Seminars and Colloquia by Series

Convergence of gradient flows and scaling limit for particle systems

Series
Other Talks
Time
Wednesday, February 17, 2016 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Max Fathi – Department of Mathematics, UC Berkeley
In this talk, I will explain how the gradient flow structure of reversible Markov chains (that was discovered by Maas and Mielke independently in 2011) and the Sandier-Serfaty approach to convergence of gradient flows can be combined to study scaling limits for interacting particle systems on lattices. The exposition will be focused on the case of the simple exclusion process on the discrete torus. Joint work with Marielle Simon (INRIA Lille).

Population biology of Schistosoma, its control and elimination: insights from mathematics and computations

Series
Mathematical Biology Seminar
Time
Wednesday, February 17, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Professor David Gurarie – CWRU –
Schistosoma is a parasitic worm that circulates between human and snail hosts. Multiple biological and ecological factors contribute to its spread and persistence in host populations. The infection is widespread in many tropical countries, and WHO has made control of schistosomiasis a priority among neglected tropical diseases.Mathematical modeling is widely used for prediction and control analysis of infectious agents. But host-parasite systems with complex life-cycles like Schistosoma, pose many challenges. The talk will outline the basic biology of Schistosoma, and the principles employed in mathematical modeling of macro parasites. We shall review conventional approaches to Schistosomiasis starting with the classical work of MacDonald, and discuss their validity and implications. Then we shall outline more detailed “stratified worm burden approach”, and show how combining mathematical and computer tools one can explore real-world systems and make reliable predictions for long term control outcomes and the problem of elimination.

On long -time behavior of solutions of 2d Euler equations

Series
PDE Seminar
Time
Tuesday, February 16, 2016 - 18:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Vladimir Sverak – University of Minneapolis, Minnesota
Long-time behavior of "generic" 2d Euler solutions is expected to be governed by conserved quantities and simple variational principles related to them. Proving or disproving this from the dynamics is a notoriously difficult problem which remains unsolved. The variational problems which arise from these conjectures are interesting by themselves and we will present some results concerning these problems.

A Grassmann algebra for matroids

Series
Algebra Seminar
Time
Monday, February 15, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Noah Giansiracusa – University of Georgia
I'll discuss joint work with my brother Jeff Giansiracusa in which we introduce an exterior algebra and wedge product in the idempotent setting that play for tropical linear spaces (i.e., valuated matroids) a very similar role as the usual ones do for vector spaces. In particular, by working over the Boolean semifield this gives a new perspective on matroids.

Massive data analysis helps modern medical datasets

Series
Applied and Computational Mathematics Seminar
Time
Monday, February 15, 2016 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Professor Hautieng Wu – University of Toronto
Explosive technological advances lead to exponential growth of massive data-sets in health-related fields. Of particular important need is an innovative, robust and adaptive acquisition of intrinsic features and metric structure hidden in the massive data-sets. For example, the hidden low dimensional physiological dynamics often expresses itself as atime-varying periodicity and trend in the observed dataset. In this talk, I will discuss how to combine two modern adaptive signal processing techniques, alternating diffusion and concentration of frequency and time(ConceFT), to meet these needs. In addition to the theoreticaljustification, a direct application to the sleep-depth detection problem,ventilator weaning prediction problem and the anesthesia depth problemwill be demonstrated. If time permits, more applications likephotoplethysmography and electrocardiography signal analysis will be discussed.

Oral exam

Series
Other Talks
Time
Monday, February 15, 2016 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 270
Speaker
John Dever – Ga. Tech
Topics: local Hausdorff dimension, local Hausdorff measure, diffusion on compact metric spaces, prospective further research.

Mean convergence of ergodic averages and continuous model theory

Series
CDSNS Colloquium
Time
Monday, February 15, 2016 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Eduardo Duenez – University of Texas at San Antonio
The Mean Ergodic Theorem of von Neumann proves the existence of limits of (time) averages for any cyclic group K = {U^n : n \in Z} acting on some Hilbert space H via powers of a unitary transformation U. Subsequent generalizations apply to so-called _multiple_ ergodic averages when Z is replaced by an arbitrary amenable group G, provided the image group K is nilpotent (Walsh's ergodic 2014 theorem for Z; generalization to G amenable by Zorin-Kranich). In this talk we survey a framework for mean convergence of polynomial group actions based on continuous model theory. We prove mean convergence of unitary polynomial Z-actions, and discuss how the full framework accomodates the most recent results mentioned above and allows generaling them.

Local Hausdorff dimension and measure

Series
SIAM Student Seminar
Time
Friday, February 12, 2016 - 15:05 for 1 hour (actually 50 minutes)
Location
Skiles 114
Speaker
John Dever – Georgia Institute of Technology
A local Hausdorff dimension is defined on a metric space. We study its properties and use it to define a local measure. We show that in many circumstances we can recover the global Hausdorff dimension from the local one. We give an example of a compact metric space with a continuum of local dimension values. We define the dimension of a measure and connect the definition to that of local Hausdorff dimension and measure for a class of spaces called (variable) Ahlfors Q-regular. Very little background knowledge, aside from basic familiarity with metric spaces, will be assumed.

The Peierls barrier in one dimensional models

Series
Dynamical Systems Working Seminar
Time
Friday, February 12, 2016 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 170
Speaker
Lei Zhang – Georgia Tech
The Peierls barrier is an observable which characterizes whether the the set minimizers with a prescribed frequency of a periodic variational problem form a continuum or have gaps. In solid state physics Peierls barrier characterizes whether ground states with a fixed density are pinned or are able to slide. The Peierls barrier is a microscopic explanation of static friction. Remarkably, in dynamical systems, Peierls barrier appears also as characterizing whether KAM circles break down into Cantor sets. Hence, the Peierls barrier has been investigated both by physicists and by mathematicians using a variety of methods. We plan to cover the basic definitions of the variational models and some of the basic results obtainedfrom the 80's.

Stochastic facilitation and selection in systems with non-smooth dynamics

Series
School of Mathematics Colloquium
Time
Thursday, February 11, 2016 - 16:05 for 1 hour (actually 50 minutes)
Location
Skiles 005
Speaker
Rachel Kuske – University of British Columbia
There have been many recent advances for analyzing the complex deterministic behavior of systems with discontinuous dynamics. With the identification of new types of nonlinear phenomena exploding in this realm, one gets the feeling that almost anything can happen. There are many open questions about noise-driven and noise-sensitive phenomena in the non-smooth context, including the observation that noise can facilitate or select "regular" dynamics, thus clarifying the picture within the seemingly endless sea of possibilities. Familiar concepts from smooth systems such as escapes, resonances, and bifurcations appear in unexpected forms, and we gain intuition from seemingly unrelated canonical models of biophysics, mechanics, finance, and climate dynamics. The appropriate strategy is often not immediately obvious from the area of application or model type, requiring an integration of multiple scales techniques, probabilistic models, and nonlinear methods.

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