Kazhdan-Lusztig theory for matroids

Algebra Seminar
Monday, February 4, 2019 - 12:50pm for 1 hour (actually 50 minutes)
Skiles 005
Botong Wang – University of Wisconsin-Madison – wang@math.wisc.eduhttp://www.math.wisc.edu/~wang/
Yoav Len
Matroids are basic combinatorial objects arising from graphs and vector configurations. Given a vector configuration, I will introduce a “matroid Schubert variety” which shares various similarities with classical Schubert varieties. I will discuss how the Hodge theory of such matroid Schubert varieties can be used to prove a purely combinatorial conjecture, the “top-heavy” conjecture of Dowling-Wilson. I will also report an on-going project joint with Tom Braden, June Huh, Jacob Matherne, Nick Proudfoot on the cohomology theory of non-realizable matroids.