Math 997
Modular Forms
Student/Office Hours
Thurs 1-2:20 pm
Fri 10:30-12pm
or by appointment
Syllabus
syllabus.pdfReferences
1-2-3 Modular Forms by Bruinier, van der Geer, Harder and Zagier
The sphere packing problem in dimension 8 by Maryna Viazovska
For further reading ...
The sphere packing problem in dimension 24 by Cohn, Kumar, Miller, Radchenko, and Viazovska
Henryk Iwaniec's Topics in Classical Automorphic Forms
Henryk Iwaniec's Spectral Methods in Automorphic Forms
Ben Brubaker's (UMN) Notes
Kimball Martin's (U of OK) Notes
My course notes from Math 997: Automorphic Forms and L-functions
Paul Garrett's Modern Analysis of Automorphic Forms by Examples
Dorian Goldfeld's Automorphic Forms and L-functions for the Group GL(n,R)
notes
Day 1: Intro & Sphere Packing (filled)
Day 2: Modular Forms (filled)
Day 3: Modular Forms cont'd (filled)
Day 4: Modular Group (filled)
Day 5: Valence Formula (filled)
Day 6: Eisenstein Series (filled)
Day 7: Fourier expansions of Eisenstein series
Day 10: Dimensions of spaces of Modular Forms (filled)
Day 11: Theta Functions (filled)
Day 12: Theta Functions cont'd (filled)
Day 13: Theta Functions and Differential Operators (filled)
Day 14: Differential Operators (filled)
Day 15: Quasimodular Forms
Day 16: Viazvovska revisited
Day 17: Constructing a (filled)
Day 18: Constructing a contd (filled)
Day 19: Constructing a contd (filled)
Day 20: Zeros of a
Day 21: Constructing b (filled)
Day 22: Constructing b contd (filled)
Day 23: Defining g
Day 24: Hecke Operators (filled)
Day 25: Hecke Eigenforms (filled)
Day 26: Hecke Theory (filled)
Day 27: Hecke Theory contd (filled)
Day 28: Atkin-Leher Theory (filled)
Day 29: Oldforms and newforms (filled)
Day 30: Finishing A-L theory (filled)
Day 31: Hecke L-functions
Day 32: Hecke L-functions contd (filled)
Day 33: Converse Theorems
Day 34: Rankin-Selberg (filled)
Day 35: R-S cont
Day 36: Automorphic forms (filled)
Day 37: Afms cont and Langlands (filled)