Wednesdays, 7:30pm; Room 507, Mathematics
~
Contact UMS
Sign up for weekly emails
Date  Speaker  Title  Abstract 
September 13 
Raymond
Cheng 
Torelli Theorems in Dimension One 
Torelli Theorems, roughly speaking, classify geometric objects via linear algebraic invariants. In this talk, I will motivate and explain various Torelli Theorems for curves.

September 20 
Sam
Mundy 
A Brief History of Cyclotomic Fields 
In this talk, I will develop chronologically the theory of cyclotomic fields, motivated by Fermat's Last Theorem and other interesting problems.

September 27 
Carl
Lian 
Rationality of Hypersurfaces 
It was known to the ancients that the solutions to the equation $x^2+y^2=1$ can completely described by rational functions in a single parameter $t$: $x=2t/(t^2+1)$ and $y=(t^21)/(t^2+1)$. With some more theory, one can show that for equations of degree 3 or higher in two variables, such a parametrization usually doesn't exist. However, generalizations of this problem quickly become difficult: an important open problem in algebraic geometry asks whether the solutions of a cubic equation in 5 variables may be described using 4 parameters. In modern language, is a cubic hyperspace in 5dimensional affine (or projective) space a rational variety? I will discuss examples of variants of these questions that are tractable, and indicate some areas of current research.

October 4 
Stanislav
Atanasov 
Diophantine Approximations 
In this talk I will trace a series of classical theorems in Diophantine approximations, culminating in the celebrated Schmidt subspace theorem. Along the way, I will prove some finiteness results on the number of solutions of certain Diophantine equations as well as explore interesting distribution properties of the digits of algebraic numbers. The talk will end with a list of seemingly unrelated problems for which Schmidt subspace theorem has been the main tool for recent advances.

October 11 
George
Drimba 
Geometry on ThreeManifolds 
The classification of geometric structures has been used to understand the analytic properties of evolving flows on manifolds. In this talk, I will motivate and explain how one can begin to approach such a classification.

October 18 
Oscar
Chang 
Ten Cool Deep Learning Papers in 2017 
I'll give a summary of ten cool deep learning papers from 2017.

October 25 
Chao
Li 
Quadratic Polynomials and Modular Forms 
We will describe a surprising phenomenon discovered by Zagier on values of quadratic polynomials. We will then provide an explanation using modular forms.

November 1 
Keaton
Naff 
An Introduction to [G_2] Manifolds 
I will give an introduction to $G_2$ manifolds, setting up the relevant definitions, discussing their properties, and timepermitting outlining some of the classical constructions of these objects.

November 8 
Adam
Block 
How to Count: Your Daily Dose of Intersection Theory 
Given two curves in a plane, how many times do they intersect? How many tangents to a given curve pass through a given point? Given a set of $r$ polynomials in $r$ variables, how many points are fixed? I will introduce some basic algebraic geometry and intersection theory and answer all of these questions.

November 15 
Akram
Alishahi 
Slice Knots and Concordance Group 
The central question of the manifold topology is "classification". Surprisingly, in some sense, this question is harder in dimension 4 compared to higher dimensions. Closely related to the classification question in dimension 4 is the study of knots in 3manifolds. In this talk, we will discuss slice knots, concordance group and the sliceribbon conjecture, one of the most important conjectures in lowdimensional topology. We will also discuss the role of invariants to study them.

November 22 

No meeting 

November 29 
Noah
Arbesfeld 


December 6 
Mikhail
Khovanov 


December 13 

No meeting 
