(\pi,V)$ a irreducible square integrable representation for $G$. Thus, a model for $V$ is the $L^2$kernel of a elliptic operator on a fiber bundle over the symmetric space $G/K$ attached to $G$. Let $H$ be a closed reductive subgroup for $G$. We say $\pi$ is $H$discretely decomposable ( $H$admissible) if the sum of the closed $H$irreducible subspaces in $V$ is dense in $V$, ($H$admissible if it is $H$discretely decomposable and the multiplicity of each irreducible factor is finite). We will give criteria for being $H$$\cdots$ in language of spherical functions as well as in terms of structure of intertwining operators. We will present some aspects of branching problems and results in OrstedVargas, Branching problems in reproducing kernel spaces, Duke mathematical journal, Vol. 169, 34783537, 2020 and some consequences. 
27.10.2020  NN 
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03.11.2020  Beatrice Pozzetti (Universität Heidelberg) 
Titel:  Orbit growth rate and Hausdorff dimensions for Anosov representations 
Abstract:  Anosov representations are a robust and well studied class of discrete subgroups of noncompact simple Lie groups, which generalize many geometric features of hyperbolic manifolds to higher rank locally symmetric spaces. After a gentle introduction motivating the study of this class of groups, I will discuss joint work with Andres Sambarino and Anna Wienhard in which we establish a relation between a suitably chosen growth rate in the symmetric space and the Riemannian Hausdorff dimension of the minimal invariant subset in a flag manifold. 
10.11.2020  Clemens Weiske (Aarhus University) 
Titel:  Symmetry breaking operators and unitary branching laws 
Abstract:  Let $\pi$ be a unitary irreducible representation of a real reductive Lie group $G$. Naturally the restriction $\pi_H$ to a reductive subgroup $H$ defines a unitary representation of $H$ and decomposes into a direct integral of unitary irreducible $H$representations. We introduce a method to prove such a direct integral decomposition for unitary representations inside principal series representations, which expands classical Plancherel theorems for homogenous $H$spaces to branching laws. This is done by an analytic continuation procedure in meromorphic parameters of certain $G$ and $H$intertwining operators, namely symmetry breaking operators and KnappStein operators. We will study examples where $G$ and $H$ are of real rank one. 
17.11.2020  Frederic Naud (Institut Mathematique Jussieu, Paris) 
Titel:  Spectral gaps of random hyperbolic surfaces 
Abstract:  We will introduce and review the notion of spectral gap related to the Laplace operator, both for compact and geometrically finite hyperbolic surfaces. We will then define a notion of random covers above a given hyperbolic surface and state some new results pertaining to the spectral gap in the large degree regime. 
24.11.2020  Stefan Hante (Universität Halle) 
Titel:  Geometric time integration of a flexible Cosserat beam model 
Abstract:  Cosserat beam models are used in industry as well as in academia to describe long and slender flexible structures like cables, hoses, rotor blades, etc. In my talk I will show how we can exploit the Lie group structure of the configuration space in order to discretize the beam model in space. Furthermore, I will introduce a numerical algorithm that can be used to approximately solve the remaining differential equation on a Lie group as well as touch on its numerical analysis. I will show computational tests as well as some industrial applications. 
01.12.2020  Nils Matthes (University of Oxford) 
Titel:  Meromorphic modular forms and their iterated integrals 
Abstract:  Meromorphic modular forms are generalizations of modular forms which are allowed to have poles. Part of the motivation for their study comes from recent work of Li–Neururer, Pasol–Zudilin, and others, which shows that integrals of certain meromorphic modular forms have integer Fourier coefficients – an arithmetic phenomenon which does not seem to exist for holomorphic modular forms. In this talk we will study iterated integrals of meromorphic modular forms and describe some general algebraic independence results, generalizing results of Pasol–Zudilin. If time permits we will also mention an algebraic geometric interpretation of meromorphic modular forms which generalizes the classical fact that modular forms are sections of a certain line bundles. 
