Department of Mathematics

 Fall 2017

We will meet on Tuesdays at 4:00 pm.
Here is a tentative list of speakers (to be extended): James Watson, Yevgeniy Kovchegov, Ed Waymire, Bruno Barbosa
Registration information: Mth 607, Sec 005 - CRN 20132



Title and abstract

Tuesday, October 10, 4:00 pm
BEXL 207
Yevgeniy Kovchegov
Oregon State University

"Random self-similar trees: dynamical pruning and its applications to inviscid Burgers equations"

Abstract. We introduce generalized dynamical pruning on rooted binary trees with edge lengths. The pruning removes parts of a tree T, starting from the leaves, according to a pruning function defined on subtrees within T. The generalized pruning encompasses a number of previously studied discrete and continuous pruning operations, including the tree erasure and Horton pruning. For example, a finite critical binary Galton-Watson tree with exponential edge lengths is invariant with respect to the generalized dynamical pruning for arbitrary admissible pruning function. We will discuss an application in which we examine a one dimensional inviscid Burgers equation with a piece-wise linear initial potential with unit slopes. The Burgers dynamics in this case is equivalent to a generalized pruning of the level set tree of the potential, with the pruning function equal to the total tree length. We give a complete description of the Burgers dynamics for the Harris path of a critical binary Galton-Watson tree with i.i.d. exponential edge lengths.

This work was done in collaboration with Ilya Zaliapin (University of Nevada Reno) and Maxim Arnold (University of Texas at Dallas).
Tuesday, October 31, 4:00 pm
BEXL 207
James Watson
CEOAS, Oregon State University

"Anticipating and Managing Risk in Marine Social-ecological Systems"

Abstract. In this presentation I introduce a new approach to managing risk in marine food-producing systems -- fisheries and aquaculture -- based on weather index and cooperative insurance. The mathematical framework is explained and then results are shown from its application to a case-study in Myanmar, where empirical data has been collected. I will also briefly introduce early work from a new project focusing on Manifold Learning, a new approach to studying the multilevel dynamics of complex systems.
Tuesday, November 21, 4:00 pm
BEXL 207
Ed Waymire
Oregon State University

"When 4th Moments Are Enough"

Abstract. This talk concerns a somewhat innocent question motivated by an observation concerning the use of Chebyshev bounds on sample estimates of p in the binomial distribution with parameters n, p. Namely, what moment order produces the best Chebyshev estimate of p? If Sn(p) has a binomial distribution with parameters n, p, then it is readily observed that argmax0 ≤ p ≤ 1ESn2(p) = argmax0 ≤ p ≤ 1np(1-p) = 1/2, and ESn2 = n/4. Rabi Bhattacharya observed (personal communication) that while the second moment Chebyshev sample size for a 95% confidence estimate within ±5 percentage points is n = 2000, the fourth moment yields the substantially reduced polling requirement of n = 775. Why stop at fourth moment? Is the argmax achieved at p = 1/2 for higher order moments and, if so, does it help, and can one easily compute the moment bound ESn2m(1/2)? As captured by the title of this talk, answers to these questions lead to a simple rule of thumb for best choice of moments in terms of an effective sample size for Chebyshev concentration inequalities. This talk is based on joint work with Chris Jennings-Shafer and Dane Skinner.
Tuesday, January 23 (Winter'18), 4:00 pm
Sidney Resnick
Cornell University


Abstract. TBA

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, Spring 2014, Fall 2014, Winter 2015, Spring 2015, Fall 2015, Winter 2016, Spring 2016, Fall 2016, Winter 2017, Spring 2017