16.04.2024

Dominik Brennecken (Paderborn)

Title:

Convolution and Elliptic Operators in Dunkl Theory

Abstract:

23.04.2024

Michael Heins (University of Würzburg)

Title:

Abstract:

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

Benjamin Delarue (Paderborn)

Title:

Axiom A flows for projective Anosov subgroups

Abstract:

Projective Anosov subgroups are higher rank generalizations of fundamental groups of convex cocompact hyperbolic manifolds. Key properties of these groups are closely related to the dynamical system given by the geodesic flow and in particular its restriction to its non-wandering set. In the projective Anosov case the latter dynamical system can be replaced by Sambarino's refraction flow (or a general Gromov geodesic flow). In my talk I will present recent joint work with Daniel Monclair and Andrew Sanders in which we show that every projective Anosov subgroup comes with an analytic contact Axiom A flow whose restriction to its non-wandering set becomes Sambarino's refraction flow. We deduce a general exponential mixing result and the existence of a discrete spectrum of Ruelle-Pollicott resonances with associated (co-)resonant states. If time allows, I will outline applications of our results to pseudo-Riemannian manifolds and Benoist subgroups.

28.05.2024

Joachim Hilgert (University of Paderborn)

Title:

Quantum resonances and scattering poles

Abstract:

tba

04.06.2024

Bartosz Trojan (TU Wroclaw) 

Title:

Compactifications of affine buildings

Abstract:

In this talk I am going to introduce affine buildings and indicate what are the analytic problems one can be interested in. In particular, I explain several compactification procedures and motive the study of random walks. In the end I am going to describe Martin compactification.
 

11.06.2024

Pawel Plewa (Torino)

Title:

Riesz transforms and spectral multiplier theorem for extensions of Bessel–Kingman hypergroups

Abstract:

We consider a one parameter extension by dilations of the Bessel–Kingman hypergroup. We prove a sharp spectral multiplier theorem for the lifted Bessel operator. Moreover, we prove L^p-boundedness of the associated Riesz transforms in the full range of p. As an application, we show the L^p boundedness of Riesz transforms corresponding to a left-invariant sub-Laplacian on a solvable extension of stratified Lie groups.
 

18.06.2024

Colin Davalo (University of Heidelberg)

Title:

Finite-sided Dirichlet domains for Anosov representations

Abstract:

25.06.2024

Elia Fioravanti (KIT)

Title:

The pressure metric on quasi-Fuchsian spaces

Abstract:

Thermodynamic formalism, as initially developed by Bowen and Ruelle, can be used to quantify the difference between two Anosov flows in terms of a "pressure semi-norm" on suitable spaces of Hölder functions. McMullen showed that the Weil-Petersson metric on Teichmüller space can be interpreted in these terms, after which "pressure metrics" were defined on broader representation varieties, for instance on quasi-Fuchsian spaces by Bridgeman and on Hitchin components by Bridgeman, Canary, Labourie and Sambarino. While the infinitesimal structure at the Fuchsian locus is well-understood in these varieties, almost nothing is known on the global behaviour of pressure metrics. In joint work with Ursula Hamenstädt, Frieder Jäckel and Yongquan Zhang, we show that the pressure metric on quasi-Fuchsian spaces has finite diameter. As a curious consequence, the Fuchsian locus is highly distorted. 

02.07.2024

Robert Yuncken (Institut Élie Cartan de Lorraine)

Title:

Abstract:

09.07.2024

Konstantinos Tsouvalas (MPI Leipzig)

Title:

Robust quasi-isometric embeddings of hyperbolic groups in SL_n(C)

Abstract:

16.07.2024

N.N.

Title:

tba

Abstract:

tba

17.10.2023

Carsten Peterson

Titel:

Abstract:

24.10.2023

Shi Wang (Shanghai) -- zoom talk

Titel:

Abstract:

31.10.2023

N.N.

Titel:

tba

Abstract:

tba

07.11.2023

Simon Becker (Zürich) -- joint with Complex Quantum Systems seminar

Titel:

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 Tarnopolsky--Kruchkov--Vishwanath. The mathematics behind this is an elementary blend of representation theory (of the Heisenberg group in characteristic three), Jacobi theta functions and

14.11.2023

Martin Hallnäs (Gothenburg) 

Titel:

Integral equations for Heckman-Opdam hypergeometric functions and a quantum Calogero-Moser 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 Calogero-Moser system. In this talk, I will consider the type A case and show that the corresponding hypergeometric functions satisfy a one-parameter family of explicit integral equations. I will also discuss an interpretation of the result in terms of a so-called Q-operator for the hyperbolic Calogero-Moser system.
 

