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Colloquia and Seminars

The Department of Mathematics is home to a dynamic group of scholars who regularly share their expertise with others. Many of our events and activities are free and open to the public, and we encourage you to get involved.

 Colloquia

JAN 25 - Zhen-qing Chen - Anomalous Diffusions and Fractional Order Differential Equations

When: Thursday, January 25, 2018  - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Zhen-qing Chen, University of Washington

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. In this talk, I will first discuss the interplay between anomalous diffusions and differential equations of fractional order. I will then present some recent results in the study of these two topics, including the counterpart of DeGiorgi-Nash-Moser-Aronson theory for non-local operators of fractional order. No prior knowledge in these two subjects is assumed. [PDF]

Host: Hong Wang

FEB 8 - Changhui Tan - Self-organized dynamics: Aggregation and Flocking

When: Thursday, February 8, 2018 - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Changhui Tan, Rice University

Abstract: Self-organized behaviors are commonly observed in nature and human societies, such as bird flocks, fish swarms and human crowds. In this talk, I will present some celebrated mathematical models, with simple small-scale interactions that lead to the emergence of global behaviors: aggregation and flocking. The models can be constructed through a multiscale framework: from microscopic agent-based dynamics, to macroscopic fluid systems. I will discuss some recent analytical and numerical results on the derivation of the systems in different scales, global wellposedness theory, large time behaviors, as well as interesting connections to some classical equations in fluid mechanics. [PDF]

FEB 15 - Andrei Tarfulea - Bounds and Aymptotic Dynamics for Nonlinear Evolution Equations

When: Thursday, February 15, 2018 - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Andrei Tarfulea, University of Chicago

Abstract: Understanding the behavior of solutions to physically motivated evolution equations is one of the most important areas of applied analysis. Developing strong bounds and asymptotics are crucial for anticipating the behavior of simulations, simplifying the methods needed to model the physical phenomena. The focus will be on recent results in three physical models: homogenization and asymptotics for nonlocal reaction-diffusion equations, a priori bounds for hydrodynamic equations with thermal effects, and the local well-posedness for the Landau equation (with initial data that is large, away from Maxwellian, and containing vacuum regions). Each problem presents unique challenges arising from the nonlinearity and/or nonlocality of the equation, and the emphasis will be on the different methods and techniques used to treat those difficulties in each case. The talk will touch on novelties in viscosity theory and precision in nonlocal front propagation for reaction-diffusion equations, as well as the emergence of "dynamic" self-regularization in the thermal hydrodynamic and Landau equations. [PDF]

FEB 20 - Xiu Yang - Uncertainty Quantification for Complex Systems using Limited Data

When: Tuesday, February 20, 2018 - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Xiu Yang, PNNL

Abstract: Realistic analysis and design of complex engineering systems require not only a fine understanding of the underlying physics, but also a significant recognition of uncertainties and their influences on the quantities of interest. Intrinsic variabilities and lack of knowledge about system parameters or governing physical models often considerably affect quantities of interest and decision-making processes. For complex systems, the available data for quantifying uncertainties or analyzing sensitivities are usually limited because the cost of conducting a large number of experiments or running many large-scale simulations can be prohibitive. Efficient approaches of representing uncertainties using limited data are critical for such problems. I will talk about two approaches for uncertainty quantification by constructing surrogate model of the quantity of interest. The first method is the adaptive functional ANOVA method, which constructs the surrogate model hierarchically by analyzing the sensitivities of individual parameters. The second method is the sparse regression based on identification of low-dimensional structure, which exploits low-dimensional structures in the parameter space and solves an optimization problem to construct the surrogate models. I will demonstrate the efficiency of these methods with PDE with random parameters as well as applications in aerodynamics and computational chemistry. [PDF]

FEB 22 - Danny Krashen

When: Thursday, February 22, 2018  - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Danny Krashen, Rutgers University / University of Georgia

Abstract: TBA

Host: Frank Thorne

MAR 1 - Lars Christensen 

When:  Thursday, March 1, 2018  - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Lars Christensen, Texas Tech University

Abstract: TBA

Host: Adela Vraciu

APR 5 - Anthony Bonato - Graph Searching Games and Probabilistic Methods

When:  Thursday, April 5, 2018  - 4:30 p.m. to 5:30 p.m.
Where: LeConte 412 (map)

Speaker: Anthony Bonato, Ryerson University

Abstract: The intersection of graph searching and probabilistic methods is a new topic within graph theory, with applications to graph searching problems such as the game of Cops and Robbers and its many variants, Firefighting, graph burning, and acquaintance time. Graph searching games may be played on random structures such as binomial random graphs, random regular graphs or random geometric graphs. Probabilistic methods may also be used to understand the properties of games played on deterministic structures. A third and new approach is where randomness figures into the rules of the game, such as in the game of Zombies and Survivors. We give a broad survey of graph searching and probabilistic methods, highlighting the themes and trends in this emerging area. The talk is based on my book (with the same title) co-authored with Pawel Pralat published by CRC Press.

Bio: Anthony Bonato’s research is in Graph Theory, with applications to the modelling of real-world, complex networks such as the web graph and on-line social networks. He has authored over 110 papers and three books with 70 co-authors. He has delivered over 30 invited addresses at international conferences in North America, Europe, China, and India. He twice won the Ryerson Faculty Research Award for excellence in research and an inaugural Outstanding Contribution to Graduate Education Award. He is the Chair of the Pure Mathematics Section of the NSERC Discovery Mathematics and Statistics Evaluation Group, Editor-in-Chief of the journal Internet Mathematics, and editor of the journal Contributions to Discrete Mathematics.

Host: Linyuan Lu

  

Seminars