Department of Mathematics

 Fall 2015

We will meet on Tuesdays at 4:00 pm.
Here is a tentative list of speakers (to be extended): Yevgeniy Kovchegov, Adam Sykulski (University College London, UK), Ed Waymire, Victor Peñaranda
Registration information: Mth 607, Sec 005 - CRN 13577



Title and abstract

Tuesday, October 13, 4:00 pm
STAG 112
Yevgeniy Kovchegov
Oregon State University

"Path Coupling and Aggregate Path Coupling"

Abstract. We describe and characterize an extension to the classical path coupling method referred to as aggregate path coupling. In conjunction with large deviations estimates, we use this aggregate path coupling method to prove rapid mixing of Glauber dynamics for a large class of statistical mechanical models, including models that exhibit discontinuous phase transitions which have traditionally been more difficult to analyze rigorously. Specifically, the parameter regions for rapid mixing for the generalized Curie-Weiss-Potts model and the mean-field Blume-Capel model are derived as an application of the aggregate path coupling method.
Joint work with Peter T. Otto of Willamette University.
Tuesday, October 20, 4:00 pm
STAG 112
Adam Sykulski
University College London, UK

"Modeling Lagrangian trajectories as stochastic processes"

Abstract. Fluid dynamics are often modeled and estimated from the Lagrangian perspective. In this talk I will discuss basic stochastic processes that mimic the behavior of Lagrangian trajectories observed in many environments - for example the motion of satellite-tracked ocean surface drifters. Although these basic processes do not exactly replicate the complex behavior of the ocean surface, fitting their parameters to observed data provides useful summaries of structure. The challenge of Lagrangian data is that it moves both in time and space, and as such I will discuss how to extend our stochastic processes to account for the inherent nonstationarity and heterogeneity of ocean dynamics. Finally, I will discuss extensions to our model to account for anisotropy and demonstrate this with application to a quasi-geostrophic turbulence simulation.
Tuesday, November 3, 4:00 pm
STAG 112
Ed Waymire
Oregon State University

"Analysis of a Particular Random Dynamical System"

Abstract. Non-irreducible random dynamical systems arise naturally in many contexts as iid iterated random maps on a metric space. Nonetheless the problem is to sort out the long time behavior. Some special theory will be described in the context of an example from mathematical biology.
This is based on joint work with Scott Peckham at the University of Colorado, Boulder, and Patrick DeLeenheer.
Tuesday, December 1, 4:00 pm
STAG 112
Victor Peñaranda
Visiting International Scholar
Oregon State University

"Geometrical Features in the Statistical Structure of Rainfall Patterns"

Abstract. Understanding rainfall patterns is and will be a challenge for those working in hydrological sciences. The complexity of rainfall resembles turbulence (not phenomenologically), and some models for describing rainfall have been inspired by turbulence. In this lecture, some ideas about the statistical description of rainfall will be presented, and how some of its geometrical features obtained from the fractal geometry can help us to identify symmetries in the physical process of rainfall. These symmetries are indexed by time and if one identifies the breaking of these symmetries, the space-time dynamics of rainfall could be explained. Some approaches related to the latter statement will also be discussed.

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,