Related papers: Character tables (modular data) for Drinfeld doubl…
This is an introduction to two-dimensional conformal field theory and its applications in string theory. Modern concepts of conformal field theory are explained, and it is outlined how they are used in recent studies of D-branes in the…
We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…
We study replication identities satisfied by conformal characters of a 2D CFT, providing a natural framework for a physics interpretation of the famous Hauptmodul property of Monstrous Moonshine, and illustrate the underlying ideas in…
We present several infinite families of potential modular data motivated by examples of Drinfeld centers of quadratic categories. In each case, the input is a pair of involutive metric groups with Gauss sums differing by a sign, along with…
A modular tensor category provides the appropriate data for the construction of a three-dimensional topological field theory. We describe the following analogue for two-dimensional conformal field theories: a 2-category whose objects are…
We introduce a new type of diagrams and prove the existence of a particular one, the "central tuned diagram", with some optimal features, for finitely generated modules of certain categories. This is achieved by getting to the idea of "the…
In this paper we investigate examples of good and optimal Drinfeld modular towers of function fields. Surprisingly, the optimality of these towers has not been investigated in full detail in the literature. We also give an algorithmic…
We explain the basics of conformal theory using the language of chiral algebras of Beilinson and Drinfeld.
We compare modular forms of characteristic $p>0$ (i.e. Drinfeld's modular forms) and automorphic forms. We prove that spaces of these modular forms (which are of characteristic $p$) can be described by function spaces of characteristic…
In the first part, we revisit the theory of Drinfeld modular curves and $\pi$-adic Drinfeld modular forms for GL(2) from the perfectoid point of view. In the second part, we review open problems for families of Drinfeld modular forms for…
These notes are our contribution to the Proceedings of the ICM 2026. We discuss some results we have obtained (in part jointly with coauthors) regarding the representation theory of reductive algebraic groups over algebraically closed…
Explicit formulae describing the genus one characters and modular transformation properties of permutation orbifolds of arbitrary Rational Conformal Field Theories are presented, and their relation to the theory of covering surfaces is…
It is known that finite crossed modules provide premodular tensor categories. These categories are in fact modularizable. We construct the modularization and show that it is equivalent to the module category of a finite Drinfeld double.
We show that the conformal characters of various rational models of W-algebras can be already uniquely determined if one merely knows the central charge and the conformal dimensions. As a side result we develop several tools for studying…
In this article, we establish the duality between the generalised Drinfeld double and generalised quantum codouble within the framework of modular or manageable (not necessarily regular) multiplicative unitaries, and discuss several…
Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which…
The modular properties of fractional level affine sl(2)-theories and, in particular, the application of the Verlinde formula, have a long and checkered history in conformal field theory. Recent advances in logarithmic conformal field theory…
In the present paper, we introduce the notion of nearly holomorphic Drinfeld modular forms and study an analogue of Maass-Shimura operators in this context. Furthermore, for a given nearly holomorphic Drinfeld modular form, we show that its…
A general procedure is presented to determine, given any suitable representation of the modular group, the characters of all possible Rational Conformal Field Theories whose associated modular representation is the given one. The relevant…
This is the first of a series of articles providing a foundation for the theory of Drinfeld modular forms of arbitrary rank r. In the present part, we develop the analytic theory. Most of the work goes into defining and studying the…