08.12.2020  Mihajlo Cekic (Universite ParisSud, Orsay) 
Titel:  First Band of PollicottRuelle resonances in dimension 3 
Abstract:  If a vector field X generates an Anosov flow, using the theory of anisotropic Sobolev spaces it is possible to define a discrete spectrum of X (as a differential operator), called PollicottRuelle resonances. In this talk we show that if X additionally preserves a contact form (eg. X is the geodesic flow), this spectrum has structure, i.e. there exists a vertical band of resonances. In particular, it follows that the flow is exponentially mixing. Our proof uses semiclassical measures, slightly exotic pseudodifferential calculus and propagation estimates, and a careful analysis near the trapped set. Joint work with Colin Guillarmou. 
15.12.2020  Jan Frahm (Aarhus University) 
Titel:  Conformally invariant differential operators on Heisenberg groups and minimal representations 
Abstract:  On Euclidean space, the Fourier transform intertwines partial derivatives and coordinate multiplications. As a consequence, solutions to a constant coefficient PDE $p(D)u=0$ are mapped to distributions supported on the variety $\{p(x)=0\}$. In the context of unitary representation theory of semisimple Lie groups, socalled minimal representations are often realized on Hilbert spaces of solutions to systems of constant coefficient PDEs whose inner product is difficult to describe (the noncompact picture of a degenerate principal series). The Euclidean Fourier transform provides a new realization on a space of distributions supported on a variety where the invariant inner product is simply an $L^{^2}$inner product on the variety. Recently, similar systems of differential operators have been constructed on Heisenberg groups. In this talk I will explain how to use the Heisenberg group Fourier transform to obtain a similar picture in this context. 
12.01.2021  Fabian Januszewski (Universität Paderborn) 
Titel:  Tensorstructures in noncommutative harmonic analysis 
Abstract:  Motivated by arithmetic questions, I will discuss approaches involving the symmetric monoidal structure of (g,K)modules in the representation theory of real reductive groups. 
19.01.2021  Paul Nelson (ETH Zürich) 
Titel:  The orbit method, microlocal analysis and applications to Lfunctions 
Abstract:  I will describe how the orbit method can be developed in a quantitative form, along the lines of microlocal analysis, and applied to local problems in representation theory and global problems concerning automorphic forms. The local applications include asymptotic expansions of relative characters. The global applications include moment estimates and subconvex bounds for Lfunctions. These results are the subject of two papers, the first joint with Akshay Venkatesh: 
26.01.2021  Jasmin Matz (University of Copenhagen) 
Titel:  Quantum ergodicity of compact quotients of SL(n,R)/SO(n) in the level aspect 
Abstract:  Suppose M is a closed Riemannian manifold with an orthonormal basis B of L^{2}(M) consisting of Laplace eigenfunctions. Berry's Random Wave Conjecture tells us that under suitable conditions on M, in the high energy limit (ie, large Laplace eigenvalue) elements of B should roughly behave like random waves of corresponding wave number. A classical result of Shnirelman and others that M is quantum ergodic if the geodesic flow on the cotangent bundle of M is ergodic, can then be viewed as a special case of this conjecture. We now want to look at a level aspect, namely, instead of taking a fixed manifold and high energy eigenfunctions, we take a sequence of BenjaminiSchramm convergent compact Riemannian manifolds together with Laplace eigenfunctions f whose eigenvalue varies in short intervals. This perspective has been recently studied in the context of graphs by Anantharaman and Le Masson, and for hyperbolic surfaces and manifolds by Abert, Bergeron, Le Masson, and Sahlsten. In my talk I want to discuss joint work with F. Brumley in which we study this question in higher rank, namely sequences of compact quotients of SL(n,R)/SO(n), n>2. 
