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4:00pm to 5:00pm - RH 340N - Geometry and Topology Emil Geisler - (UCLA) TBA |
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4:00pm - TBA - Logic Set Theory Alex Berenstein - (Universidad de los Andes) Group algebras as Banach lattices We will define L_1 Banach lattices and recall some of its model theoretic properties. We will then consider group algebras associated to locally compact groups, where the multiplication is convolution and we will consider them as L_1 Banach lattices. We will show that such expansions carry deep information about the underlying group. For example, when the group is discrete, the group will be definable inside the expansion. In particular, we show, for discrete groups, that if two group algebras are elementary equivalent, then the corresponding groups are elementary equivalent. This is joint work with K. Gannon and S. Song. |
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4:00pm to 5:00pm - RH 340N - Applied and Computational Mathematics Angxiu Ni - (UC Irvine) Differentiating unstable diffusions We derive the path-kernel formula for the linear response, the parameter derivative of averaged observables, of SDEs. Here the parameter controls initial conditions, drift coefficients, and diffusion coefficients. Our formula tempers the unstableness by gradually moving the path-perturbation to hit the probability kernel. It does not assume hyperbolicity but requires (either multiplicative or additive) noise. It extends the path-perturbation formula (or stochastic gradient method), the Bismut-Elworthy-Li formula, and a formula in Malliavin calculus (or likelihood ratio method). Then we derive a pathwise sampling algorithm and demonstrate it on the 40-dimensional Lorenz 96 system with noise. |
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3:00pm to 4:00pm - 510R Rowland Hall - Combinatorics and Probability Felix Clemen - (University of Victoria) TBA |
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2:00pm to 3:00pm - RH 440R - Dynamical Systems David Damanik - (Rice University) Deterministic Delocalization We present joint work with Artur Avila on delocalizing Schr\"odinger operators in arbitrary dimensions via arbitrarily small perturbations of the potential. |