Department of Mathematics

 Spring 2014

We will meet on Tuesdays at 4:00pm.
Here is a tentative list of speakers (to be extended): Zhen-Qing Chen (University of Washington), Yung-Pin Chen (Lewis & Clark College), Benjamin Young (University of Oregon), Sooie-Hoe Loke
Registration information: Mth 607, Sec 003 - CRN 55249



Title and abstract

Tuesday, April 29, 4:00pm
Kidder 350
Benjamin Young
University of Oregon

"Inverting the Kasteleyn matrix for the Aztec Diamond"

Abstract. I'll describe how to invert the Kasteleyn matrix for a few of the most interesting weight functions on the Aztec Diamond. This, in principle, allows the computations of correlation kernels for the associated tiling model. In some of the simpler cases, it is possible to compute asymptotics for this kernel rigorously; though this is essentially a combinatorics talk, I'll mention the sorts of asymptotics which can be derived. In more difficult cases (specifically 2-periodic weights) the asymptotics are not yet tractable, although they represent perhaps the most promising way in which one might study the transition between liquid and gaseous regimes in a dimer model. Joint work with Sunil Chhita and Kurt Johansson.
Tuesday, May 6, 4:00pm
Kidder 350
Zhen-Qing Chen
University of Washington

"Anomalous diffusions and fractional order differential equations"

Abstract. Anomalous diffusion phenomenon has been observed in many natural systems, from the signalling of biological cells, to the foraging behaviour of animals, to the travel times of contaminants in groundwater. I will first discuss the connections between anomalous diffusions and differential equations of fractional order, and then present some recent results in the study of heat kernels for non-local operators of fractional order.
Tuesday, May 13, 4:00pm
Kidder 350
Yung-Pin Chen
Lewis & Clark College

"Making two integers coprime more likely"

Abstract. I will introduce a Markov chain on the set of positive integers with the following transition probabilities: An integer will visit equally likely those integers that are coprime to it. I will discuss the probability of selecting two coprime integers if they are generated from the stationary distribution of this Markov chain. I will also discuss the evaluation of some series involving the Euler totient function.
Tuesday, June 3, 4:00pm
Kidder 350
Sooie-Hoe Loke
Oregon State University

"On the Hitting Times of Integral of Geometric Brownian Motion"

Abstract. The connection between Bessel process and the integral of geometric Brownian motion (IGBM) has been well-established. The key to this approach is the Lamperti relation. However, a common difficulty is that arguments constructed for Bessel processes with positive index generally do not carry over to the ones with negative index. In this talk, we use a differential equation approach to study the hitting times of IGBM. We discuss the paper by Metzler (2013) in which the Laplace transform of hitting times is expressed in terms of the gamma and confluent hypergeometric functions. The transform satisfies Kummer's equation which is obtained using Ito's formula and standard results on hitting times of diffusion processes.

Past probability seminars: Fall 2005, Winter 2006, Spring 2006, Fall 2006, Winter 2007, Spring 2007, Fall 2007, Winter 2008, Spring 2008, Fall 2008, Winter 2009, Spring 2009, Fall 2009, Winter 2010, Spring 2010, Fall 2010, Winter 2011, Spring 2011, Fall 2011, Winter 2012, Spring 2012, Fall 2012, Winter 2013, Spring 2013, Fall 2013, Winter 2014