02.02.2021  Andreas Mono (Universität zu Köln) 
Titel:  On small divisor functions and a construction of polar harmonic mass forms 
Abstract:  Recently, Mertens, Ono, and Rolen studied mock modular analogues of Eisenstein series. Their coefficients are given by small divisor functions, and have shadows given by classical Shimura theta functions. Here, we construct a second class of small divisor functions, and prove that these generate the holomorphic part of polar harmonic (weak) Maaß forms of weight 3/2. Specializing to a certain choice of parameters, we obtain an identity between our small divisor function and Hurwitz class numbers. Lastly, we present padic congruences of our polar (weak) harmonic Maaß form, when p is an odd prime. This is joint work with Joshua Males and Larry 
09.02.2021  Luz Roncal (BCAM Basque Center for Applied Mathematics) 
Titel:  Hardy's inequalities and an extension problem on $NA$ groups 
Abstract:  We will introduce Hardy's inequality from several points of view and we will turn into its fractional version. One of the approaches to prove fractional Hardy's inequality leads to the study of solutions of the extension problem (that has received much attention in the last few years, especially among the PDE community). It happens that these solutions are related with the eigenfunctions of LaplaceBeltrami operators, which motivates the problem of characterising such eigenfunctions. The aim of this talk is to provide an overview of the above topics and to report recent progress, putting an emphasis on the context of $NA$ groups. Joint work with Sundaram Thangavelu (Indian Institute of Sciences in Bangalore, India). 
07.04.2020  N.N. 
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14.04.2020  Tobias Weich (Paderborn) 
Titel:  RuelleTaylor Resonanzen für Anosov Wirkungen höheren Rangs 
Abstract:  In diesem Vortrag soll erklärt werden wie man mittels der Theorie des Taylor Spektrums kommutierender Operatoren sowie mikrolokaler Analysis einer Anosov Wirkung höheren Rangs ein intrinsisches diskretes Resonanzsspektrum zuordnen kann. 
21.04.2020  Lasse Wolf (Paderborn) 
Titel  QuantumClassical correspondance in higher rank 
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28.04.2020  Beatrice Pozzetti (Heidelberg) 
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Abstract:  canceled due to Corona restrictions 
05.05.2020  Margit Rösler (Paderborn) 
Titel:  RieszDistributionen im DunklSetting vom Typ A 
Abstract:  Nach einem klassischen Resultat von Gindikin ist eine RieszDistribution auf einem symmetrischen Kegel genau dann ein positivies Maß, wenn ihr Index zur Wallachmenge gehört. Gegenstand dieses Vortrags ist ein Analogon dieser Aussage im Rahmen der rationalen DunklTheorie zu Wurzelsystemen vom Typ A. Die verallgemeinerte Wallachmenge ist dabei durch die Multiplizität der DunklOperatoren parametrisiert. Wir erläutern auch die Rolle dieser verallgemeinerten Wallachmenge im Zusammenhang mit der Existenz positiver Vertauschungsoperatoren. 
12.05.2020  KaiUwe Bux (Bielefeld) 
Titel  Coarse Topological Group Invariants 
Abstract:  It is hopeless to classify infinite groups up to isomorphism. There are several invariants one can use to chart the vast area inhabited by such groups. I shall discuss several numerical group invariants coming from topology, homology, and geometry: *
I shall illustrate these concepts (with a focus on finiteness properites). Groups of matrices provide a good source of examples. 
19.05.2020  Jungwon Lee (Sorbonne Université) 
Titel  Dynamics of continued fractions and conjecture of MazurRubin 
Abstract:  Mazur and Rubin established several conjectural statistics for modular symbols. We show that the conjecture holds on average. We plan to introduce the approach based on spectral analysis of transfer operator associated to a certain skewproduct Gauss map and consequent result on mod p nonvanishing of modular Lvalues with Dirichlet twists (joint with HaeSang Sun). 
26.05.2020  Thomas Mettler (Frankfurt) 
Titel  Lagrangian minimal surfaces, hyperbolicity and dynamics 
Abstract:  The Beltrami—Klein model leads to a natural generalisation of hyperbolic surfaces in terms of socalled properly convex projective surfaces. In my talk I will relate these properly convex projective surfaces to certain Lagrangian minimal surfaces. This gives rise to a new class of dynamical systems and I will discuss some of their properties. In parts, this talk is based on joint work with Maciej Dunajski and Gabriel Paternain. 
