11/20: Matt Lamoureux, “Stirling’s Formula”

Please join us for Math Club on Wednesday at the usual time (5:30-6:30) and place (LGRT 1634).  This week, Matt Lamoureux (UConn) will be speaking on Stirling’s Formula (abstract below).   As always, pizza and soda will be provided.

Abstract:

The factorials n! = 1 ⋅ 2 ⋅ 3 ⋅ … ⋅ n, which count how many ways n objects can be arranged, show up anywhere that rearrangements have to be counted, such as combinatorics, probability, thermodynamics, statistical mechanics, and quantum mechanics. The numbers n! grow very rapidly, e.g., 100! has 158 digits. For applications in chemistry, n! may occur for n on the order of Avogadro’s number (about 6.02 ⋅ 10^23), for which an exact calculation is out of the question. When exact values are computationally inaccessible, it’s natural to seek approximations to the values.
Stirling’s formula is the standard way to estimate n! when n is large. In this talk we will see what Stirling’s formula is and how to derive it using tools from calculus.

11/13: Professor Pengfei Zhang, “Regular and chaotic billiards”

Please join us for Math Club at its usual time (Wednesday 5:30-6:30) and place (LGRT 1634).  This week, Professor Pengfei Zhang will be speaking on, “Regular and chaotic billiards” (abstract below).  As always, pizza and soda will be provided.
Abstract:
The study of many physical systems can be modeled by billiard system,
for example the electric current flows along a metal wire,
and a light beam reflects along a mirror.
To study the long time behavior of the billiard model,
we can make a mathematical assumption that there is no pocket
and no friction: the billiard will keep moving forever.
In this talk, we will present some basic properties of billiard systems,
and give various examples of regular and chaotic billiard tables.
Then we will describe some recent progress on the study of generalized
lemon billiards.

11/6: William Hu, “Modeling and Simulating Chemical Reactions”

Please join us for Math Club this week at its usual time (Wednesday 5:30-6:30) and place (LGRT 1634).  This week, William Hu will speak on, “Modeling and Simulating Chemical Reactions” (abstract below).  As always, pizza and soda will be provided.

 
Abstract:
Many people are familiar with the idea of modeling chemical reactions in terms of ordinary differential equations. However, these deterministic reaction rate equations are really a certain large-scale limit of a sequence of finer-scale probabilistic models. In studying this hierarchy of models, we can be exposed to a range of modern ideas in applied and computational mathematics. This talk introduces some of the basic concepts in an accessible manner and points to some challenges that currently occupy researchers in this area.

Key words: chemical master equation, chemical Langevin, Euler–Maruyama,
Gillespie, kinetic Monte Carlo, reaction rate equation, stochastic simulation algorithm, stoichiometric vector, tau-leaping