Math 997

Syllabus

References

• 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 8: E_2  (filled)

Day 9: Cuspforms (filled)

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)