Graduate Student Seminar

from Friday
June 01, 2018 to Monday
December 31, 2018
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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.


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