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Texas A&M University
Mathematics

Maxson Lecture Series

Spring 2022

 

Date:April 25, 2022
Time:4:00pm
Location:BLOC 117
Speaker:Dana Randall, Georgia Institute of Technology
Title:Phase transitions in sampling algorithms and applications
Abstract:Sampling algorithms based on Markov chains arise in many areas of computation, engineering and science. The idea is to perform a random walk among the elements in a large state space so that samples chosen from the stationary distribution are useful for the application. In order to get reliable results efficiently, we require the chain to be rapidly mixing, or quickly converging to equilibrium. Often there is a parameter of the system (typically related to temperature or fugacity) so that at low values many natural chains converge rapidly while at high values they converge slowly, requiring exponential time. This dichotomy is often related to phase transitions in the underlying models. In this talk we will explain this phenomenon, giving examples form the natural and social sciences including magnetization, lattice gasses, colloids, and models of segregation.

Date:April 26, 2022
Time:4:00pm
Location:BLOC 117
Speaker:Dana Randall, Georgia Institute of Technology
Title:Emergent phenomena in programmable matter
Abstract:Active matter describes ensembles of self-organizing agents, or particles, interacting with their local environments so that their micro-scale behavior determines macro-scale characteristics of the ensemble. While there has been a surge of activity exploring the physics underlying such systems, less attention has been paid to questions of how to program them to achieve desired outcomes. We will present some recent results designing programmable active matter for specific tasks, including aggregation, dispersion, speciation, and locomotion, building on insights from stochastic algorithms and statistical physics.