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Thu Oct 11

Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory
TBA
Thu Oct 18

Student Number Theory Seminar

12:20pm - Vincent Hall 313
Elliptic functions and elliptic curves in the 19th century
Devadatta Hegde, University of Minnesota

We will give an account of the work on Weierstrass and Jacobi proving a result due to Abel on meromorphic functions on the torus. These are results about complex points of elliptic curves which suggest attributes for rational points. These examples were later greatly extended at the hands of several mathematicians and reached a high-point with the GAGA principle by Serre. It's also the first example of a Riemann-Roch type theorem which were greatly extended by Grothendieck, Atiyah and Singer. Only some familiarity with Cauchy's theorem in complex analysis is needed to understand the talk.

Thu Oct 25

Student Number Theory Seminar

12:20pm - Vincent Hall 313
Cryptographic Multilinear Maps from Elliptic Curves
Mahrud Sayrafi, University of Minnesota

We will begin with defining cryptographic multilinear maps, briefly discussing some of their applications, and referencing one such map from Boneh-Silverberg '03. After that, we will extend a problem involving isogenies of elliptic curves into an open problem of finding cryptographic invariant maps from Boneh, et al. '18.stract:

Thu Nov 01

Student Number Theory Seminar

12:20pm - Vincent Hall 313
The Stone-von Neumann Theorem
Joe Dickinson, University of Minnesota

I plan to talk about some number theoretic implications of the Stone-von Neumann theorem. The Stone-von Neumann theorem is a uniqueness theorem about commutation relations between position and momentum operators. I will give a historical discussion about number theory results implied by Stone-von Neumann.

Thu Nov 08

Student Number Theory Seminar

12:20pm - Vincent Hall 313
Physics of the Riemann-zeta function
Adrienne Sands, University of Minnesota

I will give an overview of how the Riemann-zeta function plays a role in different areas of physics, from condensed matter theory to quantum mechanics.

Thu Nov 15

Student Number Theory Seminar

12:20pm - Vincent Hall 313
Physics of the Riemann-zeta function II
Adrienne Sands, University of Minnesota

We continue to discuss how the Riemann-zeta function plays a role in different areas of physics, from condensed matter theory to quantum mechanics

Thu Nov 22

Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory
TBA
Thu Nov 29

Student Number Theory Seminar

12:20pm - Vincent Hall 313
The Weil Conjectures: 0 to 100
Liam Keenan, University of Minnesota

The Weil conjectures are perhaps one of the most stunning achievements in arithmetic geometry in the 20th century. In this talk, I plan to introduce the necessary algebro-geometric language, state the conjectures, discuss the some of the tools used to prove them, and draw connections to analytic number theory.

Thu Dec 06

Student Number Theory Seminar

12:20pm - Vincent Hall 313
A Tour of the Modularity Theorem
Katy Weber, University of Minnesota

The Modularity Theorem (also known as the Taniyama-Shimura-Weil Conjecture) states, essentially, that every elliptic curve arises from a modular form. It is a special case of the Langlands correspondence and was a major part of Andrew Wiles' proof of Fermat's Last Theorem. In this talk, I will sketchily discuss the theorem in its various forms, leading up to the statement that the L-function of an elliptic curve agrees with the L-function of a modular form. Along the way, we will encounter some algebraic geometry words, e.g. "moduli space," "universal curve," and "sheaf."

Thu Dec 13

Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory
TBA
Thu Dec 20

Student Number Theory Seminar

12:20pm - Vincent Hall 313
Student Number Theory
TBA