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Events for November 1, 2017 from General and Seminar calendars

Inverse Problems Seminar

Time: 12:00PM - 1:00PM

Location: BLOC 628

Speaker: Dr. Vitaly Katsnelson, Rice University, Applied Math DEpartment

Title: Reconstruction of a piecewise smooth wave speed from exterior measurements

Abstract: We will discuss how to reconstruct a piecewise smooth wave speed inside a domain D with boundary using only measurements taken outside of D; such measurements are akin to having a hyperbolic Neumann-to-Dirichlet map as one's given data. The main obstacle is the internal multiple scattering occurring within D due to the interfaces. We will show how to control and eliminate these internal multiples to eventually reconstruct the location of the interfaces and the wave speed itself. Our methods work for the local inverse problem as well. Numerical simulations will also be presented.

Student Working Seminar in Groups and Dynamics

Time: 1:00PM - 2:00PM

Location: BLOC 628

Speaker: Krzysztof Święcicki

Title: Are L^p and l^p coarse equivalent?

Abstract: I'll give brief overview of isomorphism problem of L^p and l^p in different categories and cover importance of this question in corse setting. Then I'll prove that there's no equivariant corse embedding of L^p into l^p.

Number Theory Seminar

Time: 1:45PM - 2:45PM

Location: BLOC 220

Speaker: John Doyle, Louisiana Tech University

Title: Dynamical modular curves and strong uniform boundedness

Abstract: In an unpublished 1996 preprint, Nguyen and Saito proved the strong uniform boundedness conjecture for torsion points on elliptic curves over function fields by reducing the problem to that of showing that the gonalities of the modular curves Y_1(n) tend to infinity. By studying the geometry of dynamical modular curves, we have recently proven uniform boundedness of preperiodic points for certain interesting families of polynomial maps over function fields. I will discuss this result as well as a consequence for the dynamical uniform boundedness conjecture over number fields, originally posed by Morton and Silverman. This is joint work with Bjorn Poonen.

URL: Link


Noncommutative Geometry Seminar

Time: 2:00PM - 2:50PM

Location: BLOC 628

Speaker: Guoliang Yu, TAMU

Title: Higher eta invariants of elliptic operators and its applications

Abstract: We apply Suleyman Kagan Samurkas' recent result to extend John Lott's higher eta invariants to a more general setting. We prove a higher index theorem for manifolds with boundary using the higher eta invariants. We establish rationality of the higher eta invariants when the Baum-Connes conjecture holds. This is joint work with Zhizhang Xie.

Numerical Analysis Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Natalia Kopteva, University of Limerick, Ireland

Title: Fully computable a posteriori error estimators on anisotropic meshes

Abstract: It is well known that anisotropic meshes offer an efficient way of computing reliable numerical approximations of solutions that exhibit sharp boundary and interior layers. Our goal is to give explicitly and fully computable a posteriori error estimates on reasonably general anisotropic meshes in the energy norm. This goal is achieved by a certain combination of explicit flux reconstruction and flux equilibration. Our approach differs from the previous work, mostly done for shape-regular meshes, in a few ways. The fluxes are equilibrated within a local patch using anisotropic weights depending on the local, possibly anisotropic, mesh geometry. Prior to the flux equilibration, divergence-free corrections are introduced for pairs of anisotropic triangles sharing a short edge. We shall also give an upper bound for the constructed estimator, in which the error constant is independent of the diameters and the aspect ratios of mesh elements, and discuss the efficiency of a posteriori error estimators on anisotropic meshes.

Groups and Dynamics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Volodymyr Nekrashevych, Texas A&M

Title: Etale groupoids, hyperbolic dynamics, and dimension

Abstract: We will discuss etale groupoids associated with hyperbolic dynamical systems, their structure, and applications to group theory and operator algebras. In particular, we will give a simple proof of finitness of their tower dimension (as defined by Kerr) and asymptotic dimension (as defined by Guentner, Willet, and Yu).

Postdoc Colloquium Series

Time: 4:00PM - 5:00PM

Location: Bloc 220

Speaker: Robin Tucker-Drob, TAMU

Title: Treeability and planarity in measured group theory

Abstract: A group G is called strongly treeable if the orbit equivalence relation associated to any free probability measure preserving action of G can be measurably structured by trees. I will discuss joint work with Clinton Conley, Damien Gaboriau, and Andrew Marks in which we show that all groups with planar Cayley graphs are strongly treeable. This provides the first examples of groups with one end which are strongly treeable.

AMUSE

Time: 6:00PM - 7:00PM

Location: BLOC 220

Speaker: Dr. Maurice Rojas, Department of Mathematics, Texas A&M University

Title: Geometry, Sorting, and Optimizing

Abstract: We start with a geometric explanation of why sorting n numbers always takes at least n log n comparisons, up to small constant factor. We'll then see a nice algorithm by Snoeyink for how to find the rectangle with largest area (and axis parallel sides) inside of a polygon. We'll also explain why the last problem is relevant to architectural design.