Speaker: Duncan McElfresh and Graham Antoszewski (University of Maryland, AMSC) -

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Speaker: Danny Kaufman (UMD) -

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Speaker: Amin Gholampour (University of Maryland) - https://www.math.umd.edu/~amingh/

Abstract: We discuss situations in which the degeneracy locus of a map of vector bundles carries a natural perfect obstruction theory whose virtual cycle can be calculated by the Thom-Porteous formula. This generalizes the well-known case of the zero locus of a section of a vector bundle.

We apply this to nested Hilbert schemes of points and curves on surfaces. The resulting virtual cycles agree with the ones coming from Vafa-Witten theory and the reduced localized local Donaldson-Thomas theory of surfaces. This enables us to express some of these invariants in terms of Carlsson-Okounkov operators.

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Speaker: Martin Molina (University of Maryland) -

Abstract: http://www.terpconnect.umd.edu/~lvrmr/2017-2018-F/Classes/RIT.shtml

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Speaker: Tarik Aougab https://sites.google.com/a/brown.edu/tarikaougab/home

Abstract: For S a closed orientable surface, let N(k,S) denote the number of mapping class group orbits of closed curves with at most k self-intersections. We give upper and lower bounds on N(k,S) that both grow exponentially in the square root of k. There are three major ingredients: statistical work of Lalley describing the behavior of a "typical" geodesic on a hyperbolic surface; the geometry of Thurston's Lipschitz metric on Teichmuller space and the corresponding mapping class group action; and circle packings in hyperbolic geometry. This represents joint work with Juan Souto.

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Speaker: Guowei Sun (UMCP) -

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Speaker: Spencer Breiner (National Institute of Standards and Technology) -

Abstract: In this talk I will discuss some additional aspects of Coecke & Kissinger's diagrammatic language for quantum processes. I will begin with a brief review of string diagrams and quantum ("doubled") processes. I will introduce Frobenius algebras together with their diagrammatic analogues, called spiders. These can be used to encode orthonormal bases, providing a means for describing measurement and encoding. This allows us to incorporate both quantum and classical data, as well as their interaction, into the diagrammatic formalism.

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Speaker: Allen Gehret (UCLA) -

Abstract: I will discuss various things we know about distal and non-distal ordered abelian groups. This is joint work with Matthias Aschenbrenner and Artem Chernikov.

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