Related papers: Enumerative geometry via elliptic stable envelope
We construct stable envelopes in equivariant elliptic cohomology of Nakajima quiver varieties. In particular, this gives an elliptic generalization of the results of arXiv:1211.1287. We apply them to the computation of the monodromy of…
We explicitly construct K-theoretic and elliptic stable envelopes for certain moduli spaces of vortices, and apply this to enumerative geometry of rational curves in these varieties. In particular, we identify the quantum difference…
We show how the modular symmetries that have been found to be consistent with most available scaling data from quantum Hall systems, derive from a rigid family of algebraic curves of the elliptic type. The complicated special functions…
In this thesis we discuss various classical problems in enumerative geometry. We are focused on ideas and methods which can be used explicitly for practical computations. Our approach is based on studying the limits of elliptic stable…
We generalize the construction of elliptic stable envelopes to actions of connected reductive groups and give a direct inductive proof of their existence and uniqueness in a rather general situation. We show these have powerful enumerative…
We revisit the construction of stable envelopes in equivariant elliptic cohomology [arXiv:1604.00423] and give a direct inductive proof of their existence and uniqueness in a rather general situation. We also discuss the specialization of…
We compute quantum cohomology ring of elliptic $\mathbb{P}^1$ orbifolds via orbi-curve counting. The main technique is the classification theorem which relates holomorphic orbi-curves with certain orbifold coverings. The countings of…
We establish the equality of classical and tropical curve counts for elliptic curves on toric surfaces with fixed $j$-invariant, refining results of Mikhalkin and Nishinou--Siebert. As an application, we determine a formula for such counts…
Let $X$ be a symplectic variety equipped with an action of a torus $A$. Let $\nu \subset A$ be a finite cyclic subgroup. We show that K-theoretic stable envelope of subvarieties $X^{\nu}\subset X$ can be obtained via various limits of the…
We construct a finite dimensional representation of the face type, i.e dynamical, elliptic quantum group associated with $sl_N$ on the Gelfand-Tsetlin basis of the tensor product of the $n$-vector representations. The result is described in…
A universal system of difference equations associated with a hyperelliptic curve is derived constituting the discrete analogue of the Dubrovin equations arising in the theory of finite-gap integration. The parametrisation of the solutions…
The quantum differential equations can be regarded as examples of equations with certain universal properties which are of wider interest beyond quantum cohomology itself. We present this point of view as part of a framework which…
We determine the quantum multiplication with divisor classes on the Hilbert scheme of points on an elliptic surface $S \to \Sigma$ for all curve classes which are contracted by the induced fibration $S^{[n]} \to \Sigma^{[n]}$. The formula…
Enumerative invariants in Algebraic Geometry 'count' $\tau$-(semi)stable objects $E$ with fixed topological invariants $[E]=a$ in some geometric problem, using a virtual class $[{\cal M}_a^{\rm ss}(\tau)]_{\rm virt}$ in homology, for the…
We investigate a quantization problem which asks for the construction of an algebra for relative elliptic problems of pseudodifferential type associated to smooth embeddings. Specifically, we study the problem for embeddings in the category…
The stable envelopes of Okounkov et al. realize some representations of quantum algebras associated to quivers, using geometry. We relate these geometric considerations to quantum field theory. The main ingredients are the supersymmetric…
We solve the problem of counting elliptic curves with fixed j-invariant in projective space with tangency conditions. This is equivalent to couting rational nodal curves with condition on the node of the image. The solution is given in the…
In this article we study the equivariant elliptic cohomology of complex toric varieties. We prove a partial reconstruction theorem showing that equivariant elliptic cohomology encodes considerable non-trivial information on the equivariant…
This paper is a contribution to the development of a framework, to be used in the context of semiclassical canonical quantum gravity, in which to frame questions about the correspondence between discrete spacetime structures at "quantum…
In this expository paper we present a brief introduction to the geometrical modeling of some quantum computing problems. After a brief introduction to establish the terminology, we focus on quantum information geometry and ZX-calculus,…