## Combinatorics and Graph Theory

•  Victor Reiner, University of Minnesota
•  Conjectures on cohomology of Grassmannians
•  04/21/2021
•  3:00 PM - 3:50 PM
•  Online (virtual meeting) (Virtual Meeting Link)
•  Bruce E Sagan (bsagan@msu.edu)

The cohomology ring of the Grassmannian is well-studied, with Hilbert series given by a q-binomial coefficient. A 2003 conjecture with G. Tudose asserts that for each m = 0,1,2,..., the subring of the cohomology generated by the elements of degree at most m also has a predictable Hilbert series. After reviewing this conjecture, we will report on two pieces of progress from our Summer 2020 "Polymath Jr." REU group. The first reinterprets the conjecture in terms of the k-conjugation operation on k-bounded partitions. The second gives the Lagrangian Grassmannian analogue of the conjecture. (see arXiv:math/0309281, arXiv:2011.03179)

## Contact

Department of Mathematics
Michigan State University