Mathematics Home / A working seminar on Modular Forms
Time & Location: All talks are on Wednesday at 2:00 PM unless otherwise noted.
Organizer: Victor H. Moll, Olivia Beckwith, and Vaishavi Sharma
Wednesday, October 6
Title: Modular forms as coefficients of the P-function
Victor H. Moll | Tulane University
Abstract: The study of polynomial equations is one of the basic problems in Number Theory. In this first talk we will show that “modular forms”, the subject of this seminar, appear in a natural manner in the study of the curve “quadratic in y = cubic in x”. The details are completely elementary.
Location: Gibson 310
Zoom access:
Time: 2:00
Wednesday, October 13
Title: The First Appearance of Modular Forms
Victor H. Moll | Tulane University
Abstract: TBA
Location: Gibson 310
Zoom access:
Time: 2:00
Wednesday, October 20
Title: First examples of modular forms: Eisenstein series
Olivia Beckwith | Tulane University
Abstract: Picking right up where we left off last week, we'll examine the Taylor coefficients of the Weierstrass P function in more detail and we'll compute their Fourier expansions. Then we'll define vector spaces which contain these functions and we'll show that they are finite dimensional.
Location: Gibson 310
Zoom access: https://tulane.zoom.us/j/94370467366 Find Zoom information at the end of this webpage.
Time: 2:00
Wednesday, October 27
Title: Level One Modular Forms
Vaishavi Sharma | Tulane University
Abstract: In this meeting we'll show that the Eisenstein series G_k studied in the previous lectures live in finite-dimensional vector spaces of functions on the upper half-plane with certain transformation properties. We will also use basic properties of these spaces to prove a surprising identity for the divisor sum functions sigma_k.
Location: Gibson 310
Zoom access: https://tulane.zoom.us/j/94370467366 Find Zoom information at the end of this webpage.
Time: 2:00
Wednesday, November 3
Title: Modular forms on congruence subgroups
Olivia Beckwith | Tulane University
Abstract: Last week we defined modular forms on the special linear group SL_2(Z). This time we'll replace SL_2(Z) with certain finite index subgroups. We'll also show how to apply these ideas to obtain a formula for the number of ways an integer can be written as a sum of four squares.
Location: Gibson 310
Zoom access: https://tulane.zoom.us/j/94370467366 Find Zoom information at the end of this webpage.
Time: 2:00
Wednesday, November 10
Title: The j-function
Victor Moll | Tulane University
Abstract: We give a description of this important function and explain its role in connection to modular functions.
Location: Gibson 310
Zoom access: https://tulane.zoom.us/j/94370467366 Find Zoom information at the end of this webpage.
Time: 2:00
Wednesday, November 17
Title: Modular functions and the inevitable j-function
Armin Straub | Tulane University
Abstract: We will review previous results on modular forms and the j-function, with the goal of (re)introducing the j-function as inevitable and natural. We will discuss some of its properties as well as its fundamental role as a modular function, and might indicate extensions to the higher level case.
Location: Gibson 310
Zoom access: https://tulane.zoom.us/j/94370467366 Find Zoom information at the end of this webpage.
Time: 2:00
Wednesday, November 24
Title: TBA
TBA | Tulane University
Abstract: TBA
Location: Gibson 310
Zoom access: https://tulane.zoom.us/j/94370467366 Find Zoom information at the end of this webpage.
Time: 2:00
Wednesday, December 1
Title: Algebraic relations between modular functions
Armin Straub | University of Southern Alabama
Abstract: We will continue the discussion of modular functions and show that any two are algebraically related. This leads to the observation that modular functions like the j-function take algebraic values at quadratic irrationalities. This is the tip of an impressive iceberg, and hints at the beginning of topics including complex multiplication and class field theory.
Location: Gibson 310
Zoom access: https://tulane.zoom.us/j/94370467366 Find Zoom information at the end of this webpage.
Time: 2:00
Wednesday, December 15
Title: TBA
TBA | Tulane University
Abstract: TBA
Location: Gibson 310
Zoom access: https://tulane.zoom.us/j/94370467366 Find Zoom information at the end of this webpage.
Time: 2:00
Wednesday, December 22
Title: TBA
TBA | Tulane University
Abstract: TBA
Location: Gibson 310
Zoom access: https://tulane.zoom.us/j/94370467366 Find Zoom information at the end of this webpage.
Time: 2:00
Meeting ID: 943 7046 7366
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