Related papers: Intersection theory of toroidal compactifications …
We study the compactification of the $(2,0)$ and type-II little-string theories on $S^1$, $T^2$ and $T^3$ with an R-symmetry twist that preserves half the supersymmetry. We argue that it produces the same moduli spaces of vacua as…
Using Seiberg-Witten Floer spectrum and Pin(2)-equivariant KO-theory, we prove new Furuta-type inequalities on the intersection forms of spin cobordisms between homology $3$-spheres. As an application, we give explicit constrains on the…
In previous work, it was argued that the type IIB T^6/Z_2 orientifold with a choice of flux preserving N=2 supersymmetry is dual to a class of purely geometric type IIA compactifications on abelian surface (T^4) fibered Calabi-Yau…
We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber…
We construct non-geometric compactifications by using the F-theory dual of the heterotic string compactified on a two-torus, together with a close connection between Siegel modular forms of genus two and the equations of certain K3…
Building on our earlier work on toric residues and reduction, we give a proof for the mixed toric residue conejecture of Batyrev and Materov. We simplify and streamline our technique of tropical degenerations, which allows one to…
We prove that the generating series of special divisors in toroidal compactifications of orthogonal Shimura varieties is a mixed mock modular form. More precisely, we find an explicit completion using theta series associated to rays in the…
In a companion manuscript, we introduce a stratification of intersections of a top dimensional real Bruhat cells with another arbitrary cell. This intersection is naturally identified with a subset of the lower triangular group: these…
In this paper we describe the general theory of constructing toroidal compactifications of locally symmetric spaces and using these to compute dimension formulas for spaces of modular forms. We focus explicitly on the case of the orthogonal…
We establish a bijection between torsion pairs in the category of finite-dimensional modules over a finite-dimensional algebra A and pairs (Z, I) formed by a closed rigid set Z in the Ziegler spectrum of A and a set I of indecomposable…
We consider compactifications of the N=1, d=6, E_8 theory on tori to five, four, and three dimensions and learn about some properties of this theory. As a by-product we derive the SL(2,\IZ) duality of the N=2, d=4, SU(2) theory with N_f=4.…
We give a short new proof of a version of the Kruskal-Katona theorem due to Lov\'asz. Our method can be extended to a stability result, describing the approximate structure of configurations that are close to being extremal, which answers a…
We continue the investigation of symmetries and anomalies of $T[M]$ theories obtained by compactifying 6d SCFTs on an internal manifold $M$. We extend the notion of "polarizations on a manifold $M$" to cases where $M$ may have boundaries or…
An analysis of a special class of type II string theory compactifications is presented. We focus on recent work in one particular orientifold background of intersecting brane models and the resulting four dimensional gauge group and matter…
We prove Furuta-type bounds for the intersection forms of spin cobordisms between homology 3-spheres. The bounds are in terms of a new numerical invariant of homology spheres, obtained from Pin(2)-equivariant Seiberg-Witten Floer K-theory.…
In this paper we study compactifications of ADE type conformal matter, N M5 branes probing ADE singularity, on torus with flux for global symmetry. We systematically construct the four dimensional theories by first going to five dimensions…
We derive the noncommutative torus compactification of M(atrix) theory directly from the string theory by imposing mixed boundary conditions on the membranes. The relation of various dualities in string theory and M(atrix) theory…
In this paper we develop an equivariant intersection theory for actions of algebraic groups on algebraic schemes. The theory is based on our construction of equivariant Chow groups. They are algebraic analogues of equivariant cohomology…
We study the refinement invariance of several intersection (co)homologies existing in the literature. These (co)homologies have been introduced in order to establish the Poincar\'e Duality in variousl contexts. We found the classical…
We study the process of compactification as a topology change. It is shown how the mediating spacetime topology, or cobordism, may be simplified through surgery. Within the causal Lorentzian approach to quantum gravity, it is shown that any…