Graduate Student Seminar

from Friday
June 01, 2018 to Monday
December 31, 2018
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Wednesday
September 12, 2018

1:00 PM - 2:00 PM
Math Tower P-131
Tobias Shin, Stony Brook University
Roots of topology

We will discuss polynomials, covering spaces, and Galois theory, and how they all relate through the unifying concept of “resolvent degree”, following Farb and Wolfson. We will also see how this concept relates Hilbert’s 13th problem (among others) to classical enumerative problems in algebraic geometry, such as 27 lines on a smooth cubic, 28 bitangents on a planar quartic, etc.


Wednesday
September 19, 2018

1:00 PM - 2:00 PM
Math Tower P-131
Jack Burkart, Stony Brook University
Improving Liouville's Theorem for Harmonic Functions

Liouville's theorem says that the only harmonic functions on $R^n$ that are bounded above are actually constant. We will discuss the proof of this fact using Harnack's inequality, which is a primitive example of extremely useful "3-Ball inequalities" that show up in harmonic analysis. We will compare this continuous version to the discrete version of the Liouville theorem after defining harmonic functions on $Z^2$ in terms of the mean value property. In particular, we will discuss a recent advancement from 2017 due to Buhovsky, Logunov, Malinnikova, and Sodin, which says that, in a way that we will make precise, a harmonic function bounded on 99.999% of $Z^2$ must actually be constant.


Wednesday
September 26, 2018

1:00 PM - 2:00 PM
Math Tower P-131
Saman Habibi Esfahani, Stony Brook University
The Symplectic Vortex Equations

We define invariants...


Wednesday
October 03, 2018

1:00 PM - 2:00 PM
Math Tower P-131
Yoonjoo Kim, Stony Brook University
Compact hyperkahler manifolds

Compact hyperkahler manifolds are one of the most rigid objects in both differential and algebraic geometry. They are Ricci-flat compact Kahler manifolds with quaternion structures. In this talk, we will present a short introduction on algebro-geometric aspect of the theory. We start from definition, and present examples and their special properties, which reflect their structural rigidity.


Wednesday
October 10, 2018

1:00 PM - 2:00 PM
Math Tower P-131
Lisandra Hernandez, Stony Brook University
Hyperbolic 3-Manifolds and Their Classification

We’ll begin with an excursion into the geometry and topology of hyperbolic space. This will be followed by a brief introduction to some tools in geometric group theory that will help us understand the fundamental group of hyperbolic 3-manifolds a little better. We’ll end the talk with a discussion of Thurston’s Hyperbolization conjecture.


Wednesday
October 17, 2018

1:00 PM - 2:00 PM
Math Tower P-131
Jin-Cheng Guu, Stony Brook University
A Generalization of Fourier Analysis

Let’s see how a group G (compact, connected) smoothly acts on a complex vector space. A fundamental case is when G is abelian (Fourier series), whose applications can be found in PDE, ergodic problems, number theory,... etc. We will then look at the easiest nonabelian case and a basic application to Quantum Mechanics if time permits. This talk is an invitation to an upcoming mini-seminar on representations of compact Lie groups.


Wednesday
October 24, 2018

1:00 PM - 2:00 PM
Math Tower P-131
Ben Wu, Stony Brook University
Two Spaces Associated to a Closed Riemann Surface

In this talk, we will construct two spaces that are naturally associated to a closed Riemann surface. These spaces can be seen as a toy model for a much more general theory. One of the spaces is related to the topology of the Riemann surface, while the other is related to the smooth structure. Even in our toy model, the geometry of these spaces interesting. Although these two spaces consist of different objects, we will show that they are actually equivalent. Studying generalizations of this equivalence lead to the Riemann Hilbert correspondence which provide strong links between topology and algebra.


Wednesday
October 31, 2018

1:00 PM - 2:00 PM
Math Tower P-131
Jacob Mazor, Stony Brook University
Kakeya Sets and the Finite Field Kakeya Conjecture

If K is a set in the plane which contains a unit line segment pointing in every direction, how large must it be? It turns out that we may construct such a set with zero Lebesgue measure. (!) However any such set must be "rather large" for a measure zero set. Does this result extend to such sets in higher dimensions? We will discuss a formulation for vector spaces over finite fields: what is the minimum number of points that must be contained in some $K⊂ F^n_q$ which contains a line in every direction?


Wednesday
November 07, 2018

1:00 PM - 2:00 PM
Math Tower P-131
Jean-Francois Arbour, Stony Brook University
TBA

TBA


Wednesday
November 14, 2018

1:00 PM - 2:00 PM
Math Tower P-131
Runjie Hu, Stony Brook University
K Theory and Division Algebras

The only dimensions of division algebras over the real numbers are only 1, 2, 4 and 8. We would introduce the topological approach for this problem without assumption of norm preserving. This result is equivalent to the H-space structures on spheres, which is to require the hopf invariant of the spheres should be one. I would briefly introduce the K theory and Adams operation and use this powerful tool to prove the problem of division algebras.


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars