Ober­sem­in­ar Zah­len­the­or­ie

Wintersemester 24/25: p-adic Hodge Theory

We meet weekly on Thursday at 09:15in E2.320.

  • 24.10. L-invariants of modular forms: The Theorem of Greenberg-Stevens II (Luca Speciale)
  • 17.10. L-invariants of modular forms: The Theorem of Greenberg-Stevens I (Luca Speciale)

Sommersemester 2024: Cohomology of Arithmetic Groups

We meet weekly on Tuesday at 11:00 sharp in P1.1.02.

The aim of this semester is to get learn about the cohomology of arithmetic groups, its relation to automorphic representations and arithmetic applications

  • 16.07. Special values of automorphic L-functions
  • 09.07. An Eisenstein congruence II
  • 02.07. An Eisenstein congruence I
  • 25.06. Franke's general Eichler-Shimura isomorphism
  • 18.06. Fundamental long exact sequence and Eisenstein spectral sequence
  • 11.06. Matsushima's Formula (Mingyu Ni)
  • 04.06. Local systems on locally symmetric spaces (Fabian Januszewski)
  • 28.05. Borel-Serre compactification II (Abhijit Aryampilly Jayanthan)
  • 21.05. Borel-Serre compactification I (Abhijit Aryampilly Jayanthan)
  • 14.05. Reduction theory II (Luca Speciale)
  • 07.05. No seminar
  • 30.04. Reduction theory I (Luca Speciale)
  • 23.04. Reductive groups and adelic double quotients (Mingyu Ni)
  • 16.04. The Leray spectral sequence relating group and sheaf cohomology / The classical Eichler-Shimura isomorphism and the Hecke action (Carlo Kaul / Mingyu Ni)
  • 08.04.  Group representations of arithmetic groups and their associated local systems on locally symmetric spaces (Carlo Kaul)

Wintersemester 23/24: Arthur's Endoscopic Classification II: Langlands Constant Term Formula

We meet weekly on Monday at 9:15 in D1.303.

The aim of this semester is to understand Langlands' Theorem on the constant term of Eisenstein series.

  • 27.02. Special Talk by Kazim Büyükboduk
  • 15.02. Constant terms and L-functions (Mingyu Ni)
  • 15.02. Eisenstein series and constant terms (Fabian Januszewski)
  • 14.02. Special Talk by Oscar Rivero
  • 05.02. Admissible Representations (Luca Speciale)
  • 29.01. Induced representations and intertwining operators (Alexandre Maksoud)
  • 15.01. Langlands functoriality conjectures (Abhijit Aryampilly Jayanthan)
  • 08.01. Automorphic forms and automorphic representations (Carlo Kaul)
  • 18.12. Spectral decomposition of L^2(\Gamma \ Sl_2(R)) (Carlo Kaul)
  • 11.12. Non-holomorphic Eisenstein series (Alexandre Maksoud)
  • 04.12. Classical Holomorphic Eisenstein series (Luca Speciale)
  • 20.11. Programme discussion
  • 13.11. Preliminary meeting

Sommersemester 2023: Arthur's Endoscopic Classification I

We meet weekly on Wednesday on 11:00 (sharp) in J2.304.

The aim of this seminar is to understand Arthur's Classification of automorphic representations of classical groups. In this semester we prepare the necessary background from Langlands' theory of automorphic forms.

  • 12.07. Multiplicity One (Fabian Januszewski)
  • 05.07. Guest talk: Adjoint p-adic L-functions (Alexandre Maksoud)
  • 28.06. Langlands Functoriality, the Satake isomorphism and Langlands Group (Mingyu Ni)
  • 21.06. Non-Archimedean Langlands Classification II: Sketch of the proof (Carlo Kaul) 
  • 14.06. Non-Archimedean Langlands Classification: Weil-Deligne representations (Carlo Kaul) 
  • 07.06. Archimedean Langlands Classification (Mingyu Ni) 
  • 31.05. Bernstein-Zelevinsky Classification (Martin Baric)
  • 24.05. Representation theory of p-adic groups (Martin Baric) 
  • 17.05. Automorphic representations, parabolic induction and tensor product decomposition (Alexandre Maksoud)
  • 10.05. On Langlands' notion of an automorphic form (Alexandre Maksoud)
  • 03.05. Representations of the Weil group (Mingyu Ni)
  • 26.04. Local class field theory and the Weil group (Carlo Kaul)
  • 19.04. Overview of Arthur's Classification (Fabian Januszewski)
  • 12.04. Discussion and vote on this semester's topic (all)