Events for 09/11/2015 from all calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: Dean Baskin, Texas A&M University

Title: Asymptotics of scalar waves on asymptotically Minkowski spaces

Abstract: In this talk I will describe an asymptotic expansion for solutions of the wave equation on long-range asymptotically Minkowski spacetimes. The exponents seen in the expansion are related to the resonances of an asymptotically hyperbolic problem at timeline infinity. If time permits, I will describe the proof, which also simplifies the short-range setting. This is joint work with Andras Vasy and Jared Wunsch.

Algebra and Combinatorics Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Frank Sottile, Texas A&M University

Title: Murnaghan-Nakayama Rules in Schubert Calculus

Abstract: The Murnaghan-Nakayama rule expresses the product of a Schur function with a Newton power sum in the basis of Schur functions. As the power sums generate the algebra of symmetric functions, the Murnaghan-Nakayama rule is as fundamental as the Pieri rule. Interesting, the resulting formulas from the Murnaghan-Nakayama rule are significantly more compact than those from the Pieri formula. In geometry, a Murnaghan-Nakayama formula computes the intersection of Schubert cycles with tautological classes coming from the Chern character. In this talk, I will discuss some background, and then some recent work with Andrew Morrison establishing Murnaghan-Nakayama rules for Schubert polynomials and for the quantum cohomology of the Grassmannian. The results I discuss are contained in the preprint arXiv:1507.06569.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 117

Speaker: Michael DiPasquale

Title: Regularity of Planar Splines

Abstract: The algebra of piecewise polynomial functions (splines) of smoothness r on a subdivision by convex polytopes in an n-dimensional real vector space is of fundamental interest in approximation theory and numerical analysis. In the late 1980s, Billera pioneered the use of tools from commutative and homological algebra in the study of splines. Using this approach, Mcdonald and Schenck provided a formula for the dimension of the vector space of splines of smoothness r and degree at most r over a planar polyhedral subdivision, when d is large enough. In this talk we present an answer to how large d needs to be in order for this formula to hold. The tool we use is the Castelnuovo-Mumford regularity of the algebra of planar splines. No knowledge of spline theory will be assumed.

Linear Analysis Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 220

Speaker: Kun Wang, Texas A&M University

Title: On Invariants of C*-algebras with the ideal property

Abstract: Early in 1991, George Elliott proved that for simple AI algebras, the pair of functors (K₀,T) is a complete isomorphic invariant. After that, successful classification results have been obtained for the AH algebras (which is more general) with slow dimension growth for cases of real rank zero and simple. The ideal property (each closed two-sided nontrivial ideal is generated by the projections inside the ideal) unifies and generalizes the above two cases. In my talk, I will show some classification results by using the Elliott Invariant (for some simple and real rank zero classes of C*-algebras) and Stevens' Invariant (for some classes with the ideal property). Then I will show that these two invariants are equivalent when we consider the C*-algebra with the ideal property.