Related papers: Motivic L-Functions
This report describes the development and use of an online teaching tool giving students exercises in logical modelling, or \emph{formalisation} as it is called in the older literature. The original version of the site, `Logic for Fun',…
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…
Lecture notes on an introductory course on arithmetic lattices (EPFL 2014).
A short lecture given at the Summer School on "Modern perspectives in lattice QCD", Les Houches, August 3-28, 2009.
This is an extended abstract of lectures delivered at the 4th Warsaw Summer School on Statistical Physics in Kazimierz Dolny, June 25-July 2, 2011.
Given a smooth variety $X$ and a regular function $f$ on it, by considering the dlt modification, we define the dlt motivic zeta function $Z^{\rm dlt}_{\rm mot}(s)$ which does not depend on the choice of the dlt modification.
The importance of knowing ICT training and motivation -so relevant in today's society- which currently offers the first year college students, mostly in degrees in Education, focuses the object of interest in this study. The following…
These are the lecture notes for a short course on geometric quantization given by the author at the XVIII Modave Summer School on Mathematical Physics, Sep 5 - Sep 9.
Large language models (LLMs) often map semantically related prompts to similar internal representations at specific layers, even when their surface forms differ widely. We show that this behavior can be explained through Iterated Function…
The aim of this short paper is to give a practical introduction to functional interpretation of proofs for computer scientists interested in synthesis.
Let $A$ be an abelian variety over the function field of a smooth projective curve $C$ over an algebraically closed field $k$. We compute the $l$-adic cohomology groups of $C$ with coefficients in the locally constant sheaf associated to…
This article presents an overview of computability logic -- the game-semantically constructed logic of interactive computational tasks and resources. There is only one non-overview, technical section in it, devoted to a proof of the…
We define a notion of colimit for diagrams in a motivic category indexed by a presheaf of spaces (e.g. an \'etale classifying space), and we study basic properties of this construction. As a case study, we construct the motivic analogs of…
An article based on a four-lecture introductory minicourse on minimal surface theory given at the 2013 summer program of the Institute for Advanced Study and the Park City Mathematics Institute.
While Large Language Models (LLMs) have demonstrated impressive natural language understanding capabilities across various text-based tasks, understanding humor has remained a persistent challenge. Humor is frequently multimodal, relying on…
Interpretability of the underlying AI representations is a key raison d'\^{e}tre for Open Learner Modelling (OLM) -- a branch of Intelligent Tutoring Systems (ITS) research. OLMs provide tools for 'opening' up the AI models of learners'…
These are lecture notes for a series of lectures given at the Les Houches Summer School on Integrability in Atomic and Condensed Matter Physics, 30 July to 24 August 2018. The same series of lectures has also been given at the Tokyo…
Generating rational and generally accurate responses to tasks, often accompanied by example demonstrations, highlights Large Language Model's (LLM's) remarkable In-Context Learning (ICL) capabilities without requiring updates to the model's…
This paper proposes a conjecture on special values of L-functions of geometric motives over Z. This includes L-functions of mixed motives over Q and Hasse-Weil zeta-functions of schemes over Z. We conjecture the following: the order of L(M,…
This article describes an undergraduate physics module at a university in England that places year 3 student physicists in secondary school classrooms for a semester. This is done as a way of introducing them to the occupation of secondary…