21.11.2023

Xiaocheng Li (Shandong University) -- zoom talk

Titel:

Abstract:

28.11.2023

Paul Nelson (Aarhus) -- zoom talk

Titel:

Abstract:

05.12.2023

Andrew Sanders (Cambridge, Masschusetts) -- zoom talk

Titel:

Uniformization of Locally Flag Manifolds

Abstract:

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 so-called Hahn and Racah algebras. We will apply these formulas to prove identities involving the symmetry breaking operators involved in this problem called the Rankin-Cohen 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:

Abstract:

16.01.2024

Mostafa Sabri (NYU Abu Dhabi) -- zoom talk

Titel:

Abstract:

23.01.2024

Jean-Philippe 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 Stein-Tomas 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:

Abstract:

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 Peter-Weyl decomposition of L^2(G) and the Borel-Weil 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.

Titel:

tba

Abstract:

tba

25.04.2023

Hongwei Zhang (Ghent)

Titel:

Dispersive equations on noncompact Riemannian symmetric spaces

Abstract:

In this presentation, we provide an overview of space-time 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 Stein-Weiss inequality, also known as the Hardy-Littlewood-Sobolev 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

Titel:

tba

Abstract:

tba

09.05.2023

Karl-Hermann 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 one-parameter group of modular automorphisms from  a single state and this group often has a geometric implementation. If modular groups are contained in finite-dimensional Lie groups, they naturally lead to 3-gradings 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).

This is joint work with Jan Frahm (Aarhus), Gestur Olafsson (Baton Rouge) and Vincenzo Morinelli (Rome)

16.05.2023

no seminar due to parallel Complex Quantum systems seminar

Titel:

tba

Abstract:

tba

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 (Novikov-Shubin invariants) If time permits, we will discuss some of the ongoing attempts to generalize this to more general semisimple Lie groups (due to Herb-Wolf) such as the universal cover of Sp(2n, R).

06.06.2023

Nikhil Savale (Uni Köln)

Titel:

Spectral Theory of the Sub-Riemannian Laplacian

Abstract:

Sub-Riemannian (sR)  geometry is the geometry of bracket-generating 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

Abstract:

Link to abstract

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 half-plane 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 well-developed for billiards in *rational* polygons (with limitations that will be explained), but there are few results on the ergodic theory of *typical* polygons. Kerckhoff-Masur-Smillie 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 3-manifold. 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

18.10.2022

Allan Merino (University of Ottawa, Canada) -- online

Titel:

Classification and double commutant property for dual pairs in an orthosymplectic Lie supergroup

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 spinor-oscillator 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 G-isotypic components is irreducible. Some results have been obtained for other dual pairs (Howe, Nishiyama, Sergeev, Cheng-Wang, Howe-Lu, Davidson-Kujawa-Muth ...) 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

08.11.2022

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:

06.12.2022

Hamid Al Saqban(Universität Paderborn) -- hybrid

Titel:

13.12.2022

Ali Suri (Universität Paderborn) -- hybrid

Titel:

Curvature and stability of quasi-geostrophic motion

In this talk, first we restate the necessary background about quantomorphism group and central extension of the corresponding Lie algebra. Then we derive the quasi-geostrophic equation as an Euler-Arnold 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 quasi-geostrophic equation.  

20.12.2022

Pritam Ganguly (Universität Paderborn) -- hybrid

Titel:

17.01.2023

Frédéric Naud (Sorbonne Université, France) -- online

Titel:

31.01.2023

William Hide -- hybrid

Titel:

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 Weil-Petersson 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:

12.04.2022

Moritz Doll (Bremen)

Titel:

Divisor of the Selberg Zeta Function for Hyperbolic Surfaces with Twists

We consider a finitely generated co-compact 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 Borthwick-Judge-Perry, 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:

In models from quantum physics describing the interaction of a quantum mechanical particle with a quantum field of bosons, one observes the phenomenon of infrared-criticality 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 low-energy bosons. Mathematically, infrared-criticality 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 infrared-critical 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 infrared-divergences. Our proof combines three ingredients: a compactness argument, a Feynman-Kac-Nelson type formula and a correlation bound for one-dimensional 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

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:

24.05.2022

Javier Echevarria Cuesta (Ecole Polytechnique, Paris)

Titel:

An algorithm to compute the spectrum of the Laplace-Beltrami operator on hyperbolic surfaces

The eigenvalues and eigenfunctions of the Laplace-Beltrami 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 two-dimensional oriented surfaces of constant curvature is already very rich. Indeed, while we fully understand the spectral theory for these manifolds when the curvature is non-negative, 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

Titel:

07.06.2022

Krystal Guo (University of Amsterdam) -- Hörsaal D1

Titel:

14.06.2022

NN

Titel:

21.06.2022

Samuel Edwards (University of Bristol) -- Hörsaal D1

Titel:

28.06.2022

Guenda Palmirotta (Luxembourg) -- now ONLINE!

