Seminars and Colloquia by Series

Random graph processes: results and techniques

Series
Research Horizons Seminar
Time
Wednesday, April 24, 2019 - 00:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Lutz Warnke – Georgia Tech

During the last 30 years there has been much interest in random graph processes, i.e., random graphs which grow by adding edges (or vertices) step-by-step in some random way. Part of the motivation stems from more realistic modeling, since many real world networks such as Facebook evolve over time. Further motivation stems from extremal combinatorics, where these processes lead to some of the best known bounds in Ramsey and Turan Theory (that go beyond textbook applications of the probabilistic method). I will review several random graph processes of interest, and (if time permits) illustrate one of the main proof techniques using a simple toy example.

MATHEMATICAL BILLIARDS: Geometry, dynamics, number theory, probability

Series
Research Horizons Seminar
Time
Wednesday, April 3, 2019 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Leonid Bunimovich – Georgia Tech

Mathematical billiards naturally arise in mechanics, optics, acoustics, etc. They also form the most visual class of dynamical systems with evolution covering all the possible spectrum of behaviours from integrable (extremely regular) to strongly chaotic. Billiard is a (deterministic) dynamical system generated by an uniform (by inertia) motion of a point particle within a domain with piecewise smooth walls ("a billiard table"). I will introduce all needed notions on simple examples and outline some open problems. This talk is also a preparatory talk to a Mathematical Physics seminar (on Monday April 8) where a new direction of research will be discussed which consider physical billiards where instead of a point (mathematical) particle a real physical hard sphere moves. To a complete surprise of mathematicians and PHYSICISTS evolution of a billiard may completely change (and in different ways) in transition from mathematical to physical billiards. It a rare example when mathematicians surprise physicists. Some striking results with physicists are also already obtained. I will (again visually) explain at the end of RH why it is surprising that there could be difference between Math and Phys billiards.

Braid groups

Series
Research Horizons Seminar
Time
Wednesday, February 27, 2019 - 12:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dan Margalit – Georgia Tech
An element of the braid group can be visualized as a collection of n strings that are braided (like a hair braid). Braid groups are ubiquitous in mathematics in science, as they record the motions of a number of points in the plane. These points can be autonomous vehicles, particles in a 2-dimensional medium, or roots of a polynomial. We will give an introduction to and a survey of braid groups, and discuss what is known about homomorphisms between braid groups.

Topological Data Analysis, Automating Mapper for Novel Data

Series
Research Horizons Seminar
Time
Wednesday, February 20, 2019 - 00:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jennifer Kloke – Ayasdi
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.

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.

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