Seminar time: Thursdays 1:50-2:45pm.
Location: Math Tower MW154
October 9: Shukun Wu (Indiana University Bloomington)
Title: Bilinear estimates in F_p with application in Roth-type result
Abstract: We improve an L^2 × L^2 -> L^2 estimate for a certain bilinear operator in the finite field of size p, where p is a prime sufficiently large. Our method carefully picks the variables to apply the Cauchy-Schwarz inequality. As a corollary, we show that there exists a quadratic progression x,x+y,x+y2 for nonzero y inside any subset of F_p of density >= p^{−1/8}. This is joint work with Necef Kavrut.
October 16: Autumn break (no seminar 🙁 ).
October 23: No Seminar
Note: Vadim Gorin (UC Berkeley) will give a colloquium related to Combinatorics on October 23.
Location and time: Scott Lab E001, Thurs Oct 23, 3:00 – 3:55pm.
Title of the talk: Dunkl operators and random matrices
October 30: Houcine Ben Dali (Harvard University)
Title: A combinatorial formula for interpolation Macdonald polynomials
Abstract: In 1996, Knop and Sahi introduced a remarkable family of inhomogeneous symmetric polynomials, defined via vanishing conditions, whose top homogeneous parts are exactly the Macdonald polynomials. Like the Macdonald polynomials, these interpolation Macdonald polynomials are closely connected to the Hecke algebra, and admit nonsymmetric versions, which generalize the nonsymmetric Macdonald polynomials. I will present a combinatorial formula for interpolation Macdonald polynomials in terms of signed multiline queues. This formula generalizes the combinatorial formula for Macdonald polynomials in terms of multiline queues given by Corteel–Mandelshtam–Williams. This is based on a joint work with Lauren Williams.
November 6: Cosmin Pohoata (Emory University)
This is a joint Probability-Combinatorics seminar! Notice the unusual time!
Time and place: 10:20 — 11:15 at the usual Math Tower MW 154.
Title:
Abstract:
November 13: Marcus Michelen (Northwestern University)
This is a joint Probability-Combinatorics seminar!
Title:
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November 20: Tao Jiang (Miami University, OH)
Title:
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November 27: Thanksgiving break (no seminar 🙁 ).
December 4: