One such class of manifolds thought to have promise was 4-manifolds with effective circle actions, but the extra structure given by such manifolds turned out to be insufficient for calculating Donaldson invariants. Scott Baldridge, Louisiana State University Seiberg-Witten invariants of 4-manifolds with circle actions, with applications to symplectic topology.Įver since the introduction of Donaldson invariants in the early 1980's, efforts to calculate diffeomorphism invariants of 4-manifolds centered upon large classes of smooth manifolds that have some additional structure. Refreshments at 2:00 in the Keisler Lounge.Ĭolloquium Questions or comments? 3:30 pm - 4:30 pm 285 Lockett We describe such models where an unknown scenery is explored by a hidden random walk, and discuss when reconstruction of this underlying scenery is possible. (Joint work with Khoshnevisan and Mendez.) Hidden Markov chains are widely applicable probabilistic models: a noisy function of an underlying stochastic process is seen, while the process itself is unobserved. We discuss the existence of times where atypical random walk behavior is seen, and give connections to the Ornstein-Uhlenbeck process on Wiener space. Dynamical random walks are easily constructed "coin tossing" analogues of infinite dimensional diffusions.
I will survey some of my work relating to random walks: dynamical random walks and reconstruction of sceneries visited by a random walk. LEQSF(2002-04)-ENH-TR-13Ĭolloquium Questions or comments? 2:30 pm - 3:30 pm 285 Lockettĭavid Levin, University of Utah Modern Topics in Random Walks Visit supported by Visiting Experts Program in Mathematics, Louisianaīoard of Regents. To illustrate the motivations for studying such approximation results, I will briefly discuss some quick applications of the result to various stability and uniform stability properties. In this talk, I will discuss a complementary result which says that the approximation can be carried out over non-compact or infinite intervals provided one does not insist on the same initial values. The fundamental Filippov-Ważewski Relaxation Theorem states that the solution set of an initial value problem for a locally Lipschitz differential inclusion is dense in the solution set of the same initial value problem for the corresponding relaxation inclusion on compact intervals. Yuan Wang, Florida Atlantic University A Relaxation Theorem for Differential Inclusions with Applications to Stability Properties Control and Optimization Seminar Questions or comments? 2:30 pm 240 Lockett Hall
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