Seminars and Colloquia by Series

Tropical h-vectors of polytopes

Series
Research Horizons Seminar
Time
Wednesday, February 13, 2019 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Josephine Yu – Georgia Tech
For a polytope P, the h-vector is a vector of integers which can be calculated easily from the number of faces of P of each dimension. For simplicial polytopes, it is well known that the h-vector is symmetric (palindromic) and unimodal. However in general the h-numbers may even be negative. In this talk I will introduce the tropical h-vector of a polytope, which coincides with the usual h-vector of the dual polytope, if the polytope is simple. We will discuss how they are related to toric varieties, tropical geometry, and polytope algebra. I will also discuss some open problems.

Descriptions of three-manifolds

Series
Research Horizons Seminar
Time
Wednesday, February 6, 2019 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jennifer Hom – Georgia Tech
In this talk, we will discuss various ways to describe three-manifolds by decomposing them into pieces that are (maybe) easier to understand. We will use these descriptions as a way to measure the complexity of a three-manifold.

Some combinatorial enumeration problems: results and techniques

Series
Research Horizons Seminar
Time
Wednesday, November 14, 2018 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Prasad Tetali – Georgia Tech
There has been much interest in the past couple of decades in identifying (extremal) regular graphs that maximize the number of independent sets, matchings, colorings etc. There have been many advances using techniques such as the fractional subaddtivity of entropy (a.k.a. Shearer's inequality), the occupancy method etc. I will review some of these and mention some open problems on hypergraphs.

From Atoms to Fluids: an introduction to Statistical Mechanics

Series
Research Horizons Seminar
Time
Wednesday, November 7, 2018 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Federico Bonetto – Georgia Tech
We all know that the air in a room is made up by a huge number of atoms that zip around at high velocity colliding continuously. How is this consistent with our observation of air as a thin and calm fluid surrounding us? This is what Statistical Mechanics try to understand. I'll introduce the basic examples and ideas of equilibrium and non equilibrium Statistical Mechanics showing that they apply well beyond atoms and air.

What can SDEs do for you?

Series
Research Horizons Seminar
Time
Wednesday, October 31, 2018 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Haomin Zhou – Georgia Tech
In this chalk plus slides talk, I will give a few examples from my own experience to illustrate how one can use stochastic differential equations in various applications, and its theoretical connection to diffusion theory and optimal transport theory. The presentation is designed for first or second year graduate students.

Knot invariants and algebraic structures based on knots

Series
Research Horizons Seminar
Time
Wednesday, October 24, 2018 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Thang Le – Georgia Tech
A knot is a simple closed curve in the 3-space. Knots appeared as one of the first objects of study in topology. At first knot theory was rather isolated in mathematics. Lately due to newly discovered invariants and newly established connections to other branches of mathematics, knot theory has become an attractive and fertile area where many interesting, intriguing ideas collide. In this talk we discuss a new class of knot invariants coming out of the Jones polynomial and an algebra of surfaces based on knots (skein algebra) which has connections to many important objects including hyperbolic structures of surfaces and quantum groups. The talk is elementary.

Counting objects using tropical geometry

Series
Research Horizons Seminar
Time
Wednesday, October 17, 2018 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Yoav Len – Georgia Tech
Tropical geometry provides a combinatorial approach for studying geometric objects by reducing them to graphs and polytopes. In recent years, tropical techniques have been applied in numerous areas such as optimization, number theory, phylogenetic trees in biology, and auction systems in economics. My talk will focus on geometric counting problems and their tropical counterpart. By considering these combinatorial gadgets, we gain newinsights into old problems, and tools for approaching new problems.

Synchronization of pendulum clocks and metronomes

Series
Research Horizons Seminar
Time
Wednesday, October 10, 2018 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Guillermo Goldsztein – Georgia Tech
In 1665, Huygens discovered that, when two pendulum clocks hanged from a same wooden beam supported by two chairs, they synchronize in anti-phase mode. Metronomes provides a second example of oscillators that synchronize. As it can be seen in many YouTube videos, metronomes synchronize in-phase when oscillating on top of the same movable surface. In this talk, we will review these phenomena, introduce a mathematical model, and analyze the the different physical effects. We show that, in a certain parameter regime, the increase of the amplitude of the oscillations leads to a bifurcation from the anti-phase synchronization being stable to the in-phase synchronization being stable. This may explain the experimental observations.

Two results about points on surfaces

Series
Research Horizons Seminar
Time
Wednesday, October 3, 2018 - 12:20 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Justin Lanier – Georgia Tech
After briefly describing my research interests, I’ll speak on two results that involve points moving around on surfaces. The first result shows how to “hear the shape of a billiard table.” A point bouncing around a polygon encodes a sequence of edges. We show how to recover geometric information about the table from the collection of all such bounce sequences. This is joint work with Calderon, Coles, Davis, and Oliveira. The second result answers the question, “Given n distinct points in a closed ball, when can a new point be added in a continuous fashion?” We answer this question for all values of n and for all dimensions. Our results generalize the Brouwer fixed point theorem, which gives a negative answer when n=1. This is joint work with Chen and Gadish.

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