Math Department Events Listing

The agenda will include: Hiring, The Advisory Board and Announcements.

Interactive Internet-Based programs can change the way we do mathematics, the way we present it, and, most of all, the way we teach our courses. Presentation graphics make it possible to visualize and manipulate geometric objects in the plane, in three-space, and beyond. Communication programs can enable students to share their investigations with instructors and with classmates. This talk will explore programs for multivariable calculus and differential geometry and topology developed in collaboration with undergraduate students.

The purpose of this talk is to introduce the basic theory of quasiconformal mappings, generalizations of conformal mappings, and give a tasting of their use. The topics include the measurable Riemann mapping theorem, an extension of the Riemann mapping theorem, Teichmuller's theorem about the relation of their extremal properties and analytic functions, and examples of their use in the study of elliptic partial differential equations.

The notion of age of elements of complex linear groups was introduced by M. Reid and is of importance in algebraic geometry, in particular in the study of crepant resolutions and of quotients of Calabi-Yau varieties. In this talk, we'll describe our solution of a problem raised by J. Koll\'ar and M. Larsen on the structure of finite irreducible linear groups generated by elements of age at most 1. More generally, we bound the dimension of finite irreducible linear groups generated by elements of bounded deviation. As a consequence of our main results, we derive some properties of symmetric spaces GU_{d}(C)/G having shortest closed geodesics of bounded length, and of quotients C^{d}/G having a crepant resolution. This is joint work with R. M. Guralnick.

The stochastic differential equation, dx_t = b(x_t) + σ(x_t) dW_t, describing the motion of a particle diffusing in a medium with a variable diffusion coefficient, has a family of different interpretations, indexed by a parameter a. a = 0 is the Itō interpretation, while a = 1/2 is that of Stratonovitch. They lead to measurable (in a lab, not only by Lebesgue) differences. I will talk about a joint work with experimental physicists. We now know which value of a is correct! And we begin to understand why. Come and see!

I will only assume that you have heard something about stochastic differential equations. My previous talk in NOT a prerequisite. There will be open problems.

Simulation and modeling of fluid flow through porous media are fundamental to numerous fields of study, including chemical and petroleum engineering, hydrology, micro-fluidics, biological transport, textile science, filtration science, and solidification science. The tensor permeability provides the relationship between the pressure gradient and flow rate in these systems, and is crucial to the accurate simulation of many phenomena. While the numerical solution of Stokess equations on an ensemble of randomly generated microstructures agrees with theoretical and observed results, the stochastic properties of the permeability tensor illustrate the shortcomings of models that incorporate a deterministic model of permeability.

In the Analysis of shape, the equivalence class of geometrical objects modulo, say, the group of similarities are modelled as elements of a shape space which usually comes with a canonical non-Euclidean Riemannian structure. E.g. filtering out size naturally leads to a sphere, filtering out rotation adds additional curvature possibly creating singularities in the shape space. While over the last decades statisticians have used Euclidean approximations to these spaces thus making tools of classical multivariate analysis available for ``sufficiently concentrated data'', we aim at intrinsic generalizations of PCA and MANOVA.

Have you ever desperately needed to sample a probability distribution too complicated or ugly to have been built into MATLAB, but didnt know how?In such situations, Monte Carlo Markov Chains (MCMC) are your Swiss Army Knife.In this Brown Bag talk, I will present some background on MCMC sampling methods to elucidate why they work, and provide some practical knowledge for wielding them as well.Ill demonstrate some of the basic techniques in the ever-popular application of dating models.

Titan exhibits ample surface and crustal processes including lakes and seas, fluvial erosive features, possibly subsurface reservoirs of liquid, and rainfall. Together these constitute strong evidence for a multicomposition hydrological system, composed mostly of methane and ethane as well as trace amounts of other alkanes. Estimates of the volume of liquid methane required in streams and rainfall to produce erosional features suggest that these could be relatively recent phenomena, perhaps periodically renewed as the overall climate cycles between dry and wet periods. The end state of the longer term chemical processing of methane in the upper atmosphere is expressed on the surface in the form of deposits of solid organics organized into dunes, and lighter hydrocarbons such as ethane (in the lakes), acetylene, and other hydrocarbons and nitriles.

When we move a curve away from itself in the plane we expect an even number of intersections with the original, whether the curve is smooth or polygonal. The same question for a surface in four-space leads to Whitney's definition of the Normal Euler Class, both for smooth and polyhedral objects. An intermediate question asks about curves on a surface in three-space and its perturbations either in the surface or away from the surface. We will show some new results for this questions and for polyhedra in four-space, related to work of Gromov, Lawson, and Thurston.