Events Calendar

October 2009
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Events for October 2009:

21 (Wednesday)	Milton Wing Lecture Series Mathematical Sensors Robert Ghrist, University of Pennsylvania 3:30 pm - 4:30 pm, Dewey 2162 Sensor networks are poised to impact society in fundamental ways analogous to the impact of the networked personal computers. The rapid development of small-scale sensors coupled with wireless ad hoc networking capability foreshadows a day when our physical surroundings will wake up with sensory data, assuming it does not drown in the data first. This lecture will outline how modern mathematical tools -- sums and simplices, holes and homologies, counting and calculus -- all converge to new tools for helping the walls to wake up. Tea will be served at 2:45pm in the Math Dept. Lounge, 9th floor, Hylan Bldg.
	Probability Study Group The fractal dimension of the zero set of Brownian Motion Shannon Starr, U of R 4 pm - 4:50 pm, Hylan 1106A
22 (Thursday)	Milton Wing Lecture Series Euler Calculus For Data Robert Ghrist, University of Pennsylvania 3:30 pm - 4:30 pm, CSB 209 This talk will carefully describe a remarkable integral calculus based on the Euler characteristic. Derived from sheaf theory and combinatorial geometry, this calculus possesses strong applications to sensor networks, communications networks, and signal processing in radar systems. Tea will be served at 2:45pm in the Math Dept. Lounge, 9th floor, Hylan Bldg.
23 (Friday)	Milton Wing Lecture Series Algebraic Topology in the Engineering Sciences Robert Ghrist, University of Pennsylvania 3:30 pm - 4:30 pm, Goergen 108 This talk will discuss existing and emerging applications of algebraic topology. Though often thought to be among the least applicable branches of Mathematics, topology appears to be strangely well-suited for modern challenges in robotics, data analysis, sensing, and communications. Tea will be served at 2:45pm in the Math Dept. Lounge, 9th floor, Hylan Bldg.
29 (Thursday)	Geometry Seminar Gerbes, Objective B-fields and a Hitchin-Kobayashi Correspondence Shuguang Wang, University of Missouri 2 pm - 3 pm, Hylan 1106A The Hitchin-Kobayashi correspondence relates stable bundles to Hermitian-Einstein connections, linking algebraic objects to differential geomeric ones. This corner-stone result proved by Donaldson and Uhlenbeck-Yau has made it possible to compute the polynomial invariants using algebraic geomtery tools. In the current talk, we will state and prove a new correspondence between twisted stable bundles and H-E connections. It is based on recent work about gerbes and objective Chern classes. Tea will be served at 3:00pm in the Math Lounge, Hylan Building, 9th floor.
30 (Friday)	Analysis Seminar Nonlinear Eigenvalue Problems and Generalizations of the Fredholm Alternative Stephen Robinson, Wake Forest University 2 pm - 3 pm, Hylan 1106A Compact symmetric linear operators have a beautiful and well-understood spectral theory with an associated Fredholm Alternative that completely describes the solvability of nonhomogeneous linear problems. The last forty years have witnessed a great deal of effort to generalize these ideas to select nonlinear problems. In this talk I will review some fundamental variational ideas associated with eigenvalue problems, and I will apply those ideas to derive some generalizations of the Fredholm Alternative to nonlinear problems. Tea will be served at 1:30pm in the Math Dept. Lounge, 9th floor Hylan Bldg.
	Probability Seminar Unbounded Positive Solutions of Nonlinear Parabolic Ito Equations Paul Chow, Wayne State 3 pm - 4 pm, Hylan 1106A Nonlinear parabolic Ito equations arise as mathematical models for reaction-diffusion and branching diffusion problems in the presence of noise. In this talk, we consider the initial (boundary) value problems for a class of semilinear stochastic parabolic equations of Ito type in a bounded or unbounded domain. Suppose that the nonlinear term and the multiplier of the noise term are locally Lipschitz continuous. Then there exists a unique local solution in a Sobolev space. First we will discuss the existence question of some positive solutions to such SPDEs. Under suitable conditions, such as stochastic coercivity and positive data, we shall prove that the solution will remain positive almost surely at each time. In addition, it will be shown that, if the nonlinear term is positive, convex and its reciprocal being integrable, and the noise multiplier is of linear growth, the Lp-moment of the solution will blow up in a finite time, for any integer p greater or equal to 1. The theorems are proved by making use of some basic tools in the stochastic analysis and the theory of differential equations. Tea will be served at 2:30pm, in the Math Lounge, Hylan Building, 9th floor.
	Topology Seminar Generalized moment-angle complexes returned Fred Cohen (University of Rochester) 4 pm - 5 pm, Hylan 1106A A subspace of a product space known as 'the generalized moment-angle complex' was first defined in generality by Neil Strickland extending constructions of Davis-Januskiewicz, Buchstaber-Panov-Ray, and Goresky-MacPherson. Definitions, examples, as well as connections to other topics will be addressed. One notable case is given by subspaces of products of infinite dimensional complex projective space 'indexed by a finite simplicial complex'. These spaces encode features ranging from the structure of toric varieties in one guise, Stanley-Reisner rings of simplicial complexes, as well as 'motions of certain types of robotic legs' in other guises. What do these spaces have to do with the motions of legs of a cockroach ? This feature will be illustrated with 'before' and 'after' slides. Features of these spaces such as their cohomology as well as stable structure are developed within the context of classical homotopy theory based on joint work with A. Bahri, M. Bendersky, and S. Gitler. Applications to the motion of legs of a cockroach are based on joint work with G. Haynes and D. Koditschek.