We prove an explicit formula for the Poincaré polynomials of parabolic character varieties of Riemann surfaces with semisimple local monodromies, which was conjectured by Hausel, Letellier and Rodriguez-Villegas. Using an approach of Mozgovoy and …
Using our earlier results on polynomiality properties of plethystic logarithms of generating series of certain type, we show that Schiffmann’s formulas for various counts of Higgs bundles over finite fields can be reduced to much simpler formulas …
Using $\lambda$ operations, we give some results on the kernel of the natural map from the monoid algebra $\mathbb{Z}R$ of a commutative ring $R$ to the ring of $S$-Witt vectors of $R$. As a byproduct we obtain a very natural interpretation of a …
We establish curious Lefschetz property for generic character varieties of Riemann surfaces conjectured by Hausel, Letellier and Rodriguez-Villegas. Our main tool applies directly in the case when there is at least one puncture where the local …
We prove Boyd's conjectures relating Mahler's measures and values of L-functions of elliptic curves in the cases when the corresponding elliptic curve has conductor 14.
The subject of this paper is the big quantum cohomology rings of symplectic isotropic Grassmannians $IG(2,2n)$. We show that these rings are regular. In particular, by “generic smoothness”, we obtain a conceptual proof of generic semisimplicity of …
We propose an approach for showing rationality of an algebraic variety $X$. We try to cover $X$ by rational curves of certain type and count how many curves pass through a generic point. If the answer is $1$, then we can sometimes reduce the question …
We prove that the full twist is a Serre functor in the homotopy category of type A Soergel bimodules. As a consequence, we relate the top and bottom Hochschild degrees in Khovanov-Rozansky homology, categorifying a theorem of Kálmán.
The earlier work of the first and the third named authors introduced the algebra $A_{q,t}$ and its polynomial representation. In this paper we construct an action of this algebra on the equivariant K-theory of certain smooth strata in the flag …
For a quiver $Q$, we take $M$ an associated toric Nakajima quiver variety and $\Gamma$ the underlying graph. In this article, we give a direct relation between a specialisation of the Tutte polynomial of $\Gamma$, the Kac polynomial of $Q$ and the …