Publications

The non-commutative five-term relation $T\_{1,0} T\_{0,1}=T\_{0,1} T\_{1,1} T\_{1,0}$ is shown to hold for certain operators acting on symmetric functions. The "generalized recursion" conjecture of Bergeron and Haiman is a corollary of this result. …

We prove that the coefficients of the generating function of Hausel, Letellier, and Rodriguez-Villegas and its recent generalization by Carlsson and Rodriguez-Villegas, which according to various conjectures should compute mixed Hodge numbers of …

We prove that there is no strongly regular graph (SRG) with parameters (460, 153, 32, 60). The proof is based on a recent lower bound on the number of 4-cliques in a SRG and some applications of Euclidean representation of SRGs.

We present a proof of the compositional shuffle conjecture by Haglund, Morse and Zabrocki [Canad. J. Math., 64 (2012), 822-844], which generalizes the famous shuffle conjecture for the character of the diagonal coinvariant algebra by Haglund, …

We show that values of finite hypergeometric functions defined over Q correspond to point counting results on explicit varieties defined over finite fields.

In this paper, we prove that the constant terms of powers of a Laurent polynomial satisfy certain congruences modulo prime powers. As a corollary, the generating series of these numbers considered as a function of a p-adic variable admits an analytic …

We show that the big quantum cohomology of the symplectic isotropic Grassmanian IG(2,6) is generically semisimple, whereas its small quantum cohomology is known to be non-semisimple. This gives yet another case where Dubrovin's conjecture holds and …