## Colloquium and Seminar Schedule

Spring 2012This is the schedule of colloquia and seminars inthe Department of Mathematics and Computer Science for the Spring 2012 semester.

Click here for information about the next scheduled talk.

## February 2012

"Rolling and Controlling"

Candidate's Talk

Date: Tuesday, February 21, 2012

Time: 5:00 PM

Location: Napier 201

(Refreshments will be served beforehand.)

Abstract:

In this talk, we will investigate the geometry and differential equations governing the dynamics of two objects rolling on each other. This is a classical problem in mechanics which nevertheless continues to generate new and interesting results today, with applications in fields as diverse as robotics, computer vision, and the study of partial differential equations. We'll explore the sort of tools that you can use to attack such problems and see how it leads to a special type of geometry quite unlike that of Euclid.

Finally, we will turn the whole thing on its head and ask: what happens if space itself is rolling on another universe?

There will be a tiny bit of calculus and a tiny bit of linear algebra, but the only real requirement is the willingness to stretch your brain in new ways!

"Modeling the Dynamics of Infectious Diseases with Latency

in Spatially Heterogenous Environments"

Candidate's Talk

Date: Tuesday, February 28, 2012

Time: 5:00 PM

Location: Napier 201

(Refreshments will be served beforehand.)

Abstract:

Motivated by the SARS outbreak, we formulate a model of infectious disease transmission for a population living in two locations (cities, towns, or countries etc.) by generalizing the classic Kermack-McKendrick SIR (susceptible--infectious--recovered/removed) model to incorporate latency. The model is given by a system of delay differential equations with a fixed delay accounting for the latency and non-local terms caused by the mobility of the individuals during the latent period. The model preserves some properties that the classic Kermack-McKendrick SIR model possesses: the disease always dies out, leaving a certain portion of the susceptible population untouched (called final sizes). The ratio of the final sizes in the two locations is determined by the ratio of the dispersion rates of the susceptible individuals between the two locations. We also show that the new model may have very rich patterns for the disease to die out. E.g., unlike the classic SIR model, it allows multiple outbreaks of the disease before it goes to extinction.

## March 2012

"How Randomness Controls Our Lives"

Candidate's Talk

Date: Monday, March 5, 2012

Time: 5:00 PM

Location: Napier 201

(Refreshments will be served beforehand.)

Abstract:

Modeling and analysis of phenomena in the life sciences require techniques and tools from various disciplines. Though deterministic models have been broadly used and proved to be a powerful tool in the study of mathematical biology, stochastic models often complement them on capturing individual behavior and effects of noise, molecular fluctuations and random environmental change for example.

In this talk, I will present two examples to show when and how stochastic models can be applied to study biological problems. In the first example, an agent based model is used to study resource sharing rules among human populations under realistic ecological conditions and reveals that simple sharing is an effective risk reducing strategy that plays an important role in maintaining human populations. In the second example, Markov chains and stochastic differential equations are applied to model the dynamics of cardiac calcium that is crucial for cardiac rhythm regulation and is known to be the key to understanding many cardiac diseases.

"Twists and Turns: An Introduction to the Mapping Class Group"

Candidate's Talk

Date: Friday, March 30, 2012

Time: 4:30 PM

Location: Eaton 110

(Refreshments will be served beforehand.)

Abstract:

The Mapping Class Group classifies continuous invertible functions from a surface to itself. It is used by topologists to understand how 3- and 4-dimensional spaces are shaped, and has many applications in other branches of mathematics. The Mapping Class Group is easy to describe visually, but its implications can be complicated and far-reaching. What exactly is this object? Why is it so useful?

We will assume a willingness to draw pictures. Illustrations of donuts will be provided.

## April 2012

Continued Fractions -- A Tour Through The Ages

Candidate's Talk

Date: Monday, April 9, 2012

Time: 4:30 PM

Location: Napier 201

(Refreshments will be served beforehand.)

Abstract:

We'll begin with the ancient division algorithm ascribed to Euclid which naturally leads to the notion of a continued fraction and pause to explore a few recent viewpoints taken in the last century towards understanding this classical object and deciphering the information it encodes. The study of continued fractions continues to this day with plenty of unresolved problems pointing at various directions for future research. This will be a general talk aimed at undergraduates from all backgrounds with the barest minimum of serious mathematical preparation - come one, come all!

Design and Build: Study Sesh

Mark Benya (H'14)

A Journey Through Evolved 3D Game Development

Matt Weichselbaum (H'12)

Date: Thursday, April 12, 2012

Time: 4:45 PM

Location: Napier 101

(Refreshments will be served beforehand.)

Abstract:

Join computer science majors Mark Benya and Matt Weichselbaum as they discuss their Independent Study Projects for this semester.

A Mathematical Model: Hepatitis B and Hepatitis D Co-infection

Yaoxin Liu (H'12)

ELARA: Environmental Liaison and Automated Recycling Assistant

Marcela Melara (WS'12)

ISTAT: Online Interface for Hypothesis Testing

Shaun Viguerie (H'12)

Date: Tuesday, April 12, 2012

Time: 4:45 PM

Location: Napier 201

(Refreshments will be served beforehand.)

Abstract:

Students who have completed Honors projects this year will present their work. An Honors project is a two-semester endeavor culminating in a long Honors thesis and an oral examination by a panel of three examiners. Marcela and Shaun completed honors in Computer Science, while Yaoxin completed honors in Mathematics.

## May 2012

Combinatorics, weird dice, and a card trick

Candidate's Talk

Date: Tuesday, May 1, 2012

Time: 5:00 PM

Location: Napier 201

(Refreshments will be served beforehand.)

Abstract:

A card trick will be used to introduce a variety of topics in discrete mathematics. Topics include permutations, combinations, and the pigeonhole principle. After this, we will show that there is a weird way to label two dice so that we get the same probability distribution on the sum as we get with two standard dice.

## Past Colloquia Series

Fall 2011 Spring 2011 Fall 2010 Spring 2010 Fall 2009 Spring 2008 Fall 2008

If you have interest in giving a talk or know of someone who does,

please contact Kevin Mitchell at mitchell@hws.edu