Related papers: An Introduction to Motivic Integration
We survey certain accessible aspects of Grothendieck's theory of motives in arithmetic algebraic geometry for mathematical physicists, focussing on areas that have recently found applications in quantum field theory. An appendix (by Matilde…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We discuss how the motivic integration will be generalized to wild Deligne-Mumford stacks, that is, stabilizers may have order divisible by the characteristic of the base or residue field. We pose several conjectures on this topic. We also…
In this survey one discusses the notion of the Poincar\'e series of multi-index filtrations, an alternative approach to the definition, a method of computation of the Poincar\'e series based on the notion of integration with respect to the…
Motivated by the concept of network motifs we construct certain clustering methods (functors) which are parametrized by a given collection of motifs (or representers).
The aim of the paper is to provide a rather gentle introduction into Donaldson-Thomas theory using quivers with potential. The reader should be familiar with some basic knowledge in algebraic or complex geometry. The text contains many…
The purpose of this paper is to show how the motivic integration methods of Kontsevich, Denef-Loeser and Looijenga can be adapted to prove the McKay-Ruan correspondence, a generalization of the McKay-Reid correspondence to orbifolds that…
In this paper we introduce and study motives for rational homotopy types.
We associate canonical virtual motives to definable sets over a field of characteristic zero. We use this construction to show that very general p-adic integrals are canonically interpolated by motivic ones.
These lecture notes are derived from a graduate-level course in dynamic optimization, offering an introduction to techniques and models extensively used in management science, economics, operations research, engineering, and computer…
These lecture notes cover four topics. There is a proof of the fact that the functors represented by the motivic Eilenberg-Maclane spaces on the motivic homotopy category coincide with the motivic cohomology defined in terms of the motivic…
We develop the motivic integration theory over formal Deligne-Mumford stacks over a power series ring of arbitrary characteristic. This is a generalization of the corresponding theory for tame and smooth Deligne-Mumford stacks constructed…
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…
This monograph is a study of the category of polynomial endofunctors on the category of sets and its applications to modeling interaction protocols and dynamical systems. We assume basic categorical background and build the categorical…
We give a proposal for future development of the model theory of valued fields. We also summarize some recent results on p-adic numbers.
We develop a theory of modulus triples, for future motivic applications.
In this thesis, we use logarithmic methods to study motivic objects. Let R be a complete discrete valuation ring with perfect residue field k, and denote by K its fraction field. We give in chapter 2 a new construction of the motivic Serre…
In these talks, I discuss a few selected topics in integrable models that are of interest from various points of view. Some open questions are also described.
We give a version of geometric motivic integration that specializes to p-adic integration via point counting. This has been done before for stable sets; we extend this to more general sets. The main problem in doing this is that it requires…
In this survey, we explain how to compute both the quadratic Euler characteristic of nearby cycles, and the motivic monodromy, at a quasi-homogeneous singularity. This gives, for such singularity, a quadratic refinement to the…