Related papers: On Branching Indices of Affine A-D-E Diagrams : A …

In the Labourie-Loftin parametrization of the Hitchin component of surface group representations into SL(3,R), we prove an asymptotic formula for holonomy along rays in terms of local invariants of the holomorphic differential defining that…

Using Bruhat-Tits theory, we analyse the restriction of depth-zero representations of a semisimple simply connected $p$-adic group $G$ to a maximal compact subgroup $K$. We prove the coincidence of branching rules within classes of…

Structural properties are given for $D(K)$, the Banach algebra of (complex) differences of bounded semi-continuous functons on a metric space $K$. For example, it is proved that if all finite derived sets of $K$ are non-empty, then a…

We consider two-dimensional N=(2,2) supersymmetric gauge theory on discretized Riemann surfaces. We find that the discretized theory can be efficiently described by using graph theory, where the bosonic and fermionic fields are regarded as…

Lee and the second named author studied involutions on smooth minimal surfaces $S$ of general type with $p_g(S)=0$ and $K_S^2=7$. They gave the possibilities of the birational models $W$ of the quotients and the branch divisors $B_0$…

We give a 1-dimensional family of classical and supersingular Enriques surfaces in characteristic 2 covered by the supersingular K3 surface with Artin invariant 1. Moreover we show that there exist 30 nonsingular rational curves and ten…

This is a short note on the relation between the graded stable derived categories of 14 exceptional unimodal singularities and the derived category of K3 surfaces obtained as compactifications of the Milnor fibers. As a corollary, we obtain…

We describe the cohomology of the sheaf of twisted differential operators on the quantized flag manifold at a root of unity whose order is a prime power. It follows from this and our previous results that for the De Concini-Kac type…

We study the singularities of normalized R-matrices between arbitrary simple modules over the quantum loop algebra of type ADE in Hernandez--Leclerc's level-one subcategory using equivariant perverse sheaves, following the previous works by…

In this article we study quotients of deformations of simple singularities, and attempt to characterize them in terms of subsystems of simple root systems. The quotient of a semiuniversal deformation of a simple singularity of inhomogeneous…

We begin with a comprehensive discussion of the punctual Hilbert scheme of the regular two-dimensional local ring in terms of the Gr\"obner cells. These schemes are the most degenerate fibers of the Grothendieck-Deligne norm map (the…

The twisted boundary conditions and associated partition functions of the conformal sl(2) A-D-E models are studied on the Klein bottle and the M\"obius strip. The A-D-E minimal lattice models give realization to the complete classification…

The Seiberg-Witten family of elliptic curves defines a Jacobian rational elliptic surface $\Z$ over $\mathbb{C}\mathrm{P}^1$. We show that for the $\bar{\partial}$-operator along the fiber the logarithm of the regularized determinant $-1/2…

We consider resolutions of codimension-two enhanced singularities from $SO(12)$ to $E_7$ and from $E_7$ to $E_8$ in six-dimensional F-theory, where a half-hypermultiplet arises for generic complex structures achieving them. The exceptional…

We show that Thurston's skinning maps of Teichmuller space have finite fibers. The proof centers around a study of two subvarieties of the SL_2(C) character variety of a surface, one associated to complex projective structures and the other…

Given an oriented Riemannian surface $(\Sigma, g)$, its tangent bundle $T\Sigma$ enjoys a natural pseudo-K\"{a}hler structure, that is the combination of a complex structure $\J$, a pseudo-metric $\G$ with neutral signature and a symplectic…

We revisit the classification of rank-1 4d $\mathcal{N}=2$ QFTs in the spirit of Diophantine Geometry, viewing their special geometries as elliptic curves over the chiral ring (a Dedekind domain). The Kodaira-N\'eron model maps the space of…

The Brasselet number of a function $f$ with nonisolated singularities describes numerically the topological information of its generalized Milnor fibre. In this work, we consider two function-germs $f,g:(X,0)\rightarrow(\mathbb{C},0)$ such…

In this survey we collect some recent results obtained by the authors and collaborators concerning the fine structure of functions of bounded deformation (BD). These maps are $\mathrm{L}^1$-functions with the property that the symmetric…

We carry out a detailed intersection theoretic analysis of the Deligne-Mumford compactification of the divisor on M_{10} consisting of curves sitting on K3 surfaces. This divisor is not of classical Brill-Noether type, and is known to give…