02.06.2020  Gabriel Rivière (Nantes) 
Titel  Poincaré series and linking of Legendrian knots 
Abstract:  Given two points on a compact Riemannian surface with variable negative curvature, one can consider the lengths of all the geodesic arcs joining these two points and form a natural zeta function associated with these lengths (the socalled Poincaré series). I will explain that this Poincaré series has a meromorphic continuation to the whole complex plane. Then, I will show that the value at 0 is given by the inverse of the Euler characteristic by interpreting this value at 0 as the linking of two Legendrian knots. If time permits, I will explain how the results can be extended when one consider the geodesic arcs orthogonal to two closed geodesics. (joint work with Nguyen Viet Dang) 
09.06.2020  N.N. 
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16.06.2020  Sven Möller (Rutgers University) 
Titel:  Dimension Formulae and Generalised Deep Holes of the Leech 
Abstract:  Conway, Parker and Sloane (and Borcherds) showed that there is a natural bijection between the Niemeier lattices (the 24 positivedefinite, even, unimodular lattices of rank 24) and the deep holes of the Leech lattice, the unique Niemeier lattice without roots. 
23.06.2020  Michael Voit (TU Dortmund) 


Titel:  Limit theorems for CalogeroMoserSutherland particle models in the freezing regime 
Abstract:  CalogeroMoserSutherland models are described by some root system and some coupling constants. They are closely related with several random matrix models and, for some cases, with Brownian motions on Grassmann manifolds. 
30.06.2020  Lennart Gehrmann (Essen) 
Titel:  Big principal series and Linvariants 
Abstract:  By a result of Bertolini, Darmon and Iovita the Orton Linvariant of a modular form equals the derivative of the U_peigenvalue of a padic family passing through it. In this talk I will give a new, more conceptual proof of the result. One advatange of the method is that it can be generalized to automorphic forms on higher rank groups. This is joint work with Giovanni Rosso. 
07.07.2020  Elmar Schrohe (Hannover) 
Titel:  Degenerate Elliptic Boundary Value Problems with Nonsmooth Coefficients 
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14.07.2020  N.N. 
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08.10.2019  Nguyen Thi Dang (Universität Heidelberg) 
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Topological mixing of the Weyl chamber flow 
Abstract:  Let G be a semisimple Lie group without compact factors. Consider A a maximal split torus and a maximal compact subgroup K for which the Cartan decomposition holds. Denote by M the centralizer subgroup of A in K . Let Γ be a discrete subgroup of G, acting properly discontinuously on G/K . In the case of G = PSL(2, R), the right action of A on Γ\G identies with the action of the geodesic ow on the unit tangent bundle of Γ\H2 . The latter has been well studied and satises many chaotic properties such as topological mixing in its nonwandering set. My talk addresses the case when A is of higher dimension and Γ is not a lattice. First I will introduce the main topological property: topological mixing. Then I will state a joint result with Olivier Glorieux, a necessary and sucient condition for topological mixing of actions of one parameter subgroups φt of A on Γ\G/M . Then I will introduce a few key tools: the Benoist limit cone and Hopf coordinates of G/M . Finally, I will give the main ideas behind the proof of the topological mixing Theorem. Time permitting, I will present a generalization of this Theorem for the right action of φt on Γ\G when M is abelian and connected. 
15.10.2019  Maxime Ingremeau (Université de Nice SophiaAntipolis) 
Titel:  Around Berry’s random waves conjecture 
Abstract:  40 years ago, the physicist Michael Berry suggested that eigenfunctions of the Laplacian on manifolds of negative curvature should be well described, in the highfrequency limit, by some random function, given by an isotropic monochromatic Gaussian field. After recalling various mathematical interpretations of this conjecture, we will discuss how Bourgain’s arithmetic « derandomization technique » allow to prove the conjecture for eigenfunctions on the twodimensional torus. We will show that the conjecture holds in a weak form for some families of quasimodes, namely, longtime evaluated Lagrangian distributions on manifolds of negative curvature. 
