Related papers: Lectures on K-theoretic computations in enumerativ…
Following Braverman-Finkelberg-Feigin-Rybnikov (arXiv:1008.3655), we study the convolution algebra of a handsaw quiver variety, a.k.a. a parabolic Laumon space, and a finite W-algebra of type A. This is a finite analog of the AGT conjecture…
We propose an alternative description of 2 dimensional Conformal Field Theory in terms of Quantum Inverse Scattering. It is based on the generalized KdV systems attached to $A_2^{(2)}$, yielding the classical limit of Virasoro as Poisson…
Given a smooth curve $C$, we define and study analogues of KLR algebras and quiver Schur algebras, where quiver representations are replaced by torsion sheaves on $C$. In particular, they provide a geometric realization for certain…
Following and developing ideas of R. Karasev (Covering dimension using toric varieties, arXiv:1307.3437), we extend the Lebesgue theorem (on covers of cubes) and the Knaster-Kuratowski-Mazurkiewicz theorem (on covers of simplices) to…
We show that the shuffle algebra associated to a doubled quiver (determined by 3-variable wheel conditions) is generated by elements of minimal degree. Together with results of Varagnolo-Vasserot and Yu Zhao, this implies that the…
We study the relation between Donaldson-Thomas theory of Calabi-Yau threefolds and a six-dimensional topological Yang-Mills theory. Our main example is the topological U(N) gauge theory on flat space in its Coulomb branch. To evaluate its…
We study the reduced descendent Gromov-Witten theory of K3 surfaces in primitive curve classes. We present a conjectural closed formula for the stationary theory, which generalizes the Bryan-Leung formula. We also prove a new recursion that…
Commutative K-theory, a cohomology theory built from spaces of commuting matrices, has been explored in recent work of Adem, G\'{o}mez, Gritschacher, Lind, and Tillman. In this article, we use unstable methods to construct explicit…
Building upon the Bloch-Kato conjecture in Milnor K-theory, we relate the third unramified cohomology group with Q/Z coefficients with a group which measures the failure of the integral Hodge conjecture in degree 4. As a first consequence,…
Let M be a smooth Fredholm manifold modeled on a separable infinite-dimensional Euclidean space E with Riemannian metric g. Given an (augmented) Fredholm filtration F of M by finite-dimensional submanifolds (M_n), we associate to the triple…
Let $A$ be a finite-dimensional algebra over an algebraically closed field. The problem of constructing indecomposable $A$-modules inductively from simple ones by means of exact sequences - called accessibility - is the starting point of…
A 2015 conjecture of Codesido-Grassi-Mari\~no in topological string theory relates the enumerative invariants of toric CY 3-folds to the spectra of operators attached to their mirror curves. We deduce two consequences of this conjecture for…
We construct geometric realizations of the r-colored bosonic and fermionic Fock space on the equivariant cohomology of the moduli space of framed rank r torsion-free sheaves on CP^2. Using these constructions, we realize geometrically all…
The Katz-Klemm-Vafa conjecture expresses the Gromov-Witten theory of K3 surfaces (and K3-fibred 3-folds in fibre classes) in terms of modular forms. Its recent proof gives the first non-toric geometry in dimension greater than 1 where…
Using projective spaces as examples of toric manifolds, we examine K-theoretic fixed point localization. On the one hand, we will see how the permutation-equivariant theory of the point target space emerges as a necessary ingredient. On the…
In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on…
Oberdieck and Pandharipande conjectured that the curve counting invariants of $S\times E$, the product of a $K3$ surface and an elliptic curve, is given by minus the reciprocal of the Igusa cusp form of weight 10. For a fixed primitive…
We build on work of Muro-Raptis in [Ann. K-Theory 2 (2017), no. 2, 303-340] and Cisinski-Neeman in [Adv. Math. 217 (2008), no. 4, 1381-1475] to prove that the additivity of derivator K-theory holds for a large class of derivators that we…
We provide descriptions of the Whitehead groups, and the algebraic $K$-theory groups, of the fundamental group of a connected, oriented, closed $3$-manifold in terms of Whitehead groups of their finite subgroups and certain Nil-groups. The…
We describe an attempt to make quantum K-theory (of stable maps) more amenable to the self-duality/rigidity arguments of arXiv:1512.07363 in quasimap theory, by twisting the virtual structure sheaf. For $\mathbb{P}^n$ this twist produces…