- You are here:
- GT Home
- Home
- News & Events

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

Series: Research Horizons Seminar

The Mapper algorithm constructs compressed representations of the
underlying structure of data but involves a large number of parameters.
To make the Mapper algorithm accessible to domain experts, automation
of the parameter selection becomes critical. This talk will be accessible to graduate students.

Series: Research Horizons Seminar

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.

Series: Research Horizons Seminar

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.

Series: Research Horizons Seminar

This is a survey talk on the knot concordance group and the homology cobordism group.

Series: Research Horizons Seminar

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.

Series: Research Horizons Seminar

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.

Series: Research Horizons Seminar

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.