Related papers: Relations for quadratic Hodge integrals via stable…

We analyse the local structure of moduli space of genus one stable quasimaps. Combining it with the p-fields theory developed in \cite{L}, we prove the splitting formula for the virtual cycle of stable quasimaps to complete intersections in…

We construct vector-valued modular forms on moduli spaces of curves and abelian varieties using effective divisors in projectivized Hodge bundles over moduli of curves. Cycle relations tell us the weight of these modular forms. In…

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 construct coarse moduli spaces of semiquasihomogeneous hypersurface singularities with respect to right equivalence and contact equivalence. We have to fix the principal part of the semiquasihomogeneous singularities. For the moduli…

Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…

It is shown that certain transformations on quiver-dimension vector pairs induce isomorphisms on the corresponding moduli spaces of quiver representations and map a stable dimension vector to a stable dimension vector. This result combined…

In this paper, we consider the preservation of stability by using the notion of Twisted stability. As applications, (1) we show that moduli spaces of vector bundles on K3 and abelian surfaces are irreducible, (2) we compute Hodge…

We study the moduli space of logarithmic connections of rank $2$ on $\mathbb{P}^1 \setminus \{ t_1, \dots, t_5 \}$ with fixed spectral data. The aim of this paper is to compute the cohomology of such space, and this computation will be used…

There are multiple conjectures relating the cohomological Hall algebras (CoHAs) of certain substacks of the moduli stack of representations of a quiver $Q$ to the Yangian $Y^{Q}_{MO}$ by Maulik-Okounkov, whose construction is based on the…

In this thesis quadratic and cubic algebras, which are extensions of SU(1,1) and SU(2) are studied in detail, with particular attention being given to their construction, their finite and infinite dimensional irreducible representations and…

We introduce a new method of calculating intersections on \bar{M}_{g,n}, using localization of equivariant cohomology. As an application, we give a proof of Mirzakhani's recursion relation for calculating intersections of mixed psi and…

We compute the intersection cohomology of the moduli spaces $M_{r,d}$ of semistable vector bundles having rank $r$ and degree $d$ over a curve. We do this by relating the Hodge-Deligne polynomial of the intersection cohomology of $M_{r,d}$…

A finitely generated quadratic module or preordering in the real polynomial ring is called stable, if it admits a certain degree bound on the sums of squares in the representation of polynomials. Stability, first defined explicitly by…

Let F be a holomorphic map whose components satisfy some polynomial relations. We present an algorithm for constructing Nash maps locally approximating F, whose components satisfy the same relations.

We establish a homotopy-theoretic description of the homology of stable moduli spaces of $(2n+1)$-dimensional manifold triads $(N, \partial^h N, \partial^v N)$ with fixed $\partial^v N$, whenever $n \geq 3$ and $(N, \partial^h N)$ is…

We introduce the notion of a logarithmic stable map from a minimal log prestable curve to a log twisted semi-stable variety of form $xy=0$. We study the compactification of the moduli spaces of such maps and provide a perfect obstruction…

Special bases of orthogonal polynomials are defined, that are suited to expansions of density and potential perturbations under strict particle number conservation. Particle-hole expansions of the density response to an arbitrary…

We show that the generating function for the higher Weil-Petersson volumes of the moduli spaces of stable curves with marked points can be obtained from Witten's free energy by a change of variables given by Schur polynomials. Since this…

We show the smoothness over the affine line of the Hodge moduli space of logarithmic t-connections of coprime rank and degree on a smooth projective curve with geometrically integral fibers over an arbitrary Noetherian base. When the base…

We relate various approaches to coefficient systems in relative integral $p$-adic Hodge theory, working in the geometric context over the ring of integers of a perfectoid field. These include small generalised representations over…