The Quot scheme of points $\mathrm {Quot} _ {d, n}(X) $ on a variety $ X $ over a field $ k $
parametrizes quotient sheaves of $\mathcal {O} _X^{\oplus d} $ of zero-dimensional support …

We consider two motivic generating functions defined on a variety, and reveal their tight
connection. They essentially count torsion-free bundles and zero-dimensional sheaves. On …

Given a semisimple element in the loop Lie algebra of a reductive group, we construct a
quasi-coherent sheaf on a partial resolution of the trigonometric commuting variety of the …

These notes cover the lectures of the first named author at 2021 IHES Summer School on
“Enumerative Geometry, Physics and Representation Theory” with additional details and …

Abstract We compute the Borel–Moore homology of unramified affine Springer fibers for
under the assumption that they are equivariantly formal and relate them to certain ideals …

We show that Hilbert schemes of planar curve singularities and their parabolic variants can
be interpreted as certain generalized affine Springer fibers for, as defined by Goresky …

Let $ R $ be the complete local ring of a complex plane curve germ and $ S $ its
normalization. We propose a conjecture relating the virtual weight polynomials of the Hilbert …

Let g be a semisimple Lie algebra, let t be its Cartan subalgebra, and let W be the Weyl
group. The goal of this paper is to prove an isomorphism between suitable completions of …

We show that the Frobenius character of the equivariant Borel-Moore homology of a certain
positive $ GL_n $-version of the unramified affine Springer fiber $ Z_k $ studied by Goreski …

We present an LLT-type formula for a general power of the nabla operator applied to the
Cauchy product for the modified Macdonald polynomials, and use it to deduce a new proof …