Related papers: The model theory of perfectoid fields [after Jahnk…
A countable set of quantum superintegrable systems for arbitrary spin is solved explicitly using tools of supersymmetric quantum mechanics. It is shown that these systems (introduced by Pronko, J. Phys. A: Math. Theor. 40 (2007) ) include…
In this expository article we present Rosenlicht's work on geometric class field theory, which classifies abelian coverings of smooth, projective, geometrically connected curves over perfect fields.
Certain integrable models are described by pairs (X,Y) of ADET Dynkin diagrams. At high energy these models are expected to have a conformally invariant limit. The S-matrix of the model determines algebraic equations, whose solutions are…
This survey article is the written version of a talk given at the Bourbaki seminar in April 2021. We give an introduction to Zagier's conjecture on special values of Dedekind zeta functions, and its relation to $K$-theory of fields and the…
This is a brief review of my work on the correspondence between four-dimensional $\mathcal{N} = 1$ supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable…
The Grothendieck conjecture for hyperbolic curves over finite fields was solved affirmatively by Tamagawa and Mochizuki. On the other hand, (a ``weak version'' of) the Grothendieck conjecture for some hyperbolic curves over algebraic…
The goal of this text is to exhibit some of the ideas and methods from geometric model theory, translated to the particular context of differentially closed fields, exhibiting in a more or less self-contained way the tools needed for the…
An algebraic description of basic physical fields (neutrino field, electron-positron field and electromagnetic field) is studied. It is sown that the electromagnetic field can be described within a quotient representation of the proper…
This thesis studies matrix field theories, which are a special type of matrix models. First, the different types of applications are pointed out, from (noncommutative) quantum field theory over 2-dimensional quantum gravity up to algebraic…
The main goal of this project is to prove the equivalency of several characterizations of completeness of Archimedean ordered fields; some of which appear in most modern literature as theorems following from the Dedekind completeness of the…
Let $k$ be a perfect field of characteristic $p > 2$. We extend the equivalence of categories between Fontaine-Laffaille modules and $\mathbb{Z}_p$ lattices inside crystalline representations with Hodge-Tate weights at most $p-2$ of…
As an application of P. Delgine's theorem (Esnault and Kerz in Acta Math. Vietnam. 37:531-562, 2012) on a finiteness of $l$-adic sheaves on a variety over a finite field, we show the finiteness of \'etale coverings of such a variety with…
This is a set of lecture notes on the operator algebraic approach to 2-dimensional conformal field theory. Representation theoretic aspects and connections to vertex operator algebras are emphasized. No knowledge on operator algebras or…
We find the model completion of the theory modules over $A$, where $A$ is a finitely generated commutative algebra over a field $K$. This is done in a context where the field $K$ and the module are represented by sorts in the theory, so…
We give a detailed proof of the conjecture by Hohm and Zwiebach in double field theory. This result implies that their proposal for large gauge transformations in terms of the Jacobian matrix for coordinate transformations is, as required,…
These notes develop the foundations of Milnor-Witt K-theory for fields of arbitrary characteristic, without any perfectness assumptions. Extending the work of Morel and Feld, we establish all functorial properties of Milnor-Witt K-theory…
We obtain a power saving in the error term for a semigroup congruence lattice point count related to continued fractions. This is done by adapting arguments from recent work of Oh and Winter (2014) that give uniform bounds for certain…
Following ideas given by John Bell in a paper entitled \textit{Beables for quantum field theory}, we show that it is possible to obtain a realistic and deterministic interpretation of any quantum field-theoretic model involving Fermi…
Permutation polynomials over finite fields constitute an active research area and have applications in many areas of science and engineering. In this paper, two conjectures on permutation polynomials proposed recently by Wu and Li [19] are…
Let $K$ be a complete discrete valuation field of characteristic $0$ with not necessarily perfect residue field of characteristic $p>0$. We define a Faltings extension of $\mathcal{O}_K$ over $\mathbb{Z}_p$, and we construct a Hodge-Tate…