## Colloquium and Seminar Schedule

Spring 2016This is the schedule of colloquia and seminars inthe Department of Mathematics and Computer Science for the Spring semester.

## February 2016

"Mathematics of Combinatorial (and other) Games "

Candidate's Talk

Date: Friday, February 5

Time: 4:00 PM

Location: Napier 201

Refreshmentswill be served at 3:45.

Abstract:

People have been creating and playing games for millennia, perhaps to satisfy our inherent drive for challenges that are fun and entertaining. In this talk, I will present the theory of two-person games of perfect information, starting from the classical game of Nim and other impartial games (those where the players have the same set of moves available), to partisan games (like Chess and Go). Mathematicians and computer scientists have studied models of game playing and have produced amazing results (just last week a breakthrough was announced in championship level Go), and I will also discuss some of these models.

"Modeling in Mathematical Neuroscience"

Candidate's Talk

Date: Monday, February 8

Time: 4:30 PM

Location: Napier 201

Refreshmentswill be served at 4:15.

Abstract:

Neuroscience is the study of the brain and nervous system. In this talk, I will discuss how mathematics can be used to model single synapses as well as networks of neurons. I will describe two different projects, one modeling the photoreceptor synapse in the visual system and another studying what the structure of a neural network can tell us about the behavior of the network.

"Coxeter groups and some (fun) problems related to them"

Candidate's Talk

Date: Thursday, February 11

Time: 4:30 PM

Location: Napier 201

Refreshmentswill be served at 4:15.

Abstract:

Coxeter groups can be realized (loosely speaking) as groups of reflections of certain geometric objects called root systems. Important examples include symmetric groups, dihedral groups, and Weyl groups. In this talk I will give an introduction to Coxeter groups, and discuss some interesting problems related to them. For example, I will discuss the notion of "peaks" of permutations. A peak of a permutation π = π_1, π_2, ..., π_n is a position i where π_{i-1} < π_i > π{i+1}. Several questions come to mind: How many permutations have a certain collection of peaks? Is there a closed formula? Can we play the same game with signed permutations? Interestingly enough, some of these questions are still unanswered and will be discussed. I will only assume some basic theory of groups covered in an (undergraduate) abstract algebra course.

"Graph coloring with polynomials"

Candidate's Talk

Date: Wednesday, February 17

Time: 4:30 PM

Location: Napier 201

Refreshmentswill be served at 4:15.

Abstract:

The four-color theorem is a classic theorem from mathematics which states roughly that you only need four colors to color any map. In this talk we will see how this is really a problem about coloring graphs and that we can answer graph-coloring questions by encoding the information of the graph into a set of polynomials and studying the algebra of the polynomials.

"Quivers, mutations, and a small collection of bad math puns"

Candidate's Talk

Date: Friday, February 19

Time: 4:30 PM

Location: Napier 201

Refreshmentswill be served at 4:15.

Abstract:

Quivers are just directed graphs, and mutation is a way of taking one of these graphs and "transforming it" into a new graph. What is particularly fascinating about mutation is the many different areas of math where this comes into play. Mutation models things in geometry, number theory, topology, representation theory, and even plays a role in the world of string theory. This talk will introduce this exciting new area of combinatorics, by looking at the definitions, some key examples, and then exploring some of the connections to these other areas of mathematics and providing you with a few open problems in the subject.

"Spider Trees and the Graceful Labeling Conjecture"

Candidate's Talk

Date: Wednesday, February 24

Time: 4:30 PM

Location: Napier 201

Refreshmentswill be served at 4:15.

Abstract:

The decades-old graceful labeling conjecture is one of the major unanswered problems in graph theory. It is simple to state, easy to understand, and (evidently) extremely difficult to solve. It is also the kind of addictive puzzle that will keep you up at night: Anton Kotzig, one of the authors of the conjecture, famously called the effort to settle it a "disease". We will begin with the statement of the graceful labeling conjecture, introduce a stronger "oriented" version, and investigate this new conjecture for a certain class of graphs known as "spider trees." Fair warning: this disease is contagious.

## April 2016

"What to expect from your first mathematics conference"

Speakers: Casey Coffey, Jacqueline Kane, Theresa Lohr and Haley Okun

Date: Wednesday, April 20

Time: 7:15 PM

Location: Napier 101

Refreshmentswill be served at 7:00.

Abstract:

The Nebraska Conference for Undergraduate Women in Mathematics (NCUWM) is held annually. It aims to arm participants with knowledge, self-confidence, and a network of peers to help them become successful mathematicians. The Conference is open to undergraduate women mathematicians at all stages of their careers. Thanks to the Metzger Fund, the William Smith Deans' Office and the Department of Mathematics and Computer Science, Casey, Jacque, Theresa and Haley were able to attend the 2016 NCUWM. This talk will be about their experiences at the conference including some of the mathematics they learned.

"What do Tomahawk Missiles, the International Space Station and Carbon Sequestration have in Common? --The Kalman Filter: An Introduction and Derivation"

Speaker: Trevor Gionet, H'12

Date: Friday, April 22

Time: 4:16 PM

Location: Napier 201

Refreshmentswill be served at 4:00.

Abstract:

From tracking cruise missiles and navigating the International Space Station to weather forecasting and mitigating climate change, this talk will provide an overview of the Kalman filter, its uses and applications. A complete derivation will be presented for the linear model scenario. This will be followed by a look into some of the extensions, concluding with the Local Ensemble Transform Kalman Filter (LETKF), a filter which is currently being studied for its use in forecasting forest variables. Other data assimilation methods will be mentioned to shed light on the advantages of this simple yet powerful approach.

## Past Colloquia Series

Fall 2015 Spring 2015 Fall 2014 Spring 2014 Fall 2013 Spring 2013

Fall 2012 Spring 2012 Fall 2011 Spring 2011

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

please contact Prof. Yan Hao at hao@hws.edu