相关论文: Motivic measures
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…
We present a general, functorial approach to Motivic Integration for separated schemes of finite type in lieu of recent work by Hans Schoutens on the subject. Presented is a change of variables formula and a hierarchy of stability…
We introduce notions of information/entropy and information loss associated to exponentiable motivic measures. We show that they satisfy appropriate analogs to the Khinchin-type properties that characterize information loss in the context…
A functional equation for the motivic integral corresponding to the Milnor number of an arc is derived using the Denef-Loeser formula for the change of variables. Its solution is a function of five auxiliary parameters, it is unique up to…
This work brings Mellin transforms into the realm of motivic integration. The new, larger class of motivic functions is stable under motivic Mellin and Fourier transforms, with general Fubini results and change of variables formulas. It…
This is an introduction to measure theory, integration and function spaces, with all the needed preliminaries included, and with some applications included as well. We first discuss some basic motivations, coming from discrete probability,…
Complexity measures in the context of the Integrated Information Theory of consciousness try to quantify the strength of the causal connections between different neurons. This is done by minimizing the KL-divergence between a full system…
Through a cascade of generalizations, we develop a theory of motivic integration which works uniformly in all non-archimedean local fields of characteristic zero, overcoming some of the difficulties related to ramification and small residue…
The problem of advancing coordinatization of mathematics is considered. The need to develop a theory for measuring value and complexity of mathematical implications and proofs is discussed including motivations, benefits and implementation…
Context: Motivation is known to improve performance. In software development in particular, there has been considerable interest in the motivation of contributors to open source. Objective: We identify 11 motivators from the literature…
An intuitive probabilistic alternative for the construction of the Martin boundary is presented along with a construction of maximal representing measures for positive harmonic functions.
I review recent progress in defining a probability measure in the inflationary multiverse. General requirements for a satisfactory measure are formulated and recent proposals for the measure are clarified and discussed.
We associate motivic zeta functions to a large class of infinite dimensional Lie algebras
We survey some results on toric topology.
We extend the definitions of upper and lower valuations on partially ordered sets, and consider the metrics they induce, in particular the metrics available (or not) based on the logarithms of such valuations. Motivating applications in…
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…
Remarks on mathematical proof and the practice of mathematics.
In this short note we establish some properties of all those motivic measures which can be exponentiated. As a first application, we show that the rationality of Kapranov's zeta function is stable under products. As a second application, we…
Motivation is a central driver of human behavior, shaping decisions, goals, and task performance. As large language models (LLMs) become increasingly aligned with human preferences, we ask whether they exhibit something akin to motivation.…
We review the status of inclusive |Vub| measurements where many new results have become available recently.