Titel:

In the Euclidean case, it is well-known, 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 non-compact type $X=G/K$. More precisely, we will present a possible strategy to solve this problem by using the Fourier transform and its Paley-Wiener(-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.

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 Meyer-Guinand type relating the orthogeodesic spectrum between two convex bodies and the spectrum of the magnetic Laplacian on the torus.

06.07.2022

11:15-12:45

Job Kuit (Paderborn) -- Raum J3.330

Titel:

The most continuous part of the Plancherel decomposition for a real spherical space

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.
In this talk we consider real spherical homogeneous spaces Z. In particular, we will focus on the most continuous part of L^2(Z), i.e., the closed subspace of L^2(Z)  that decomposes in the largest continuous families. Recently, Eitan Sayag and I finished an article in which we give a precise description of the Plancherel decomposition of the most continuous part. I will discuss some of the ingredients and key ideas that went into this article.

12.07.2022

Norio Konno (Yokohama National University) -- zoom

Titel:

19.10.2021

Kein Seminar

Titel:

26.10.2021

Lasse Wolf (Universität Paderborn)

Titel:

02.11.2021

Mohammad Talebi (Universität Oldenburg)

Titel:

Analytic Torsion for manifolds with fibred boundary metrics

The Analytic Torsion was introduced by Daniel Burrill Ray and Isadore M.
Singer as analytic counterpart of R-Torsion from Topology.
In this talk we define the Analytic Torsion for Manifolds with Geometry at
infinity using structure results of Heat kernel in short and long time regimes.
We determine the structure of heat kernel by means of Geometric Microlocal
Analysis in the sense of Melrose et al.

09.11.2021

N.n.

Titel:

16.11.2021

Simon Roby (Tsinghua University)

Titel:

Resonances of the Laplace operator on homogeneous vector bundles over the real hyperbolic space

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)

Titel:

30.11.2021

Damian Osajda (University of Wroclaw)

Titel:

Helly graphs and their automorphism groups

A graph is Helly if each family of pairwise intersecting (combinatorial) balls has non-empty 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

Titel:

14.12.2021

Andreas Juhl (Humboldt-Universität Berlin)

Titel:

21.12.2021

Antoine Meddane (Université de Nantes)

Titel:

11.01.2022

Dominik Brennecken (Universität Paderborn)

Titel:

18.01.2022

Philipp Schütte (Universität Paderborn)

Titel:

25.01.2022

Anders Karlsson (University of Geneva)

Titel:

01.02.2022

Khalid Koufany (Université de Lorraine)

Titel:

13.04.2021

NN

Titel:

tba

tba                                                                                                      

20.04.2021

Corina Ciobotaru (IHÉS)

Titel:

Chabauty limits of subgroups of SL(n,Q_p)

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, well-behaved, 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 Paris-Saclay)

Titel:

Closed geodesics with prescribed intersection numbers

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

Given a hyperbolic 3-manifold 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 Champagne-Ardenne)

Titel:

Symmetry breaking operators and orthogonal polynomials

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 Rankin-Cohen 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

Titel:

tba

tba                                                                                                      

01.06.2021

NN

Titel:

tba

tba                                                                                                      

08.06.2021

Benjamin Küster (Universität Paderborn)

Titel:

Oscillatory integrals in equivariant cohomology

15.06.2021

Jean-Philippe Anker (Universite d'Orleans)

Titel:

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  Laplace-Beltrami 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 Hong-Wei Zhang [arXiv:2006.06473].

