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Events for September 15, 2017 from General and Seminar calendars

Mathematical Physics and Harmonic Analysis Seminar

Time: 1:50PM - 2:50PM

Location: BLOC 628

Speaker: In-Jee Jeong, Princeton University

Title: Evolution of singular vortex patches

Abstract: A vortex patch is a solution to the 2D Euler equations whose vorticity is given by the characteristic function of a domain in the plane which evolves in time. In the 90s it was shown by Chemin, Bertozzi-Constantin, and Serfati that if the boundary of the domain is initially smooth (at least C^{1,\alpha} for \alpha > 0), then this smoothness propagates for all time. Much less is known for patches supported on domains with not so smooth boundaries, for example when the domain is initially a polygon. In this work, we show global well-posedness for vortex patches with corners when there is a certain rotational symmetry. We also prove some ill-posedness results in the absense of symmetries. This is joint work with Tarek M. Elgindi.

Algebra and Combinatorics Seminar

Time: 3:00PM - 3:50PM

Location: BLOC 117

Speaker: Michael Anshelevich, Texas A&M University

Title: Product formulas on posets and Wick products.

Abstract: We will construct "incomplete" version of several familiar posets, and prove a product formula on posets. Then we will apply these results to the study of Wick products corresponding to the Charlier, free Charlier, and Laguerre polynomials. For the fourth and perhaps most interesting example of Wick products, I do not know the appropriate poset structure. However their inversion and product formulas can still be obtained by less conceptual techniques. As a consequence, we obtain the formula for the linearization coefficients of the free Meixner polynomials.

Geometry Seminar

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Souvik Goswami, TAMU

Title: Higher arithmetic Chow groups

Abstract: For a regular scheme, which is flat and quasi-projective over an arithmetic ring (typically the ring of integers of a number field), Gillet and Soul ́e defined an arithmetic version of the usual Chow groups, taking into account the complex embeddings of the scheme. Typically the complex embeddings add more complex analytic/ Hodge-theoretic informations to the usual Chow groups. On the other hand, higher Chow groups were defined by Spencer Bloch as a simple example of a motivic cohomology. In this talk, we will explore the possibility to obtain a good definition for higher arithmetic Chow groups. This is a joint work with Jos ́e Ignacio Burgos from ICMAT, Madrid.