Related papers: Extended Bloch group and the Cheeger-Chern-Simons …
We obtain some sufficient conditions for reducibility of a Schlesinger isomonodromic family with the (block) upper-triangular monodromy to the same (block) upper-triangular form via a constant gauge transformation. We also obtain integral…
We study Seiberg-like dualities in three dimensional N=2 supersymmetric theories, emphasizing Chern-Simons terms for the global symmetry group, which affect contact terms in two-point functions of global currents and are essential to the…
We introduce a class of multidimensional Schr\"odinger operators with elliptic potential which generalize the classical Lam\'e operator to higher dimensions. One natural example is the Calogero--Moser operator, others are related to the…
We prove a result motivated by Williams's classification of expanding attractors and the Franks-Newhouse Theorem on codimension-1 Anosov diffeomorphisms: If a mixing hyperbolic attractor has 1-dimensional unstable manifolds then it is…
The Chen series map giving the universal monodromy representation of $\mathbb{P}^1\backslash\{0,1,\infty\}$ is extended to an injective 1-cocycle of $PSL(2, \mathbb{Z})$ into power series with complex coefficients in two non-commuting…
Coboundary and cosystolic expansion are notions of expansion that generalize the Cheeger constant or edge expansion of a graph to higher dimensions. The classical Cheeger inequality implies that for graphs edge expansion is equivalent to…
In a previous paper, we developed general techniques for constructing a variety of pseudo-collars, as defined by Guilbault and Tinsley, with roots in earlier work by Chapman and Siebenmann. As an application of our techniques, we exhibited…
Combining the "method of restriction equations" of Rim\'anyi et al. with the techniques of symmetric functions, we establish the Schur function expansions of the Thom polynomials for the Morin singularities $A_3: ({\bf C}^{\bullet},0)\to…
This article has three goals. First, we generalize the result of Deuring and Serre on the characterization of supersingular locus of modular curves to all Shimura varieties given by totally indefinite quaternion algebras over totally real…
We continue to investigate the relation between the Mahler measure of certain two variable polynomials, the values of the Bloch--Wigner dilogarithm $D(z)$ and the values $\zeta_F(2)$ of zeta functions of number fields. Specifically, we…
In this paper we present the Hietarinta Chern-Simons supergravity theory in three space-time dimensions which extends the simplest Poincar\'e supergravity theory. After approaching the construction of the action using the Chern-Simons…
We study the relationship between refined Chern-Simons theory on lens spaces S^3/Z_p and (q,t)-deformed Yang-Mills theory on the sphere S^2. We derive the instanton partition function of (q,t)-deformed U(N) Yang-Mills theory and describe it…
We extend the N=4 superconformal Chern-Simons theories of Gaiotto and Witten to those with additional twisted hyper-multiplets. The new theories are generically linear quiver gauge theories with the two types of hyper-multiplets alternating…
This note is a sequel to Shu-Xue-Yao's paper \cite{BYY} where the author studied the so-called enhanced groups and related dualities for type $A$. In this note, we continue to investigate the enhanced dualities for classical groups of type…
We propose a way to derive polynomial invariants of closed, orientable $3$-manifolds from Heegaard diagrams via cellularly embedded graphs. Given a Heegaard diagram of an irreducible $3$-manifold $M$, we associate a Heegaard graph $G\subset…
The purpose of this paper is to extend our previous work on the variational formula for the Bismut-Cheeger eta form without the kernel bundle assumption by allowing the spin$^c$ Dirac operators to be twisted by isomorphic vector bundles,…
We give a definition of differentiable cohomology of a Lie group G (possibly infinite-dimensional) with coefficients in any abelian Lie group. This differentiable cohomology maps both to the cohomology of the group made discrete and to Lie…
In this paper we study the relationship of hyperbolicity and (Cheeger) isoperimetric inequality in the context of Riemannian manifolds and graphs. We characterize the hyperbolic manifolds and graphs (with bounded local geometry) verifying…
We consider an invariant quantum Hamiltonian $H=-\Delta_{LB}+V$ in the $L^{2}$ space based on a Riemannian manifold $\tilde{M}$ with a countable discrete symmetry group $\Gamma$. Typically, $\tilde{M}$ is the universal covering space of a…
We present the unoriented versions of the Schur and Bogomolov multipliers associated with a finite group $G$. We show that the unoriented Schur multiplier is isomorphic to the second cohomology group $H^2(G;\ZZ_2)$. We define the unoriented…