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Texas A&M University
Mathematics

Events for 10/06/2021 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

iCal  iCal

Time: 10:00AM - 11:00AM

Location: Zoom

Speaker: Ivan Veselic, Dortmund (Germany)

Title: Scale free unique continuation estimates and applications for periodic and random operators

Abstract: With Ivica Nakic, Matthias Taeufer and Martin Tautenhahn we established a quantitative unique continuation estimate for spectral projectors of Schroedinger operators. It compares the L^2 norm of a function in a spectral subspace associated to a bounded energy interval to the L^2 norm on an equidistributed set. These estimates allow to give quantitative two-sided bounds on the lifting of edges of bands of essential spectrum, as well as on discrete eigenvalues between two such bands. It also allows to deduce Anderson localization in regimes where this was not possible before. For instance, Albrecht Seelmann and Matthias Taeufer showed that Anderson localization occurs at random perturbations of band edges of periodic potentials, whether the edges exhibit regular Floquet eigenvalue minima or not.


Inverse Problems and Machine Learning

iCal  iCal

Time: 12:40PM - 1:40PM

Location: Zoom

Speaker: Sergio Brenner Miguel, Universität Heidelberg

Title: Multiplicative Deconvolution in nonparametric estimations

Abstract: In this talk we are interested in the estimation of an unknown density f with support on the positive real line based on an i.i.d. sample with multiplicative measurement errors. Using the rich theory of Mellin transform we identify and study the underlying inverse problem. The proposed fully-data driven procedure is based on the estimation of the Mellin transform of the density f, a regularisation of the inverse of the Mellin transform by a spectral cut-off and a data-driven model selection in order to deal with the upcoming bias-variance trade-off. We introduce and discuss further the Mellin-Sobolev spaces which characterize the regularity of the unknown density f through the decay of its Mellin transform. Additionally we show minimax-optimality over Mellin-Sobolev spaces of the data-driven density estimator and hence its adaptivity.

URL: Event link


Noncommutative Geometry Seminar

iCal  iCal

Time: 2:00PM - 3:00PM

Location: Zoom

Speaker: Jesus Sanchez Jr, Penn State

Title: The Geometry of Mehler's Kernel

Abstract: Mehler's Kernel made its first appearance in Index Theory through the work of Ezra Getzler in his computation of the index of a Dirac Operator. The appearance of Mehler's Kernel in this approach is through the introduction of a symbol calculus which refines the usual symbol calculus of differential operators and smoothing operators. In a different approach to computing the index of a Dirac Operator, Nicole Berline and Michele Vergne study heat flow on the principal Spin bundle and show that the corresponding Index density arises naturally by studying the local geometry in this setting. What we will show is that we can extend the insight of Berline and Vergne to fully recover Mehler's Kernel and give geometric insight into the curvature terms appearing within the kernel. This will give a more unified treatment of these two seemingly different proofs of the local index theorem for Dirac Operators.


Groups and Dynamics Seminar

iCal  iCal

Time: 3:00PM - 4:00PM

Location: online

Speaker: Frank Wagner, UC Riverside

Title: Torsion Subgroups of Groups with Quadratic Dehn Function

Abstract: The Dehn function of a finitely presented group is a useful invariant closely related to the solvability of the group's word problem. It is well-known that a finitely presented group is word hyperbolic if and only if it has sub-quadratic (and thus linear) Dehn function. A result of Ghys and de la Harpe states that no hyperbolic group can contain a (finitely generated) infinite torsion subgroup. We show that this property does not carry over to classes of groups of larger Dehn function. In particular, for every m>1 and n sufficiently large (and either odd or divisible by 2^9), there exists a quasi-isometric embedding of the infinite free Burnside group B(m,n) into a finitely presented group with quadratic Dehn function.


Topology Seminar

iCal  iCal

Time: 4:00PM - 5:00PM

Location: Zoom

Speaker: Shu Shen, Sorbonne University

Title: The Fried conjecture for admissible twists

Abstract: The relation between the spectrum of the Laplacian and the closed geodesics on a closed Riemannian manifold is one of the central themes in differential geometry. Fried conjectured that the analytic torsion, which is an alternating product of regularized determinants of the Laplacians, equals the zero value of the dynamical zeta function. In this talk, I will show the Fried conjecture on locally symmetric spaces twisted by an acyclic flat vector bundle obtained by the restriction of a representation of the underlying Lie group. This generalises the results of myself for unitary twists, and the results of Brocker, Muller, and Wotzker on closed hyperbolic manifolds.