Mathematics Colloquium: Schubert calculus, old and new

Wednesday, February 19 at 3:30pm to 4:30pm

This is a past event.

Kaprielian Hall (KAP), 414
3620 South Vermont Avenue, Los Angeles, CA 90089

Allen Knutson, Cornell University

Abstract: How many points in the plane lie on two generic lines? One. How many lines in 3-space intersect four generic lines? Two. Hilbert's 15th problem was to put calculations of such numbers (via principles of Schubert) onto a rigorous footing, and motivated the definition of cohomology ring (here, of the "Grassmannian" of lines in 3-space).

I'll talk about many generalizations of this original problem -- going beyond cohomology to equivariant cohomology, quantum cohomology, K-theory, or any combination; also going
beyond Grassmannians to other moduli spaces -- all of which have answers that are easy to compute, but only a few of which have manifestly positive formulae (some very recent). Parts of this talk are joint work with Terry Tao, Paul Zinn-Justin, and Iva Halacheva.

Event Type

Lecture / Talk / Workshop

Campus

University Park Campus

Department
Mathematics
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