Kazhdan-Lusztig and singular Hodge theory for matroids

Kazhdan-Lusztig and singular Hodge theory for matroids

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June Huh, Princeton University
Fine Hall 314

In-Person and Online Talk 

Zoom link:  https://princeton.zoom.us/j/99136657600

Passcode: required

There is a remarkable parallel between the theory of Coxeter groups (think of the symmetric group or the dihedral group) and matroids (think of your favorite graph or vector configuration). After giving an overview of the similarity, I will report proofs of two combinatorial conjectures, the nonnegativity conjecture for Kazhdan-Lusztig coefficients and the top-heavy conjecture for the number of flats of matroids. The key step is to formulate and prove an analogue of the decomposition theorem in a combinatorial setup. The talk should be enjoyable without specialized knowledge.

Joint work with Tom Braden, Jacob Matherne, Nick Proudfoot, and Botong Wang.