22.10.2019  Lasse Wolf (Universität Paderborn) 
Titel  Spectral Asymptotics for kinetic Brownian Motion on hyperbolic surfaces 
Abstract:  The kinetic Brownian motion on the sphere bundle of a Riemannian manifold M is a stochastic process that models a random perturbation of the geodesic flow. If M is a orientable compact constant negatively curved surface, we show that in the limit of infinitely large perturbation the L2spectrum of the infinitesimal generator of a time rescaled version of the process converges to the Laplace spectrum of the base manifold. In addition, we give explicit error estimates for the convergence to equilibrium. The proofs are based on noncommutative harmonic analysis of SL2(R). 
29.10.2019  Fabian Januszewski 
Titel:  Rationalität von LWerten 
Abstract:  Dieser Vortrag ist der erste in einer Serie von zwei Vorträgen über spezielle Werte von LFunktionen. In diesem ersten Vortrag über Rationalität von LWerten wird auf die konzeptionelle Motivation und Resultate eingegangen. Im Kontext letzterer spielen (g,K)Moduln eine wichtige Rolle. 
05.11.2019  N.N 
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12.11.2019  N.N. 
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19.11.2019  N.N. 
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26.11.2019  N.N. 
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03.12.2019  Markus Schwagenscheidt, Universität zu Köln 
Titel  Generating series involving meromorphic modular forms 
Abstract:  To each nonzero discriminant D one can associate a modular form f_k,D of weight 2k, which is a cusp form if D > 0 and a meromorphic modular form if D < 0. It is well known that the twovariable generating series obtained by summing up the cusp forms f_k,D with D > 0 is modular in both variables. It yields the KohnenZagier kernel function for the Shimura correspondence. Furthermore, the generating series of traces of geodesic cycle integrals of f_k,D for fixed D > 0 is a cusp form of halfintegral weight 1/2+k. In this talk we explain how the twovariable generating series of the meromorphic modular forms f_k,D for D < 0 as well as the generating series of traces of cycle integrals of f_k,D for fixed D < 0 can be completed to realanalytic modular forms. Furthermore, we explain some rationality results for the traces of cycle integrals of the meromorphic modular forms f_k,D for D < 0. 
10.12.2019  Julia Budde, Universität Paderborn 
Titel:  Wellenfrontmengen unitärer Darstellungen 
Abstract:  Wir geben eine Einführung in Definition und elementare Eigenschaften von Wellenfrontmengen unitärer Darstellungen von Lie Gruppen. 
17.12.2019  N.N. 
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07.01.2020  Martin Raum, Chalmers University of Technology 
Titel:  Congruences of modular forms on arithmetic progressions 
Abstract:  One purpose of modular forms, and more generally, weakly holomorphic 
14.01.2020  Julia Budde 
Titel:  Wellenfrontmengen von Darstellungen Nilpotenter Lie Gruppen 
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21.01.2019  Jens Funke, Durham University 
Titel:  Theta series and (singular) theta lifts 
Abstract:  In this talk we give an introduction to theta series and theta lifts and its representationtheoretic background. We then explain singular theta lifts of Borcherds type and employ the reductive dual pair U(p, q) × U(1, 1) to construct two different kinds of Green forms for codimension qcycles in Shimura varieties associated to unitary groups. In particular, we establish an adjointness result between the singular theta lift and the KudlaMillson theta lift and discuss further applications in the context of the Kudla Program. This is joint work with Eric Hofmann.

28.01.2020  N.N. 
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10.04.2019  Claudia AlfesNeumann  Universität Paderborn 
Titel:  Harmonic weak Maass forms and HarishChandra modules 
Abstract:  In this talk we review results of Bringmann and Kudla on the classification of harmonic Maass forms. In their paper they gave a classification of the HarishChandra modules generated by the pullback (to SL_2(R)) of harmonic weak Maass forms for congruence subgroups of SL_2(Z). 
