Events for 12/02/2020 from all calendars

Probability Seminar

Time: 09:00AM - 10:00AM

Location: Zoom

Speaker: Dario Cordero-Erausquin, Université Pierre et Marie Curie (Paris 6)

Title: On Talagrand’s influence inequality (part I)

Abstract: Talagrand's influence inequality (1994) is an asymptotic improvement of the classical $L_2$-Poincaré inequality on the Hamming cube $\{-1,1\}^n$ with numerous applications to Boolean analysis, discrete probability theory and geometric functional analysis. In these talks, we shall discuss various refinements of Talagrand's inequality, including its $L_p$ analogues and Banach space-valued versions. Emphasis will be given to the probabilistic aspects of the proofs. We will also explain a geometric application of these new refinements to the bi-Lipschitz embeddability of a natural family of finite metrics and mention related open problems

Seminar on Banach and Metric Space Geometry

Time: 09:00AM - 09:50AM

Location: online seminar

Speaker: Dario Cordero-Erausquin, Sorbonne Université

Title: On Talagrand’s influence inequality (part I)

Abstract: Talagrand's influence inequality (1994) is an asymptotic improvement of the classical L₂ Poincaré inequality on the Hamming cube {-1,1}ⁿ with numerous applications to Boolean analysis, discrete probability theory and geometric functional analysis. In these talks, we shall discuss various refinements of Talagrand's inequality, including its L_p analogues and Banach space-valued versions. Emphasis will be given to the probabilistic aspects of the proofs. We will also explain a geometric application of these new refinements to the bi-Lipschitz embeddability of a natural family of finite metrics and mention related open problems.

Groups and Dynamics Seminar

Time: 12:00PM - 1:00PM

Location: online

Speaker: Wenhao Wang, Vanderbilt University

Title: Dehn Functions of Finitely Presented Metabelian Groups

Abstract: The Dehn function was introduced by computer scientists Madlener and Otto to describe the complexity of the word problem of a group, and also by Gromov as a geometric invariant of finitely presented groups. In this talk, I will show that the upper bound of the Dehn function of finitely presented metabelian group $G$ is $2^\{n^\{2k\}\}$, where $k$ is the minimal torsion-free rank of abelian group T such that there exists an abelian group $A$ satisfying $G/A \cong T$, answering the question that if the Dehn functions of metabelian groups are uniformly bounded. I will also talk about the relative Dehn function of finitely generated metabelian group and its relation to the Dehn function.

Noncommutative Geometry Seminar

Time: 1:00PM - 2:00PM

Location: Zoom 942810031

Speaker: Sheagan John, Texas A&M University

Title: Pairing of Secondary Higher Invariants and Cyclic Cohomology for Virtually Nilpotent Groups

Abstract: We prove that if G is a virtually nilpotent group, then each delocalized cyclic cocycle on the group algebra has a representative of polynomial growth. For each delocalized cyclic cocyle we thus define a higher analogue of Lott’s delocalized eta invariant and prove its convergence for invertible differential operators. We also use a determinant map construction of Xie and Yu to prove that if G is of polynomial growth then there is a well defined pairing between delocalized cyclic cocyles and K-theory classes of C*-algebraic secondary higher invariants. When this K-theory class is that of a higher rho invariant of an invertible differential operator we show this pairing is precisely the aforementioned higher analogue of Lott’s delocalized eta invariant.

URL: Event link