Bonn-Paris hybrid workgroup on automorphic forms (2021-2022)
Microlocal methods in automorphic forms
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The aim of this workgroup is to understand the recent use of microlocal methods in the theory of automorphic forms, most notably in the works of Nelson and Nelson-Venkatesh.
- Stanford course notes by Akshay Venkatesh on geometric quantization
- The following paper of Nelson and Venkatesh
- The following paper of Nelson The idea of this learning group is to go through the Stanford course notes during the first semester, and then tackle the Nelson--Venkatesh paper in the second semester.
- October 7 (Farrell Brumley): Introduction, part I (sections 1-2 of the Stanford notes)
- October 14 (Farrell Brumley): Introduction, part II (sections 1-2 of the Stanford notes)
- October 21 (Valentin Blomer): Pseudo-differential operators (section 3 of the Stanford notes)
- October 28 (Edgar Assing): The Kirillov paradigm for the Heisenberg group (section 4 of the Stanford notes)
- November 11 (Thibaut Ménès): The Stone-von Neumann theorem (section 5 of the Stanford notes)
- November 18 (Subhajit Jana): The Weil representation I (section 6 of the Stanford notes)
- November 25 (Bart Michels): The Weil representation II (section 6 of the Stanford notes)
- December 2 (Asbjørn Nordentoft): Nilpotent groups (section 7 of the Stanford notes)
- December 9 (Petru Constantinescu) : Background on symplectic geometry (section 8 of the Stanford notes)
- December 16 (Radu Toma) : Duistermaat--Heckman localization (section 9 of the Stanford notes)
- January 13 (Edgar Assing) : The Kirillov formula for U(n) (section 10 of the Stanford notes)
- January 20 (Louis Ioos) : Holomorphic quantisation (section 12 of the Stanford notes)
- March 3 (Valentin Blomer): Overview and sketch (Section 28 of N-V)
- March 10 (Farrell Brumley): Microlocal analysis I (Part I of N-V)
- March 17 (Farrell Brumley): Microlocal analysis II (Part II of N-V) Lecture notes
- March 24 (Edgar Assing): Limiting states (Section 26 of N-V)
- March 31 (Farrell Brumley and Edgar Assing): Loose ends
- April 7 (Philippe Michel): Equidistribution and Ratner's theorem, I (Section 27 of N-V)
- April 14 (Philippe Michel): Equidistribution and Ratner's theorem, II (Section 27 of N-V)
- April 21 (Bart Michels): Stability (sections 13-14 of N-V)
- April 28 (Asbjørn Nordentoft): Satake parameters and L-functions (section 15 of N-V)
- May 5 (Louis Ioos) : Volume forms, measures and integrals (sections 16-17 of N-V)
- May 12 (Subhajit Jana) : Inverse branching and asymptotic I (sections 18, 19 and 22 of N-V)
- May 19 (Subhajit Jana) : Inverse branching and asymptotic II (sections 18, 19 and 22 of N-V)
The relevant sources are
Here is a schedule of the talks for Part I.
All talks are on Thursdays, from 3-4:30pm Central European time. E-mail me or Valentin Blomer for the Zoom link.
Here is the schedule for Part II, on the paper of Nelson--Venkatesh.
All talks will be from 4:30-6pm Paris local time. E-mail me or Valentin Blomer for the Zoom link.