22.06.2021

Gerhard Keller (Universität Erlangen)

Titel:

I plan to start with a brief introduction to B-free dynamical systems (derived from B-free numbers like e.g. the square-free 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 B-free systems which are "as chaotic as possible" (like the square-free 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

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

Dunkl theory is a generalization of Fourier analysis and special function
theory related to root systems and reflections groups. The Dunkl operators T_j, which were introduced by C. F. Dunkl in 1989, are deformations of directional derivatives by difference operators related to the reflection group. The goal of this talk will be to study harmonic analysis and Hardy spaces in the rational Dunkl setting. The first part will be devoted to two results: improved estimates of the heat kernel h_t(x,y) of the Dunkl heat semigroup generated by the Dunkl--Laplace operator Delta_k=\sum_{j=1}^NT_j^2, and a theorem regarding the support of Dunkl translations  of L^2 compactly supported functions  (not necessarily radial). This kind of results turn out to be useful tools in studying harmonic analysis in Dunkl setting. We will discuss this kind of applications in the second part of the talk. We will discuss how our tools can be used to for studying singular integrals of convolution type or Littlewood-Paley square functions in the Dunkl setting.

This talk is based on the joint articles with J-Ph. Anker and J. Dziubanski.

13.07.2021

Malte Behr (Universität Oldenburg)

Titel:

Quasihomogeneous Blow-Ups and Pseudodifferential Calculus on SL(n,R)

We consider the quasihomogeneous blow-up of a submanifold Y in a surrounding manifold with corners X. It generalizes the concept of radial blow-up and revolves around the idea of assigning different weights to functions vanishing at the submanifold Y. In the second part, we consider the hd-compactification of SL(n,R), introduced by Albin, Dimakis, Melrose and Vogan. . We introduce a resolution of this compactification, on which right-invariant 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 blow-ups.                                                                                                      

20.07.2021

Jorge Vargas (Universidad Nacional de Córdoba)

Titel:

Restriction of square-integrable representations

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 Orsted-Vargas, Branching problems in reproducing kernel spaces, Duke mathematical journal, Vol. 169, 3478-3537, 2020 and some  consequences.

27.10.2020

NN

Titel:

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tba                                                                                                      

03.11.2020

Beatrice Pozzetti (Universität Heidelberg)

Titel:

Anosov representations are a robust and well studied class of discrete subgroups of non-compact 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

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 Knapp--Stein operators. We will study examples where $G$ and $H$ are of real rank one.                                                                                                                                                                                                                                                                                                                                                                  

17.11.2020

Frederic Naud (Institut Mathematique Jussieu, Paris)

Titel:

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

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

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 Paris-Sud, Orsay)

Titel:

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 Pollicott-Ruelle 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

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, so-called minimal representations are often realized on Hilbert spaces of solutions to systems of constant coefficient PDEs whose inner product is difficult to describe (the non-compact 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:

Tensor-structures in non-commutative harmonic analysis

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:

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 L-functions.  These results are the subject of two papers, the first joint with Akshay Venkatesh:

https://arxiv.org/abs/1805.07750

https://arxiv.org/abs/2012.02187                                                                                                                                                                                                                       

26.01.2021

Jasmin Matz (University of Copenhagen)

Titel:

Quantum ergodicity of compact quotients of SL(n,R)/SO(n) in the level aspect

Suppose M is a closed Riemannian manifold with an orthonormal basis B of L²(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 Benjamini-Schramm 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

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 p-adic congruences of our polar (weak) harmonic Maaß form, when p is an odd prime. This is joint work with Joshua Males and Larry
Rolen.                                                 

09.02.2021

Luz Roncal (BCAM- Basque Center for Applied Mathematics)

Titel:

Hardy's inequalities and an extension problem on $NA$ groups

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 Laplace-Beltrami 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.

Titel:

tba

Abstract:

14.04.2020

Tobias Weich (Paderborn)

Titel:

Ruelle-Taylor Resonanzen für Anosov Wirkungen höheren Rangs

 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

Quantum-Classical correspondance in higher rank

Abstract:

 tba

28.04.2020

Beatrice Pozzetti (Heidelberg)                                  

Titel:

tba

Abstract:

canceled due to Corona restrictions                                                                                                                               

05.05.2020

Margit Rösler (Paderborn)

Titel:

Riesz-Distributionen im Dunkl-Setting vom Typ A

Abstract:

Nach einem klassischen Resultat von Gindikin ist eine Riesz-Distribution 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 Dunkl-Theorie zu Wurzelsystemen vom Typ A. Die verallgemeinerte Wallachmenge ist dabei durch die Multiplizität der Dunkl-Operatoren parametrisiert. Wir erläutern auch die Rolle dieser verallgemeinerten Wallachmenge im Zusammenhang mit der Existenz positiver Vertauschungsoperatoren.

