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Events for February 16, 2018 from General and Seminar calendars

Newton-Okounkov Bodies

Time: 1:00PM - 2:30PM

Location: BLOC 624

Speaker: Frank Sottile, Texas A&M University

Title: Mixed volumes and an extension of intersection theory of divisors

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 628

Speaker: Alex Kunin, Penn State University

Title: Hyperplane neural codes and the polar complex

Abstract: This talk concerns combinatorial and algebraic questions arising from neuroscience. Combinatorial codes arise in a neuroscience setting as sets of co-firing neurons in a population; abstractly, they record intersection patterns of sets in a cover of a space. Hyperplane codes are a class of combinatorial codes that arise as the output of a one layer feed-forward neural network, such as Perceptron. Here we establish several natural properties of non-degenerate hyperplane codes, in terms of the {\it polar complex} of the code, a simplicial complex associated to any combinatorial code. We prove that the polar complex of a non-degenerate hyperplane code is shellable. Moreover, we show that all currently known properties of hyperplane codes follow from the shellability of the appropriate polar complex. Lastly, we connect this to previous work by examining some algebraic properties of the Stanley-Reisner ideal associated to the polar complex. This is joint work with Vladimir Itskov and Zvi Rosen.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Sara Maloni, University of Virginia

Title: The geometry of quasi-Hitchin symplectic Anosov representations

Abstract: In this talk we will focus on our joint work in progress with Daniele Alessandrini and Anna Wienhard about quasi-Hitchin representations in Sp(4,C), which are deformations of Fuchsian representations which remain Anosov. These representations acts on the space Lag(C^4) of complex lagrangian subspaces of C^4. We will show that the quotient of the domain of discontinuity for this action is a fiber bundle over the surface and we will describe the fiber. In particular, we will describe how the projection map comes from an interesting parametrization of Lag(C^4) as the space of regular ideal hyperbolic tetrahedra and their degenerations.