Department of

Mathematics

Seminar Calendar
for events the day of Tuesday, December 17, 2019.

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Tuesday, December 17, 2019

11:15 am in 245 Altgeld Hall,Tuesday, December 17, 2019

Log-concave polynomials, matroids, and expanders

Cynthia Vinzant   [email] (North Carolina State University)

Abstract: Complete log-concavity is a functional property of real multivariate polynomials that translates to strong and useful conditions on its coefficients. I will introduce the class of completely log-concave polynomials in elementary terms, discuss the beautiful real and combinatorial geometry underlying these polynomials, and describe applications to random walks on faces of simplicial complexes. Consequences include proofs of Mason's conjecture that the sequence of numbers of independent sets is ultra log-concave and the Mihail-Vazirani conjecture that the basis exchange graph of a matroid has expansion at least one. This is based on joint work with Nima Anari, Kuikui Liu, and Shayan Oveis Gharan.

12:20 pm in 341 Altgeld Hall,Tuesday, December 17, 2019

On strongly norm attaining Lipschitz maps

Luis Garcia Lirola (Kent State University)

Abstract: In this talk, we focus on the set SNA(M, Y) of those Lipschitz maps from a complete metric space M to a Banach space Y which strongly attain their Lipschitz norm (i.e. the supremum defining the Lipschitz norm is a maximum). We prove that this set is not norm-dense when M is a length space, when M is a closed subset of R with positive Lebesgue measure, and when M is the unit circle. This provides new examples which have very different topological properties than the previously known ones. In addition, we study the linear properties which are sufficient to get Lindenstrauss property A for the Lipschitz-free space over M, and show that all of them actually provide the norm-density of SNA(M, Y). This is part of a joint work with B. Cascales, R. Chiclana, M. Martín and A. Rueda Zoca.