12.05.2020

Kai-Uwe 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: *

• finiteness properties 

• (co)homologicial and geometric dimensions 

• isoperimetric inequalities

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 Mazur-Rubin

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 skew-product Gauss map and consequent result on mod p non-vanishing of modular L-values with Dirichlet twists (joint with Hae-Sang 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 so-called 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 so-called 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.

Titel:

tba

Abstract:

16.06.2020

Sven Möller (Rutgers University)

Titel:

Dimension Formulae and Generalised Deep Holes of the Leech
Lattice Vertex Operator Algebra

Abstract:

Conway, Parker and Sloane (and Borcherds) showed that there is a natural bijection between the Niemeier lattices (the 24 positive-definite, even, unimodular lattices of rank 24) and the deep holes of the Leech lattice, the unique Niemeier lattice without roots.

We generalise this statement to vertex operator algebras (VOAs), i.e. we show that all 71 holomorphic VOAs (or meromorphic 2-dimensional conformal field theories) of central charge 24 correspond to generalised deep holes of the Leech lattice VOA.

The notion of generalised deep hole occurs naturally as an upper bound in a dimension formula we obtain by pairing the character of the VOA with a certain vector-valued Eisenstein series of weight 2.

(This is joint work with Nils Scheithauer.)                                                                                                                                  

23.06.2020

Michael Voit (TU Dortmund)

Titel:

Limit theorems for Calogero-Moser-Sutherland particle models in the freezing regime

Abstract:

Calogero-Moser-Sutherland 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.
In this talk we discuss some limit results when the the coupling constants tend to infinity. Here the limits can be described  in terms of deterministic limit dynamical systems and zeroes of classical orthogonal polynomials. We also present some results when the number of particles tends to infinity.                                                                                                                         

30.06.2020

Lennart Gehrmann (Essen)

Titel:

Big principal series and L-invariants

Abstract:

By a result of Bertolini, Darmon and Iovita the Orton L-invariant of a modular form equals the derivative of the U_p-eigenvalue of a p-adic 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 Non-smooth Coefficients

Abstract:

Abstract (as pdf file)

14.07.2020

N.N.

Titel:

tba

Abstract:

tba                                                                                                                                   

08.10.2019

Nguyen Thi Dang (Universität Heidelberg)

Titel:

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 non-wandering 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 Sophia-Antipolis)

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 high-frequency 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 two-dimensional torus. We will show that the conjecture holds in a weak form for some families of quasi-modes, namely, long-time 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 L2-spectrum 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 L-Werten

Abstract:

Dieser Vortrag ist der erste in einer Serie von zwei Vorträgen über spezielle Werte von L-Funktionen. In diesem ersten Vortrag über Rationalität von L-Werten wird auf die konzeptionelle Motivation und Resultate eingegangen. Im Kontext letzterer spielen (g,K)-Moduln eine wichtige Rolle.                                                                                                                                    

05.11.2019

N.N

Titel:

tba

Abstract:

tba                                                                                                                   

12.11.2019

N.N.

Titel

tba

Abstract:

tba                                                                                                                                 

19.11.2019

N.N.

Titel

tba

Abstract:

tba
                                                                                                                               

26.11.2019

N.N.

Titel

tba

Abstract:

tba                                                                                                                                   

03.12.2019

Markus Schwagenscheidt, Universität zu Köln

Titel

Generating series involving meromorphic modular forms

Abstract:

To each non-zero 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 two-variable generating series obtained by summing up the cusp forms f_k,D with D > 0 is modular in both variables. It yields the Kohnen-Zagier 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 half-integral weight 1/2+k. In this talk we explain how the two-variable 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 real-analytic 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.

Titel:

tba

Abstract:

tba                                                                                                                                   

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
modular forms is to aid or even enable the analysis of certain
generating series, namely modular generating series. A common question
asked for coefficients $c(n)$ of a generating series is which patterns
of divisibility they satisfy. Among the most accessible patterns, there
is divisibility on arithmetic progressions: $c(an + b)$ is divisible by
a given positive integer $\ell$ for all $n$. The theory of modular forms
modulo primes yields a good handle on such question as long as $a$ and
$b$ are remain fixed and $\ell$ is prime.

