Wednesday, November 28, 2018 - 12:20 , Location: Skiles 005 , JungHwan Park , Georgia Tech , Organizer: Trevor Gunn
This is a survey talk on the knot concordance group and the homology cobordism group.
Wednesday, November 14, 2018 - 12:20 , Location: Skiles 005 , Prasad Tetali , Georgia Tech , Organizer: Trevor Gunn
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.
Wednesday, November 7, 2018 - 12:20 , Location: Skiles 005 , Federico Bonetto , Georgia Tech , Organizer: Trevor Gunn
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.
Wednesday, October 31, 2018 - 12:20 , Location: Skiles 005 , Haomin Zhou , Georgia Tech , Organizer: Trevor Gunn
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.
Wednesday, October 24, 2018 - 12:20 , Location: Skiles 005 , Thang Le , Georgia Tech , Organizer: Trevor Gunn
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.
Wednesday, October 17, 2018 - 12:20 , Location: Skiles 005 , Yoav Len , Georgia Tech , Organizer: Trevor Gunn
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.