Related papers: An Introduction to Perfectoid Fields
The main purpose of this paper is to find the fixed point in such cases where existing literature remain silent. In this paper we introduce partial completeness, a new type of contraction and many other definitions. Using this approach the…
Line bundles of rational degree are defined using Perfectoid spaces, and their co-homology computed via standard \v{C}ech complex along with Kunneth formula. A new concept of `braided dimension' is introduced, which helps convert the curse…
In this paper we study differential forms and vector fields on the orbit space of a proper action of a Lie group on a smooth manifold, defining them as multilinear maps on the generators of infinitesimal diffeomorphisms, respectively. This…
The study of many problems in additive combinatorics, such as Szemer\'edi's theorem on arithmetic progressions, is made easier by first studying models for the problem in F_p^n for some fixed small prime p. We give a number of examples of…
We follow some (wild) speculations on trying to understand the uniqueness of our physical world, from the field concept to F-Theory.
In this thesis we study classical aspects of superconformal field theory via symmetry principles. Specifically, by employing the powerful setup of conformal superspace, we obtain a plethora of new results in the fields of geometric and…
Conformal primary fields are of central importance in a conformal field theory with d > 2 spacetime dimensions. They can be defined in two ways. A first definition involves commutators between the field and the generators of the conformal…
We explain how to use computer experiments over finite fields to gain heuristic information about the solution set of polynomial equations in characteristic zero. These are notes of a tutorial I gave at the NATO Advanced Study Institute on…
Double Field Theory (DFT) is a proposal to incorporate T-duality, a distinctive symmetry of string theory, as a symmetry of a field theory defined on a double configuration space. The aim of this review is to provide a pedagogical…
New features are described for models with multi-particle area-dependent potentials, in any number of dimensions. The corresponding many-body field theories are investigated for classical configurations. Some explicit solutions are given,…
We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…
In this paper I attempt to summarize the fundamental principles which underlie to Arrangement Field Theory. In my intention the exposition would be the most possible intelligible and self-contained. However the exposed concepts are…
In what follows we give a quick tour through the field of minimal submanifolds, starting at the definition and the classical results and ending up with current areas of research.
We investigate the mathematical structure of the world sheet in two-dimensional conformal field theories.
The goal is to review the notion of a complete Segal space and how certain categorical notions behave in this context. In particular, we study functoriality in complete Segal spaces via fibrations. Then we use it to define limits and…
These notes offer a lightening introduction to topological quantum field theory in its functorial axiomatisation, assuming no or little prior exposure. We lay some emphasis on the connection between the path integral motivation and the…
In this paper, we give an accessible introduction to the theory of orbispaces via groupoids. We define a certain class of topological groupoids, which we call orbigroupoids. Each orbigroupoid represents an orbispace, but just as with…
These are notes from the lectures I gave at the Oberwolfach seminar `Tensor Triangular Geometry and Interactions' which was held in October 2025. The aim of these notes is to give an introduction to tensor triangular geometry, for both…
A ringoid is a set with two binary operations that are linked by the distributive laws. We study special classes of ringoids that are congruence-simple or ideal-simple. In particular, we examine generalised parasemifields and…
We give a combinatorial description of shape theory using finite topological $T_0$-spaces (finite partially ordered sets). This description may lead to a sort of computational shape theory. Then we introduce the notion of core for inverse…