相关论文: Motivic L-Functions
These notes overlap with lectures given at the TASI summer schools in 2014 and 2011, as well as at the European School of High Energy Physics in 2013. This is primarily an attempt at transcribing my hand-written notes, with emphasis on…
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…
Lecture notes from a minicourse given at the ICTP in May 2002.
Language Models (LMs) have emerged as powerful sources of evidence for linguists seeking to develop theories of syntax. In this paper, we argue that causal interpretability methods, applied to LMs, can greatly enhance the value of such…
These are the notes from the summer school in G\"ottingen sponsored by NATO Advanced Study Institute on Higher-Dimensional Geometry over Finite Fields that took place in 2007. The aim was to give a short introduction on zeta functions over…
This is an attempt to illustrate the glorious history of logical foundations and to discuss the uncertain future.
This article gives an introduction to arithmetic motivic integration in the context of p-adic integrals that arise in representation theory. A special case of the fundamental lemma is interpreted as an identity of Chow motives.
There is a growing interest and literature on intrinsic motivations and open-ended learning in both cognitive robotics and machine learning on one side, and in psychology and neuroscience on the other. This paper aims to review some…
We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative cases. This allows us to define a motivic Fourier transformation for which we get…
This is an attempt at an elementary exposition, with examples, of the theory of motivic integration developed by R. Cluckers and F. Loeser, with the view towards applications in representation theory of p-adic groups.
Given a curve $C$ over a number field $K$ equipped with the action of a finite group $G$ by $K$-automorphisms, one obtains a factorisation of $L(C,s)$ into a product of $L$-functions of `motivic pieces of curves' associated to irreducible…
We give a concise exposition of Voevodsky's theory of motives.
We introduce spaces of exponential constructible functions in the motivic setting for which we construct direct image functors in the absolute and relative cases. This allows us to define a motivic Fourier transformation for which we get…
Large language models (LLMs) have led to breakthroughs in language tasks, yet the internal mechanisms that enable their remarkable generalization and reasoning abilities remain opaque. This lack of transparency presents challenges such as…
This article presents a survey of computability logic: its philosophy and motivations, main concepts and most significant results obtained so far. A continuously updated online version of this article is maintained at…
We construct new six-functor formalisms capturing cohomological invariants of varieties with potentials. Starting from any six-functor formalism $C$, encoded as a coefficient system, we associate a new six-functor formalism…
As a paradigm that delves into the deep seated drivers of user behavior, motivation-based recommendation systems have emerged as a prominent research direction in the field of personalized information retrieval. Unlike traditional…
We establish the motivic six-functor formalism for fs log schemes. In particular, we prove the exact base change property, projection formula, and Poincar\'e duality. We also define Borel-Moore motivic homology, G-theory, and Chow homology…
This note is an invitation to the theory of geometric functions. The foundation techniques and some of the developments in the field are explained with the mindset that the audience is principally young researchers wishing to understand…
These informal notes are an expanded version of lectures on the moduli space of elliptic curves given at Zhejiang University in July, 2008. Their goal is to introduce and motivate basic concepts and constructions (such as orbifolds and…