17.04.2019  Jan Frahm (geb Möllers)  Universität ErlangenNürnberg 
Titel:  Periodenintegrale, LFunktionen und Multiplizität Eins 
Abstract:  Einer automorphen Form auf der oberen Halbebene kann man durch Ihre Fourierkoeffizienten eine LFunktion zuordnen. Allgemeiner kann man zwei automorphen Formen auf der oberen Halbebene die sogenannte RankinSelberg LFunktion zuordnen, die durch Faltung der Fourierkoeffizienten gegeben ist. Diese Konstruktion lässt sich auf Paare automorpher Formen auf GL(m) und GL(n) verallgemeinern und hängt eng zusammen mit der Restriktion automorpher Formen von GL(m) auf GL(n) (m\geq n) und Periodenintegralen. Im Vortrag wird dieser Zusammenhang erklärt und die Beziehung zur Restriktion (unendlichdimensionaler) Darstellungen von GL(m) auf GL(n) hergestellt. Dadurch wird es möglich Abschätzungen für RankinSelberg LFunktionen mit darstellungstheoretischen Methoden zu erreichen, insbesondere mit der Multiplizität Eins Eigenschaft. 
24.04.2019  Polyxeni Spilioti  Universität Tübingen 
Titel  Dynamical zeta functions, trace formulae 
Abstract:  The dynamical zeta functions of Ruelle and Selberg are functions of a complex variable s and are associated with the geodesic flow on the unit sphere bundle of a compact hyperbolic manifold. Their representation by Eulertype products traces back to the Riemann zeta function. In this talk, we will present trace formulae and Lefschetz formulae, and the machinery that they provide to study the analytic properties of the dynamical zeta functions and their relation to spectral invariants. In addition, we will present other applications of the Lefschetz formula, such as the prime geodesic theorem for locally symmetric spaces of higher rank. 
01.05.2019  Feiertag 
08.05.2019  Joachim Hilgert  Universität Paderborn 
Titel:  SatakeKompaktifizierung 
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15.05.2019  Valentin Blomer  Universität Göttingen 
Titel:  Spurformeln in der Analytischen Zahlentheorie 
Abstract:  Mit der Poissonschen Summationsformel als Ausgangspunkt werden spektrale Summationsformeln auf lokalsymmetrischen Räumen vorgestellt zusammen mit einer Reihe arithmetischer und analytischer Anwendungen.

22.05.2019  Anna von Pippich  TU Darmstadt 
Titel  The special value Z'(1) of the Selberg zeta function 
Abstract:  In this talk, we report on an explicit formula for the special value at s=1 of the derivative of the Selberg zeta function for the modular group Gamma=PSL_2 (Z). The formula is a consequence of a generalization of the arithmetic RiemannRoch theorem of Deligne and GilletSoule to the case of the trivial sheaf on Gamma\H, equipped with the hyperbolic metric. The proof uses methods of zeta regularisation and relies on MayerVietoris type formulas for determinants of Laplacian. This is joint work with Gerard Freixas.
Achtung: Der Vortrag findet von 12:3014h im Raum N 3.211 statt.

29.05.2019  Michael Baake  Universität Bielefeld 
Titel  Spectral aspects of point sets and their dynamical systems 
Abstract:  The plan of this talk is to recall some properties around 
05.06.2019  Anna Wienhard  Universität Heidelberg 
Titel  Vortrag entfällt 
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12.06.2019  Christopher Voll 
Titel  Zeta functions of groups and rings  uniformity at the edge of the wilderness 
Abstract:  In asymptotic group theory, zeta functions have become important tools to study the asymptotic and finer arithmetic properties of the distribution of finitary invariants of infinite groups. Defined as Dirichlet generating series, they encode, for instance, the numbers of finiteindex subgroups or finitedimensionsional representations of a given infinite group. 
19.06.2019  Kein Seminar 
26.06.2019  Jasmin Matz 
Titel:  Asymptotics of traces of Hecke operators 
Abstract:  The distribution of spectral parameters in families of automorphic 
03.07.2019  N.N. 
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10.07.2019  Fällt aus wegen 