Course 18.784: Seminar in Number Theory

Talks

• Wednesday, February 3, 2010. Introduction, organization.
• Friday, February 5, 2010. Lattices, evaluation discussion.
• Monday, February 8, 2010. QY, SL₂(Z) and the upper half plane.
• Wednesday, February 10, 2010. MD, holomorphic functions.
• Friday, February 12, 2010. JE, modular forms and q-expansions.
• Tuesday, February 16, 2010. AZ, Eisenstein series.
• Wednesday, February 17, 2010. WS, The cusp form Δ.
• Friday, February 19, 2010. AF, Spaces of modular forms.
• Monday, February 22, 2010. BW, Hecke operators.
• Wednesday, February 24, 2010. SK, The j-function.
• Friday, February 26, 2010. AH, Integral lattices.
• Monday, March 1, 2010. PE, Theta functions of even unimodular lattices.
• Wednesday, March 3, 2010. CK, Theta functions of unimodular lattices.
• Friday, March 5, 2010. Project discussion, miscellaneous.
• Monday, March 8, 2010. PE and CK, Congruence subgroups.
• Wednesday, March 10, 2010. AH and QY, Normal forms for elliptic curves.
• Friday, March 12, 2010. AF and AZ, Theta functions of positive definite lattices.
• Monday, March 15, 2010. SK and WS, Congruence groups and Hecke operators.
• Wednesday, March 17, 2010. MD and BW, Elliptic curves, group laws, and possibly generalized elliptic curves.
• Friday, March 19, 2010. JE, The Tate curve (half day).
• Monday, March 29, 2010. AH and QY, Project introductions.
• Wednesday, March 31, 2010. SK and PE, Project introductions.
• Friday, April 2, 2010. WS and CK, Affine varieties.
• Monday, April 5, 2010. AF and AZ, Projective varieties.
• Wednesday, April 7, 2010. JE and SC, Algebraic curves.
• Friday, April 9, 2010. MD and BW, Riemann-Roch and Hurwitz
• Monday, April 12, 2010. Discussion on modular curves as algebraic curves.
• Wednesday, April 14, 2010. Discussion on modular forms as sections of line bundles.
• Friday, April 16, 2010. AZ, Final project.
• Wednesday, April 21, 2010. MD, Final project.
• Friday, April 23, 2010. AF, Final project.
• Monday, April 26, 2010. BW, Final project.
• Wednesday, April 28, 2010. SK, Final project.
• Friday, April 30, 2010. CK, Final project.
• Monday, May 3, 2010. JE, Final project.
• Wednesday, May 5, 2010. WS, Final project.
• Friday, May 7, 2010. AH, Final project.
• Monday, May 10, 2010. QY, Final project.
• Wednesday, May 12, 2010. PE, Final project.