Departmental Colloquium

	Date	Speaker	Talk Information
View details	January 24	Srikanth Iyengar University of Nebraska, Lincoln	The goal of this talk will be to describe a bridge between the modular representation theory of finite groups and modules over polynomial rings. This has given us new insights and results concerning modular representations, and has also lead to unexpected results in commutative algebra. The talk with be based on joint work with Avramov, Benson, Carlson, Buchweitz, Krause, and Claudia Miller.
View details	January 31	Peter Trapa University of Utah	Unitary representations of Lie groups appear in many places in mathematics: in harmonic analysis (as generalizations of the sines and cosines appearing in classical Fourier analysis); in number theory (as spaces of modular and automorphic forms); in quantum mechanics (as "quantizations" of classical mechanical systems); and in many other places. They have been the subject of intense study for decades, but their classification has only recently recently emerged. Perhaps surprisingly, the classification has inspired connections with interesting geometric objects (equivariant mixed Hodge modules on flag varieties). These connections have made it possible to extend the classification scheme to other related settings. The purpose of this talk is to explain a little bit about the history and motivation behind the study of unitary representations and offer a few hints about the algebraic and geometric ideas which enter into their study. This is based on a recent preprint with Adams, van Leeuwen, and Vogan.
View details	February 7	Sébastien Motsch Center for Scientific Computation and Mathematical Modeling, University of Maryland	In many biological systems, we observe the emergence of self-organized dynamics (e.g. school of fish, ant colonies, pedestrian traffic). Modeling is an essential tool to better understand their behavior. Based on experimental data, we introduce some recent models which aim to explain such dynamics. Since biological systems can reach up to millions of individuals, we discuss in a second part how we can derive “macroscopic models” from several microscopic models. In contrast with particle systems in physics, models of self-organized dynamics do not conserve momentum or energy. This lack of conservation requires to introduce new tools to derive and analyze their macroscopic limits.
View details	February 14	Jun Allard University of California, Davis	Crawling cells, including the white blood cells that patrol your body in search of infections, display several distinct dynamical patterns driven by both biochemistry (diffusion and reactions between chemical species) and mechanics (physical forces between the components inside cells). Our understanding of these spatiotemporal patterns has been aided by mathematical modeling using techniques including partial differential equations (PDEs). Recently, traveling waves have been observed in the protein actin, which powers certain cells’ ability to crawl. Following experimental observation of one type of crawling cell, the fish epithelial keratocyte, we hypothesized that traveling waves are excitable waves arising from interactions of three components: actin, adhesion sites that attach the cell to its environment, and VASP, a protein that regulates actin. We developed a mathematical model formulated as a system of PDEs with a nonlocal integral term and noise. Numerical solutions lead to a number of predictions, including that VASP also exhibits a traveling wave out of phase with the actin wave, later discovered in further experiments. Our model also reveals a role for tension in the membrane that surrounds the cell, which would otherwise be difficult to observe directly by experiment.
View details	March 7	Clint Dawson University of Texas at Austin	Flow and transport in the coastal ocean are described by coupled hydrodynamic systems describing currents, water levels, waves and atmosphere-ocean coupling. In addition, ocean circulation models can be used to drive transport models of, e.g., hydrocarbons in the coastal environment. In this talk, we will describe a discontinuous Galerkin framework for solving coupled systems arising in coastal ocean applications. DG methods have proven to be accurate at modeling coastal ocean physics, we will also discuss local time stepping methods aimed at improving the efficiency of DG methods.
View details	March 28	Jean-Luc Thiffeault University of Wisconsin-Madison	As fish, micro-organisms, or other bodies move through a fluid, they stir their surroundings. This can be beneficial to some fish, since the plankton they eat depends on a well-stirred medium to feed on nutrients. Bacterial colonies also stir their environment, and this is even more crucial for them since at small scales there is no turbulence to help mixing. It has even been suggested that the total biomass in the ocean makes a significant contribution to large-scale vertical transport, but this is still a contentious issue. We propose a simple model of the stirring action of moving bodies through both inviscid and viscous fluids. An attempt will be made to explain existing data on the displacements of small particles, which exhibits probability densities with exponential tails. A large-deviation approach helps to explain some of the data, but mysteries remain. This is joint work with Steve Childress, George Lin, and Peter Mueller.
View details	April 4	Lisa Fauci Tulane University	Locomotion due to body undulations is observed across the entire spectrum of swimming organisms, from microorganisms to fish. The internal force generating mechanisms range from the action of dynein molecular motors within a mammalian sperm to muscle activation in lamprey. We will present recent progress in building multiscale computational models that couple biochemistry, passive elastic properties and active force generation with a surrounding fluid for these two swimmers.
View details	April 11	Mark Andrea de Cataldo State University of New York, Stony Brook	In this talk, which is aimed at non-experts, I will introduce two moduli spaces of structures on a compact Riemann surface, relate them via a result called non-abelian Hodge theorem, and then discuss a recently observed and somewhat mysterious symmetry relating their cohomology rings. This is joint work with T. Hausel and L. Migliorini. Fall 2012

Date

Speaker

Talk Information

January 24

Srikanth Iyengar
University of Nebraska, Lincoln

The goal of this talk will be to describe a bridge between the modular representation theory of finite groups and modules over polynomial rings. This has given us new insights and results concerning modular representations, and has also lead to unexpected results in commutative algebra. The talk with be based on joint work with Avramov, Benson, Carlson, Buchweitz, Krause, and Claudia Miller.

