Related papers: Comments on Arithmetic Teichmuller Spaces
This is a continuation of my work on Arithmetic Teichmuller Spaces developed in the present series of papers. In this paper, I show that the Theory of Arithmetic Teichmuller Spaces leads, using Shinichi Mochizuki's rubric, to a proof of the…
In this paper after proving (in Section 2) the Berkovich analytic space analog of the familiar fact that there exist many non-isomorphic Riemann surfaces of the fixed topological type, I introduce the precise notion of Arithmetic…
We survey explicit coordinate descriptions for two (A and X) versions of Teichmuller and lamination spaces for open 2D surfaces, and extend them to the more general set-up of surfaces with distinguished collections of points on the…
This is a survey article to appear in the "Handbook on Teichmueller Theory".
These supplementary notes in the ArXiv are a companion to our paper "Bocher contractions of conformally superintegrable Laplace equations" [arXiv:1512.09315]. They contain background material and the details of the extensive computations…
Some formulas and speculations are presented relative to integrable systems and quantum mechanics.
These are some informal notes concerning topological vector spaces, with a brief overview of background material and basic notions, and emphasis on examples related to classical analysis.
This paper deals with three consequences of the existence of Arithmetic Teichmuller spaces of arXiv:2106.11452. Let $\mathscr{X}_{F,\mathbb{Q}_p}$ (resp. $B=B_{\mathbb{Q}_p}$) be the complete Fargues-Fontaine curve (resp. the ring)…
The paper surveys several results on the topology of the space of arcs of an algebraic variety and the Nash problem on the arc structure of singularities.
The article surveys published and not yet published results about moduli spaces of algebraic surfaces.
A brief comment on the paper hep-th/0508051 (with the title mentioned above) by F. Nasseri.
We review our construction of the Teichm\"uller TQFT. We recall our volume conjecture for this TQFT and the examples for which this conjecture has been established. We end the paper with a brief review of our new formulation of the…
This paper uses differential spaces to obtain some new results in integrable Hamiltonian systems
This paper deals with consequences of the existence of Arithmetic Teichmuller spaces established in arXiv:2106.11452 and arXiv:2210.11635. Theorem~9.2.1 provides a proof of a local version of Mochizuki's Corollary~3.12. Local means for a…
This short note provides an overview of some theorems and conjectures obtained by the author and his collaborators. It is an extended abstract for the Oberwolfach workshop "New Trends in Teichm\"uller Theory and Mapping Class Groups", 2…
These are notes on adic spaces. They are made available upon some requests in order to make quoting them easier.
This is a review of the paper "Anomalies in Quantum Field Theory and Cohomologies of Configuration Spaces" (arXiv:0903.0187).
This article describes some aspects of Cauchy integrals and related geometry of sets and measures in Euclidean spaces, etc.
The aim of these lecture notes is, after having quickly described various compactifications of the Teichm\"{u}ller space of a compact connected oriented surface minus finitely many points, to give a construction, by the equivariant Gromov…
Here we consider a few topics related to Lipschitz classes for functions and curves in metric spaces.