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K-State Today

February 17, 2015

Mathematics Colloquium lecture Feb. 17

Submitted by Reta McDermott

Erik Carlsson, International Center for Theoretical Physics, Trieste, Italy, will present "Hall-Littlewood Polynomials and Vector Bundles on the Hilbert Scheme" as part of the Mathematics Department Colloquium lecture series at 2:30 p.m. Tuesday, Feb. 17, in 122 Cardwell Hall.

The abstract for the lecture is: I will present a recent result with the same title as this talk, in which sections of vector bundles on the Hilbert scheme are "counted" by certain multiplication constants for Hall-Littlewood polynomials. A formula for a special case of these constants was identified as the count of some combinatorial objects by Lascoux and Schutzenberger, but their positivity in general remains a conjecture. It would be very desirable to prove this positivity by explicitly identifying the desired sections.