View details

January 31

Peter Trapa
University of Utah

Unitary representations of Lie groups appear in many places in mathematics: in harmonic analysis (as generalizations of the sines and cosines appearing in classical Fourier analysis); in number theory (as spaces of modular and automorphic forms); in quantum mechanics (as "quantizations" of classical mechanical systems); and in many other places. They have been the subject of intense study for decades, but their classification has only recently recently emerged. Perhaps surprisingly, the classification has inspired connections with interesting geometric objects (equivariant mixed Hodge modules on flag varieties). These connections have made it possible to extend the classification scheme to other related settings. The purpose of this talk is to explain a little bit about the history and motivation behind the study of unitary representations and offer a few hints about the algebraic and geometric ideas which enter into their study. This is based on a recent preprint with Adams, van Leeuwen, and Vogan.

View details

February 7

Sébastien Motsch
Center for Scientific Computation and Mathematical Modeling, University of Maryland

In many biological systems, we observe the emergence of self-organized dynamics (e.g. school of fish, ant colonies, pedestrian traffic). Modeling is an essential tool to better understand their behavior. Based on experimental data, we introduce some recent models which aim to explain such dynamics. Since biological systems can reach up to millions of individuals, we discuss in a second part how we can derive “macroscopic models” from several microscopic models. In contrast with particle systems in physics, models of self-organized dynamics do not conserve momentum or energy. This lack of conservation requires to introduce new tools to derive and analyze their macroscopic limits.

View details

February 14

Jun Allard
University of California, Davis

Crawling cells, including the white blood cells that patrol your body in search of infections, display several distinct dynamical patterns driven by both biochemistry (diffusion and reactions between chemical species) and mechanics (physical forces between the components inside cells). Our understanding of these spatiotemporal patterns has been aided by mathematical modeling using techniques including partial differential equations (PDEs). Recently, traveling waves have been observed in the protein actin, which powers certain cells’ ability to crawl. Following experimental observation of one type of crawling cell, the fish epithelial keratocyte, we hypothesized that traveling waves are excitable waves arising from interactions of three components: actin, adhesion sites that attach the cell to its environment, and VASP, a protein that regulates actin. We developed a mathematical model formulated as a system of PDEs with a nonlocal integral term and noise. Numerical solutions lead to a number of predictions, including that VASP also exhibits a traveling wave out of phase with the actin wave, later discovered in further experiments. Our model also reveals a role for tension in the membrane that surrounds the cell, which would otherwise be difficult to observe directly by experiment.

View details

March 7

Clint Dawson
University of Texas at Austin

Flow and transport in the coastal ocean are described by coupled hydrodynamic systems describing currents, water levels, waves and atmosphere-ocean coupling. In addition, ocean circulation models can be used to drive transport models of, e.g., hydrocarbons in the coastal environment. In this talk, we will describe a discontinuous Galerkin framework for solving coupled systems arising in coastal ocean applications. DG methods have proven to be accurate at modeling coastal ocean physics, we will also discuss local time stepping methods aimed at improving the efficiency of DG methods.

View details

March 28

Jean-Luc Thiffeault
University of Wisconsin-Madison

As fish, micro-organisms, or other bodies move through a fluid, they stir their surroundings. This can be beneficial to some fish, since the plankton they eat depends on a well-stirred medium to feed on nutrients. Bacterial colonies also stir their environment, and this is even more crucial for them since at small scales there is no turbulence to help mixing. It has even been suggested that the total biomass in the ocean makes a significant contribution to large-scale vertical transport, but this is still a contentious issue. We propose a simple model of the stirring action of moving bodies through both inviscid and viscous fluids. An attempt will be made to explain existing data on the displacements of small particles, which exhibits probability densities with exponential tails. A large-deviation approach helps to explain some of the data, but mysteries remain. This is joint work with Steve Childress, George Lin, and Peter Mueller.

View details

April 4

Lisa Fauci
Tulane University

Locomotion due to body undulations is observed across the entire spectrum of swimming organisms, from microorganisms to fish. The internal force generating mechanisms range from the action of dynein molecular motors within a mammalian sperm to muscle activation in lamprey. We will present recent progress in building multiscale computational models that couple biochemistry, passive elastic properties and active force generation with a surrounding fluid for these two swimmers.

View details

April 11

Mark Andrea de Cataldo
State University of New York, Stony Brook

In this talk, which is aimed at non-experts, I will introduce two moduli spaces of structures on a compact Riemann surface, relate them via a result called non-abelian Hodge theorem, and then discuss a recently observed and somewhat mysterious symmetry relating their cohomology rings. This is joint work with T. Hausel and L. Migliorini. Fall 2012

Department of Mathematics

College of Science

Spring 2013