Related papers: Harmonic Cheeger-Simons characters with applicatio…

The random matrix ensembles are applied to the quantum chaotic systems. The quantum systems are studied using the finite dimensional real, complex and quaternion Hilbert spaces of the eigenfunctions. The linear operators describing the…

Quantum-chemical calculations often make use of point-group theory to exploit molecular symmetry, resulting in a reduction of the computational cost and in insights into the electronic structure. This exploitation is often limited to…

We investigate border ranks of twisted powers of polynomials and smoothability of symmetric powers of algebras. We prove that the latter are smoothable. For the former, we obtain upper bounds for the border rank in general and prove that…

We develop a harmonic analysis on objects of some category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. It includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite…

We provide a topological procedure to obtain geometric realizations of both classical and `exotic' $G$-manifolds, such as spheres, bundles over spheres and Kervaire manifolds. As an application, we apply the process known as Cheeger…

In this note, we introduce arithmetic Heilbronn supercharacters that generalize the notions of arithmetic Heilbronn characters and Heilbronn supercharacters and discuss several properties of them.

We establish the correspondence between tame harmonic bundles and $\mu_L$-stable parabolic Higgs bundles with trivial characteristic numbers. We also show the Bogomolov-Gieseker type inequality for $\mu_L$-stable parabolic Higgs bundles.…

We study the affine schemes of modules over gentle algebras. We describe the smooth points of these schemes, and we also analyze their irreducible components in detail. Several of our results generalize formerly known results, e.g. by…

We use large language models (LLM) to approach a question about Lagrangian smoothability proposed by Abouzaid et al. in "First Proof" arXiv:2602.05192.

We generalise the analysis carried out in [arXiv:0710.5796], and find that our previous results can be extended beyond the case of SL(N,C). In particular, we show that an equivalence--at the level of the holomorphic chiral algebra--between…

We present algorithms used in the computational part of the article "Special homogeneous linear systems on Hirzebruch surfaces".

In a joint work with Palmer we have formulated sufficient conditions under which there exist continuous and invertible transformations of the form $H_n(x,y)$ taking solutions of a coupled system \begin{equation*} x_{n+1} =A_nx_n+f_n(x_n,…

We give a survey of results on the geometry of complex algebraic Q-acyclic surfaces, so-called 'Q-homology planes', including some recent results.

Expansions of abelian categories are introduced. These are certain functors between abelian categories and provide a tool for induction/reduction arguments. Expansions arise naturally in the study of coherent sheaves on weighted projective…

We prove a criterion for the existence of harmonic metrics on Higgs bundles that are defined on smooth loci of klt varieties. As one application, we resolve the quasi-etale uniformisation problem for minimal varieties of general type to…

We extend some Cheney-Sharma type operators to a triangle with one curved side. We construct their product and Boolean sum, we study their interpolation properties, the orders of accuracy and we give different expressions of the…

We study harmonic maps from a subset of the complex plane to a subset of the hyperbolic plane. In \cite{FotDask}, harmonic maps are related to the sinh-Gordon equation and a B{\"a}cklund transformation is introduced, which connects…

We formulate a few conjectures on some hypothetical coherent sheaves on the stacks of arithmetic local Langlands parameters, including their roles played in the local-global compatibility in the Langlands program. We survey some known…

We introduce the notion of approximate smoothness in a normed linear space. We characterize this property and show the connections between smoothness and approximate smoothness for some spaces. As an application, we consider in particular…

This paper can be considered as an extension to our paper [On symplectically harmonic forms on six-dimensional nilmanifolds, Comment. Math. Helv. 76 (2001), n 1, 89-109]. Also, it contains a brief survey of recent results on symplectically…