Wednesday, December 6, 2023
Time | Items |
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All day |
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10am |
12/06/2023 - 10:30am Abstract: Given a proper CY A-infinity category C, a notion closely related to that of a 2d extended TQFT, I explain how the Loday-Quillen-Tsygan map fits into a commutative diagram of dg-BV algebras. The first two corners are built from the cyclic cohomology of C, respectively from a cyclic L-infinity algebra associated to C. The other two corners are of a more geometric nature, given by chains on the moduli space of Riemann surfaces with corners, free boundaries decorated by objects of C, respectively chains on the moduli space of metric graphs. I indicate how this generalizes an observation by Kontsevich producing cocycles on M_g,n. Further I compare this to the story of closed SFT developed by Costello, Caldararu-Tu, which led to the definition of categorical Gromov-Witten invariants for categories C as above that are also smooth. Location:
KT 801
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3pm |
12/06/2023 - 3:00pm Integrating the data from large numbers of neurons responding to an ensemble of stimuli in behaving animals is one of the key challenges facing computational neuroscience. We introduce neural encoding manifolds, a construct in which each point is a neuron and nearby neurons respond similarly in time to similar stimuli. The advantages of this unsupervised machine learning approach will be demonstrated in two very different neural systems. First, in the mouse, naturalistic stimuli drove both the retina and visual cortex. Encoding manifolds were developed for each, and trajectories across the manifold reveal how stimulus selectivity is organized differently in these two populations. Surprisingly, convolutional neural networks are even more topologically extreme. Second, when applied to the nematode C. elegans, our encoding manifold organizes neurons into neighborhoods that relate to specific functional roles. These inform whether the available anatomical connectomes are sufficient to explain behavior, and suggest direct combinations of neurons that could comprise behavioral modules. Location:
LOM 214
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4pm |
12/06/2023 - 4:00pm I will describe some recent results on the first order rigidity of homeomorphism groups of compact manifolds, and their applications to dynamics of group actions on manifolds. I will also describe how to find “syntactic” invariants of manifolds, and how these can be used to give a conjectural model-theoretic characterization of the genus of a surface.
Location:
KT 219
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