Related papers: On the Chow rings of classifying spaces for classi…

The group classification of a class of semilinear reaction-diffusion equations with exponential nonlinearity is carried out using the technique of mapping between classes, which was recently proposed in [O.O. Vaneeva, R.O. Popovych and C.…

The purpose of this dissertation is to study the intersection theory of the moduli spaces of stable maps of degree two from two-pointed, genus zero nodal curves to arbitrary-dimensional projective space. Toward this end, first the Betti…

We introduce equivariant Chow-Witt groups in order to define Chow-Witt groups of quotient stacks. We compute the Chow-Witt ring of the moduli stack of stable (resp. smooth) elliptic curves, providing a geometric interpretation of the new…

Let $\mathscr{J}^d_g \to \mathscr{M}_g$ be the universal Picard stack parametrizing degree $d$ line bundles on genus $g$ curves, and let $\mathscr{J}^d_{2,g}$ be its restriction to locus of hyperelliptic curves $\mathscr{H}_{2,g} \subset…

We prove that any element in the Chow ring of the Hilbert scheme $\text{Hilb}_n$ of $n$ points on a smooth surface $S$ is a universal class, i.e. the pushforward of a polynomial in the Chern classes of the universal subscheme on…

The moduli space of principally polarized abelian varieties $A_g$ of genus g is defined over the integers and admits a minimal compactification $A_g^*$, also defined over the integers. The Hodge bundle over $A_g$ has its Chern classes in…

We propose a generalization of quantization as a categorical way. For a fixed Poisson algebra quantization categories are defined as subcategories of R-module category with the structure of classical limits. We construct the generalized…

Let $Y$ be a Pl\"ucker hypersurface in a symplectic Grassmannian $I_1 Gr(3,n)$ or a bisymplectic Grassmannian $I_2 Gr(3,n)$. We show that many Chow groups of $Y$ inject into cohomology.

In this paper, we explore the theme of orbifold stratified spaces and establish a general criterion for them to be smooth orbifolds. This criterion utilizes the notion of linear stratification on the gluing bundles for the orbifold…

We introduce a space of stable meromorphic differentials with poles of prescribed orders and define its tautological cohomology ring. This space, just as the space of holomorphic differentials, is stratified according to the set of…

We present an algebraic characterization of the complexity classes Logspace and NLogspace, using an algebra with a composition law based on unification. This new bridge between unification and complexity classes is inspired from proof…

We study the fixed singularities imposed on members of a linear system of surfaces in P^3_C by its base locus Z. For a 1-dimensional subscheme Z \subset P^3 with finitely many points p_i of embedding dimension three and d >> 0, we determine…

We survey different topologizations of the set $\mathcal{S}(G)$ of all closed subgroups of a topological group $G$ and demonstrate some applications in Topological Grous, Model Theory, Geometric Group Theory, Topological Dynamics.

The algebras $\mathcal{L}_{g,n}(H)$ have been introduced by Alekseev-Grosse-Schomerus and Buffenoir-Roche in the middle of the 1990's, in the program of combinatorial quantization of the moduli space of flat connections over the surface…

In an earlier paper we derived an analogue of the classical Voronoi summation formula for automorphic forms on GL(3), by using the theory of automorphic distributions. The purpose of the present paper is to apply this theory to derive the…

In this paper, we present a generalisation of a theorem of David and Rob Pollack. In 'A construction of rigid analytic cohomology classes for congruence subgroups of SL(3,Z)', they give a very general argument for lifting ordinary…

We suggest a generalization of \pi_0 for topological groupoids, which encodes incidence relations among the strata of the associated quotient object, and argue for its utility by example, starting from the orbit categories of the theory of…

We derive Glynn's formula from Ryser's formula for the permanent. We further establish via an orbital argument that Glynn's formula yields an optimal row-homogeneous Chow-decomposition of the permanent. We introduce a method for…

The group PGL(3) of linear transformations of the projective plane acts naturally on the projective space parametrizing curves of a given degree. In this note we begin the study of the orbits of smooth curves under this action: we construct…

We present a systematic study of symmetries, invariants and moduli spaces of classes of coframes. We introduce a classifying Lie algebroid to give a complete description of the solution to Cartan's realization problem that applies to both…