In this talk, we showcase a new technique that allows us to answer in
the affirmative the question of whether there is a connection among
congruences for varying $b$ and fixed $a$. As a result, we discover
surprisingly strong restrictions on maximal arithmetic progressions that
admit a congruence. We primarily build upon results by Deligne-Rapoport
on the arithmetic compactification of the moduli of elliptic curves. We
reduce the original problem to a very concrete one in the modular
representation theory of finite groups of Lie type and their covers,
which in our motivating setting can be solved by a calculation.                                                                                                                              

14.01.2020

Julia Budde

Titel:

Wellenfrontmengen von Darstellungen Nilpotenter Lie Gruppen

Abstract:

tba                                                                                                                                   

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 representation-theoretic 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 q-cycles in Shimura varieties associated to unitary groups. In particular, we establish an adjointness result between the singular theta lift and the Kudla-Millson 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.

Titel:

tba

Abstract:

tba                                                                                                                                   

10.04.2019

Claudia Alfes-Neumann -- Universität Paderborn

Titel:

 Harmonic weak Maass forms and Harish-Chandra 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 Harish-Chandra modules generated by the pullback (to SL_2(R)) of harmonic weak Maass forms for congruence subgroups of SL_2(Z).

ACHTUNG:  Gemeinsames Oberseminar mit AG Algebra Vortrag findet in  D1 320 statt und startet schon um 14h.

17.04.2019

Jan Frahm (geb Möllers) -- Universität Erlangen-Nürnberg

Titel:

Periodenintegrale, L-Funktionen und Multiplizität Eins

Abstract:

Einer automorphen Form auf der oberen Halbebene kann man durch Ihre Fourierkoeffizienten eine L-Funktion zuordnen. Allgemeiner kann man zwei automorphen Formen auf der oberen Halbebene die sogenannte Rankin-Selberg L-Funktion 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 (unendlich-dimensionaler) Darstellungen von GL(m) auf GL(n) hergestellt. Dadurch wird es möglich Abschätzungen für Rankin-Selberg L-Funktionen mit darstellungstheoretischen Methoden zu erreichen, insbesondere mit der Multiplizität Eins Eigenschaft.

24.04.2019

Polyxeni Spilioti -- Universität Tübingen

Titel

Dynamical zeta functions, trace formulae
and applications

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 Euler-type 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:

Satake-Kompaktifizierung

Abstract:

tba                                                                                                                                   

15.05.2019

Valentin Blomer -- Universität Göttingen

Titel:

Spurformeln in der Analytischen Zahlentheorie

Abstract:

Mit der Poissonschen Summationsformel als Ausgangspunkt werden spektrale Summationsformeln auf lokal-symmetrischen 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 Riemann--Roch theorem of Deligne and Gillet-Soule 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 Mayer-Vietoris type formulas  for determinants of Laplacian. This is joint work with Gerard Freixas.

Achtung: Der Vortrag findet von 12:30-14h 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
the diffraction and dynamical spectra of cut and project
and inflation point sets, with some emphasis on cases with
mixed spectrum and some examples of number-theoretic origin.
                                                                                                                               

05.06.2019

Anna Wienhard -- Universität Heidelberg

Titel

Vortrag entfällt

Abstract:

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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 finite-index subgroups or finite-dimensionsional representations of a given infinite group.

Zeta functions associated to arithmetic groups often enjoy Euler products, indexed by the (Archimedean and non-Archimedean) places of number fields. The non-Archimedean factors tend to be rational functions. To understand how these functions vary with the place is among the fundamental challenging questions in the field.

I will report on recent work with Angela Carnevale and Michael Schein: we prove a conjecture of Grunewald, Segal, and Smith on the variation of local normal subgroup zeta functions of finitely generated free class-2-nilpotent groups under base extension with number rings. Our result establishes that, in this setup, the variation is "uniform on primes of fixed decomposition type" in the relevant number field.

ACHTUNG:  Es finden an diesem Tag aufgrund der Lesewoche zwei Vorträge 11:00-12:30 (in J 2.213) und 14:00-15:30 (E 2.304) statt.                                                                         

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
representations has many applications, such as density estimates for
exceptional eigenvalues or low-lying zeros in families of L-functions.
I want to talk about joint work with T. Finis in which we prove an
effective equidistribution result for Satake parameters of spherical
automorphic forms on many split reductive groups with growing Laplace
eigenvalue. Compared to previously known results for GL(n), we can
improve the bounds for the remainder terms. As a special case we also
obtain the Weyl law on the associated locally symmetric space together
with an upper bound for the remainder.

03.07.2019

N.N.

Titel:

tba

Abstract:

tba                                                                                                                                   

10.07.2019

Fällt aus wegen

PBMath Sommerschule