Related papers: Analytical moduli for unfoldings of saddle-node ve…
Let $C_n$ denote a cyclic group of order $n$. In this paper we investigate modules and chain complexes over the constant integral Mackey functor $\underline{\mathbb{Z}}$ and perform some related homological calculations. Along the way we…
We study vertex algebras and their modules associated with possibly degenerate even lattices, using an approach somewhat different from others. Several known results are recovered and a number of new results are obtained. We also study…
We study moduli spaces of twisted maps to a smooth pair in arbitrary genus, and give geometric explanations for previously known comparisons between orbifold and logarithmic Gromov--Witten invariants. Namely, we study the space of twisted…
We compute cohomology of the moduli space of genus three curves with level two structure and some related spaces. In particular, we determine the cohomology groups of the moduli space of plane quartics with level two structure as…
This paper is a fundamental study of comodules and contramodules over a comonoid in a symmetric closed monoidal category. We study both algebraic and homotopical aspects of them. Algebraically, we enrich the comodule and contramodule…
The classification, both up to isomorphism or up to equivalence, of the gradings on a finite dimensional nonassociative algebra A over an algebraically closed field F, such that its group scheme of automorphisms is smooth, is shown to be…
Let G be a finite group of exponent m and let k be a field of characteristic prime to m, containing the m-th roots of unity. For any Rost cycle module M over k, we construct exact sequences detecting the unramified elements in Serre's group…
We construct a ${\rm KO}$-valued families index for a class of $1|1$-dimensional Euclidean field theories. This realizes a conjectured cocycle map in the Stolz--Teichner program. We further show that a bundle of spin manifolds leads to a…
Recently an algebra of smooth valuations was attached to any smooth manifold. Roughly put, a smooth valuation is finitely additive measure on compact submanifolds with corners which satisfies some extra properties. In this note we initiate…
Explicit methods are presented for computing the cohomology of stable, holomorphic vector bundles on elliptically fibered Calabi-Yau threefolds. The complete particle spectrum of the low-energy, four-dimensional theory is specified by the…
We show that Verdier duality for certain sheaves on the moduli spaces of graphs associated to Koszul operads corresponds to Koszul duality of operads. This in particular gives a conceptual explanation of the appearance of graph cohomology…
We give necessary and sufficient local conditions for the simultaneous unitarizability of a set of analytic matrix maps from an analytic 1-manifold into SL_n(C) under conjugation by a single analytic matrix map. We apply this result to the…
We connect the homotopy type of simplicial moduli spaces of algebraic structures to the cohomology of their deformation complexes. Then we prove that under several assumptions, mapping spaces of algebras over a monad in an appropriate…
In this paper, we study normal forms of analytic saddle-nodes in $\mathbb C^{n+1}$ with any Poincar\'e rank $k\in \mathbb N$. The approach and the results generalize those of Bonckaert and De Maesschalck from 2008 that considered $k=1$. In…
In this paper we define 2-vector bundles as suitable bundles of 2-vector spaces over a base space, and compare the resulting 2-K-theory with the algebraic K-theory spectrum K(V) of the 2-category of 2-vector spaces, as well as the algebraic…
Modular flow is a symmetry of the algebra of observables associated to spacetime regions. Being closely related to entanglement, it has played a key role in recent connections between information theory, QFT and gravity. However, little is…
We study the moduli space of flat maximal space-like embeddings in $\mathbb{H}^{2,2}$ from various aspects. We first describe the associated Codazzi tensors to the embedding in the general setting, and then, we introduce a family of…
Consider real-analytic mapping-germs, (R^n,o)-> (R^m,o). They can be equivalent (by coordinate changes) complex-analytically, but not real-analytically. However, if the transformation of complex-equivalence is identity modulo higher order…
We associate to any holomorphic vertex algebra a collection of Teichm\"{u}ller modular forms, one in each genus. In genus one we obtain the character of the vertex algebra, and we thus reprove Zhu's modularity result. In higher genus, we…
The continuity, in a suitable topology, of algebraic and geometric operations on real analytic manifolds and vector bundles is proved. This is carried out using recently arrived at seminorms for the real analytic topology. A new…