Fri, March 10, 2017
Public Access

Category: All

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10:00am [10:30am] Amritanshu Prasad (IMSc)
Title: The Robinson-Schensted-Knuth Algorithm for Real Matrices Abstract: The Robinson-Schensted-Knuth (RSK) correspondence is a bijection from the set of matrices with non-negative integer entries onto the set of pairs of semistandard Young tableaux (SSYT) of the same shape. SSYT can be expressed as integral Gelfand-Tsetlin patterns. We will show how Viennot's light-and-shadows algorithm for computing the RSK correspondence can be extended from matrices with non-negative integer entries to matrices with non-negative real entries, giving rise to real Gelfand-Tsetlin patterns. This real version of the RSK correspondence is piecewise-linear. Indeed, interesting combinatorial problems count lattice points in polyhedra, and interesting bijections are induced by volume-preserving piecewise-linear maps.

3:00pm [3:30pm] Dr. Neeraj Kumar
Title: Koszul algebras V Abstract: In the first half of the talk, we shall recall Koszul filtation and Grobner flag. Let R be a standard graded algebra. If R has a Koszul filtation, then R is Koszul. If R has a Grobner flag, then R is G-quadratic. I will mention an important result of Conca, Rossi, and Valla: Let R be a quadratic Gorenstein algebra with Hilbert series 1 + nz + nz^2 + n^3. Then for n=3 and n=4, R is Koszul. In the second half of the talk, we shall focus on class of strongly Koszul algebras. If time permits, I will prove that Koszul algebras are preserved under various classical constructions, in particular, under taking tensor products, Segre products, fibre products and Veronese subrings.