MenuEvents for 10/22/2018 from all calendars
Postdoc Lunch Time Talks
Time: 12:00PM - 12:20PM
Location: BLOC 220
Speaker: Li Gao, Texas A&M University
Description:
Title: Logarithmic Sobolev inequalities for matrices and matrix-valued functions.
Abstract: Logarithmic Sobolev inequality is a powerful functional tool to derive the convergence properties of a Markov semigroup and also isoperimetric inequaliies and concentration inequalities. I will discuss log-Sobolev inequalities for matrices and matrix-valued functions that are stable under tensorization.
Postdoc Lunch Time Talks
Time: 12:35PM - 12:55PM
Location: BLOC 220
Speaker: Shuhui Shi, Texas A&M University
Description:
Title: Multiple zeta values over F_q[t]
Abstract: In this talk, I will introduce some analogies among the objects of study in number theory and function fields related to the multiple zeta values and explain the motivation of why we are interested in these values. Then I will talk about some related results I have worked in my thesis.
Postdoc Lunch Time Talks
Time: 12:55PM - 1:15PM
Location: BLOC 220
Speaker: Diane Guignard, Texas A&M University
Description:
Title: Approximation of parametric PDEs
Abstract:
Number Theory Seminar
Time: 3:00PM - 4:00PM
Location: BLOC 220
Speaker: Changningphaabi Namoijam, Texas A&M University
Title: Hyperderivatives of periods and quasi-periods of t-modules
Abstract: Brownawell and Denis constructed, as extensions of Drinfeld modules by additive groups, divided derivatives of a Drinfeld module whose periods can be expressed in terms of hyperderivatives of the periods and quasi-periods of the given Drinfeld module. In this talk, we discuss how to obtain hyperderivatives of periods and quasi-periods of an abelian Anderson t-module as periods and quasi-periods of the t-module given by the minimal quasi-periodic extension of Maurischat's prolongation t-module of the given t-module. We also determine how periods, quasi periods, logarithms and quasi-logarithms of an abelian Anderson t-module appear as evaluations of solutions of Frobenius difference equations. This is joint work with Matt Papanikolas.
URL: Event link
Douglas Lectures
Time: 4:00PM - 5:00PM
Location: Blocker 117
Speaker: Stefanie Petermichl, University of Toulouse
Title: A workout program using weights: I
Abstract: The Hilbert transform is a singular integral operator that gives access to harmonic conjugate functions via a convolution of boundary values. This operator is trivially a bounded linear operator in the space of square integrable functions. This is no longer obvious if we introduce a positive weight with respect to which we integrate the square. In this case, conditions on the weight need to be imposed, the so-called characteristic of the weight, both necessary and sufficient for boundedness. It is a delicate question to find the exact way in which the operator norm grows with this characteristic. Interest was spiked by a classical question surrounding quasiconformality and the Beltrame equation. Through an optimal weighted estimate of the Beurling-Ahlfors operator, the sibling of the Hilbert transform, a deep borderline regularity result of the Beltrami equation was solved. We give a historic perspective of the developments in this area of weights that spans about twenty years and that has changed our understanding of these important classical operators. We will see that the Hilbert transform is an average of dyadic shift operators. These can be seen as a coefficient shift and multiplier in a Haar wavelet expansion or as a time shifted operator on simple martingale differences. Such connections between martingale transforms and operators similar to the Hilbert transform had been understood for some time. It allows us to develop powerful tools with a probabilistic flavour to obtain deep results central to harmonic analysis. The central conjecture in sharp weighted theory was on the norm of the Hilbert transform. Its first solution involved the precise model of the dyadic shift. Since then, weighted theory evolved through many outstanding contributions, giving deep insight into the nature of such singular operators via so-called sparse domination. We highlight a probabilistic and geometric perspective on these new ideas, giving dimensionless estimates of Riesz transforms on Riemannian manifolds wi
