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Texas A&M University

Events for 10/14/2020 from all calendars

Geometry Seminar

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Time: 11:00AM - 12:00PM

Location: zoom

Speaker: Markus Blaeser

Title: Irreversibility of tensors of minimal border rank and barriers for fast matrix multiplication

Abstract: Determining the asymptotic algebraic complexity of matrix multiplication is a central problem in algebraic complexity theory. The best upper bounds on the so-called exponent of matrix multiplication if obtained by starting with an "efficient" tensor, taking a high power and degenerating a matrix multiplication out of it. In the recent years, several so-called barrier results have been established. A barrier result shows a lower bound on the best upper bound for the exponent of matrix multiplication that can be obtained by a certain restriction starting with a certain tensor. We prove the following barrier over the complex numbers: Starting with a tensor of minimal border rank satisfying a certain genericity condition, except for the diagonal tensor, it is impossible to prove ω = 2 using arbitrary restrictions. This is astonishing since the tensors of minimal border rank look like the most natural candidates for designing fast matrix multiplication algorithms. We prove this by showing that all of these tensors are irreversible, using a structural characterisation of these tensors. Joint work with Vladimir Lysikov.

Noncommutative Geometry Seminar

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Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Paolo Piazza, Università di Roma La Sapienza

Title: Higher genera and C*-indices on G-proper manifolds

Abstract: Higher general for a G-proper manifold without boundary can be defined in analogy with Galois coverings and they are, by definition, geometric objects. To understand their stability properties we need to connect them to higher C^*-indices of suitable Dirac operators. This is possible but under additional assumptions on the group G, for example G semisimple and connected and more generally G satisfying the Rapid Decay condition and G/K of nonpositive sectional curvature. I will begin my talk by explaining these results. I will then move to manifolds with boundary and explain how it is possible to define higher genera in this more complicated situation. Crucial to the analysis is a higher C^*-index theorem of Atiyah-Patodi-Singer type. All these results, the last very recent, are in collaboration with Hessel Posthuma.

URL: Event link

Probability Seminar

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Time: 2:30PM - 3:00PM

Location: Zoom

Speaker: Galyna Livshyts, Georgia Tech

Title: On the Brunn-Minkowski type and isoperimetric-type inequalities for probability measures under symmetry

Abstract: We shall discuss Brunn-Minkowski type inequalities for probability measures. We provide a sharp lower estimate for the so-called concavity exponent of a symmetric convex set, and show that round k-cylinders (direct products of balls and subspaces of lower dimension) are the only equality cases in this inequality. This relies on the equality case characterization in the Brascamp-Lieb inequality for restrictions of Gaussian measure to smooth convex sets, as well as on various aspects of Gaussian energy minimization. We further provide explicit non-sharp lower bounds for the exponent in the Gaussian Brunn-Minkowski inequality for symmetric convex sets whose measure is explicitly lower-bounded from below, with applications to isoperimetric-type inequalities. Lastly, we discuss Brunn-Minkowski-type inequalities for symmetric convex sets with respect to other probability measures, and obtain several estimates, some of which rely on estimates for poincare constants of restrictions of isotropic log-concave measures to symmetric convex sets.

Topology Seminar

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Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Shaoyun Bai, Princeton University

Title: Equivariant Cerf theory and SU(n) Casson invariants

Abstract: I will present joint work with Boyu Zhang on defining perturbative SU(n)-Casson invariant for integer homology 3-spheres. Ideas from the studies of J-holomorphic curves in symplectic manifolds play important roles in the construction, in particular issues related to equivariant transversalities. Time permitting, I will discuss about possible generalizations and topological applications. Video recording available at (Access Password: u5d2W?mS)