Events for 04/29/2022 from all calendars

Noncommutative Geometry Seminar

Time: 08:00AM - 09:00AM

Location: ZOOM

Speaker: Christian Bär

Title: Boundary value problems for Dirac operators

Abstract: This introduction to boundary value problems for Dirac operators will not focus on analytic technicalities but rather provide a working knowledge to anyone who wants to apply the theory, i.e. in the study of positive scalar curvature. We will systematically study "elliptic boundary conditions" and discuss the following topics: * typical examples of such boundary conditions * regularity of the solutions up to the boundary * Fredholm property and index computation * geometric applications

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Noncommutative Geometry Seminar

Time: 09:15AM - 10:15AM

Location: ZOOM

Speaker: Simone Cecchini

Title: Distance estimates in the spin setting and the positive mass theorem

Abstract: The positive mass theorem states that a complete asymptotically Euclidean manifold of nonnegative scalar curvature has nonnegative ADM mass. It relates quantities that are defined using geometric information localized in the Euclidean ends (the ADM mass) with global geometric information on the ambient manifold (the nonnegativity of the scalar curvature). It is natural to ask whether the positive mass theorem can be ``localized’’, that is, whether the nonnegativity of the ADM mass of a single asymptotically Euclidean end can be deduced by the nonnegativity of the scalar curvature in a suitable neighborhood of E. I will present the following localized version of the positive mass theorem in the spin setting. Let E be an asymptotically Euclidean end in a connected Riemannian spin manifold (M,g). If E has negative ADM-mass, then there exists a constant R > 0, depending only on the geometry of E, such that M must either become incomplete or have a point of negative scalar curvature in the R-neighborhood around E in M. This gives a quantitative answer, for spin manifolds, to Schoen and Yau's question on the positive mass theorem with arbitrary ends. Similar results have recently been obtained by Lesourd, Unger, and Yau without the spin condition in dimensions <8 assuming Schwarzschild asymptotics on the end E. I will also present explicit quantitative distance estimates in case the scalar curvature is uniformly positive in some region of the chosen end E. The bounds obtained are reminiscent of Gromov's metric inequalities with scalar curvature. This is joint work with Rudolf Zeidler.

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Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 302

Speaker: Luther Rinehart, TAMU

Title: Uniform acceleration radiation with a Proca field

Abstract: I will present results of a study of radiation from a uniformly accelerating particle coupled to a Proca field. The fact that a Proca field allows non-conservation of charge facilitates the use of regularizations where the charge changes in time. Using several classical methods, I obtain expressions for the field, and expressions for the rate of emitted energy and particle number. I also obtain general expressions for the quantity of radiation when the charge is an arbitrary function of time, both when the charge is at rest, and when it is uniformly accelerating.

Noncommutative Geometry Seminar

Time: 2:00PM - 3:00PM

Location: ZOOM

Speaker: Anna Marie Bohmann, Vanderbilt

Title: Assembly in the Algebraic K-theory of Lawvere Theories

Abstract: Lawvere’s algebraic theories are an elegant and flexible way of encoding algebraic structures, ranging from group actions on sets to modules over rings and beyond. We discuss a construction of the algebraic K-theory of such theories that generalizes the algebraic K-theory of a ring and show that this construction allows us to build Loday assembly-style maps. This is joint work with Markus Szymik.

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