Wednesdays, 7:30pm; Room 507, Mathematics
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Date  Speaker  Title  Abstract 
January 24 
Stanislav
Atanasov 
The Weil Conjectures 
In this talk, we start with a wellknown example of counting points on Grassmannians over finite fields. This will provide us motivation for introducing the deep and farreaching connections between nonsingular complex varieties and their realizations over finite fields, known as the Weil Conjectures. These conjectures concern properties of zeta functions, and we explain how some of these properties follow easily from the existence of an appropriate cohomology theory.

January 31 
Theo
Coyne

Symplectic Manifolds
and Embeddings 
I will introduce and motivate the basic concepts in symplectic geometry and explain why they are important (in physics, for example). One important problem in symplectic geometry is determining when one symplectic manifold embeds symplectically into another. I will summarize some methods and results used to address this question.

February 7 
Noah
Olander 
How to use finite fields
for problems concerning infinite fields 
Following J.P. Serre’s paper of the same title as this talk, I will give an algebraic proof of the AxGrothendieck Theorem  which appears to be a theorem of complex analysis  using finite fields. I will discuss what makes this argument work, and if time permits, I will prove another result that appears in Serre’s paper.

February 14 
Henry
Liu 
Topological Quantum 
The study of QFTs has inspired many modern mathematical constructions and results. QFTs which are unchanged by diffeomorphism are called topological; we will play around with the structure of such QFTs in (1+1) dimensions and prove a baby version of the celebrated Verlinde formula. If time permits, we’ll define gauge theories and their quantizations, and apply the baby Verlinde formula to them to get some interesting group/representation theoretic identities.

February 21 
Kevin
Kwan 
Definitely maybe  Probability and Statistics in Number Theory 
There has been a series of profound advancements in number theory in the 20th century, thanks to the understanding of the anatomy of integers and the fruitful interactions between statistics, probability theory, analysis and number theory. This will be a light survey talk on the heuristics and results in this direction, with emphasis on the distributions of prime divisors and prime gaps.

February 28 
Alex Zhang 


March 7 
Semon Rezchikov 

March 14 

No meeting 

March 21 
Shizhang
Li

Igusa Formula and Hypergeometric Series 

March 28 
Linh
Truong 


April 4 
PakHin
Lee 


April 11 
Alex
Pieloch 


April 18 
George
Drimba



April 25 
Alex Perry 

May 2 

No meeting 
