NTSGrad Spring 2020/Abstracts
This page contains the titles and abstracts for talks scheduled in the Spring 2020 semester. To go back to the main GNTS page, click here.
|Representation theory and arithmetic geometry|
In this talk I will talk about the relation between representation theory and arithmetic geometry. In particular, I will try to discuss several examples that connect representation theory and arithmetic geometry closely. Then if time permits, I will give a brief introduction to trace formula approach, which is the most powerful and promising tools in this field.
|Modular forms and class groups|
In preparation for Thursday's talk, I will review some concepts from Galois Cohomology. I will also give an introduction to the Herbrand-Ribet theorem.
|ABC's of Shimura Varieties|
I'll present some of the formalization of Shimura varieties, with a strong emphasis on examples so that we can all get a small foothold whenever someone says the term Shimura variety.
|Will Hardt and John Yin|
|Primality Tests Arising From Counting Points on Elliptic Curves Over Finite Fields|
We will give some background on counting the rational points on an elliptic curve over a finite field. Then we will apply this theory to a couple of specific elliptic curves and explain how it results in (impractical) primality tests.