Michael Zhao Memorial Student Colloquium
Each week, the Michael Zhao Memorial Student Colloquium holds 45minute talks by Columbia mathematics
faculty about their own research. The talks are intended for current PhD students in mathematics at Columbia.
If you are an undergraduate student or external graduate student and would like to come, please email
ams2637@columbia.edu or
rh3101@columbia.edu.
When: Tuesday 6:00  7:00 PM ET
Where: Mathematics Building, Room 520
Organizers: Alex Scheffelin, Rafah Hajjar Muñoz
When: Tuesday 6:00  7:00 PM ET
Where: Mathematics Building, Room 520
Organizers: Alex Scheffelin, Rafah Hajjar Muñoz
Exceptions: On September 26th, the Colloquium will meet in room 528.
Date  Speaker  Title and Abstract 

September 19  James Hotchkiss 
I will give an introduction to Brauer groups as they appear in a few different contexts:
fields and algebraic varieties, topological spaces, and complex manifolds.
In each context, one meets the same two problems, known as Grothendieck's question and the
periodindex problem. I will explain what is known and what is open, and describe some recent
progress in all three cases.

September 26  Yoonjoo Kim 
A compact hyperKähler manifold is an extremely special compact Kähler manifold,
whose local charts are given by the quaternionic space H^n. It naturally appears
in certain classification theorems in both differential and algebraic geometry.
Its rigid and special nature is well reflected in its (singular) cohomology.
I will introduce the definition of a compact hyperKähler manifold and its basic
cohomology theory. We will focus on its Hodge theoretic behavior.

October 17  Shaoyun Bai 
Given the twosphere, if we consider the standard rotation with
an irrational angle, we see that the north pole and the south pole are the only periodic points,
aka fixed points of all its iterates. A celebrated theorem of Franks says that,
for any areapreserving diffeomorphism of the twosphere, if it has at least three fixed points,
then it has infinitely many periodic points. In this lecture, I will discuss a recent generalization
of Franks' theorem to all toric symplectic manifolds: if a Hamiltonian diffeomorphism thereon
has at least the toric fixed points worth of fixed points plus one, then it has infinitely many
periodic points. Surprisingly, quasimaps in certain disguised forms play an important role in the proof.

October 31  Qiao He 
Theta correspondence is a classical and very useful theory to lift automorphic representation.
Under certain circumstances, there is a nice criterion to determine whether a theta lifting is nontrivial
in terms of localglobal compatibility and special values of Lfunction. When the theta lifting is trivial due
to local reason, people expect there exists certain arithmetic theta lifting and a criterion of triviality in
terms of derivatives of Lfunction. In this talk, I will survey this theory and explain how this fits into the
broader Kudla program.

November 7    
November 14  Abigail Hickok 
Discrete data sets (e.g., graphs or points clouds) often turn out to have manifold structure. In the field
of geometric data analysis (GDA), we use ideas from differential geometry and topology to analyze such data.
In this talk, we’ll focus on the role of discrete curvature in data science. First we’ll introduce the idea
of “OllivierRicci curvature”, a definition of graph curvature that is inspired by ideas in optimal transport.
Then we’ll discuss ways that curvature is connected to various other techniques in GDA, such as manifold
learning and topological data analysis. I’ll close by presenting some of my ongoing research and open questions
related to discrete curvature.

November 21  Juan Esteban Rodriguez Camargo 
In this talk I will motivate the new theory of analytic geometry constructed by Clausen and Scholze
via condensed mathematics. We will see different examples of classical analytic spaces and how this
theory allows a clean framework to study all of them simultaneously.

November 28  Yin Li 
Geometric representation theory studies the interactions between representation theory and
algebraic/symplectic geometry. In this talk, I will give a friendly introduction to the concept
of a Fukaya category associated to a symplectic manifold and illustrate its role in geometric
representation theory with two elementary examples: quiver 3folds and hypertoric varieties.

December 5  Evan Sorensen 
The last 20 years has seen remarkable growth in studying a class of random growth models said
to lie in the KPZ universality class. This class consists of (1+1)dimensional models (1 time
and 1 space dimension) that describe physical phenomena such as the growth of forest fires,
bacteria colonies, tumors, and many others. In this field, we see deep connections to many areas
of mathematics, including representation theory, combinatorics, and PDEs. I will give an overview
of KPZ universality and discuss how my research fits in to this bigger picture. Topics of my own
work may include joint works with Ofer Busani, Sean Groathouse, Firas RassoulAgha, and Timo Seppalainen.
