相关论文: Motivic L-Functions

Inferring the abstract relational and causal structure of the world is a major challenge for reinforcement-learning (RL) agents. For humans, language--particularly in the form of explanations--plays a considerable role in overcoming this…

These are the notes accompanying three lectures given by the second author at the Motivic Geometry program at CAS, which aim to give an introduction and an overview of some recent developments in the field of reciprocity sheaves.

These are expended notes of my talk at the summer institute in algebraic geometry (Seattle, July-August 2005), whose main purpose is to present a global overview on the theory of higher and derived stacks. This text is far from being…

Inductive logic programming (ILP) has been a deeply influential paradigm in AI, enjoying decades of research on its theory and implementations. As a natural descendent of the fields of logic programming and machine learning, it admits the…

My doctoral research focuses on understanding semantic knowledge in neural network models trained solely to predict natural language (referred to as language models, or LMs), by drawing on insights from the study of concepts and categories…

In this paper we study the logical foundations of automated inductive theorem proving. To that aim we first develop a theoretical model that is centered around the difficulty of finding induction axioms which are sufficient for proving a…

In this treatment a text is considered to be a series of word impulses which are read at a constant rate. The brain then assembles these units of information into higher units of meaning. A classical systems approach is used to model an…

Language models (LLMs) offer potential as a source of knowledge for agents that need to acquire new task competencies within a performance environment. We describe efforts toward a novel agent capability that can construct cues (or…

This work is the first exploration of proof-theoretic semantics for a substructural logic. It focuses on the base-extension semantics (B-eS) for intuitionistic multiplicative linear logic (IMLL). The starting point is a review of…

The purpose of this informal article is to introduce the reader to some of the objects and methods of the theory of p-adic representations. My hope is that students and mathematicians who are new to the subject will find it useful as a…

This is a mostly expository note concerning the following question: How fast can we compute the value of an L-function at the center of the critical strip? It is the writeup of my talk at the Matrix Ensembles and L-Functions workshop at the…

This is a lecture note produced for DS-GA 3001.003 "Special Topics in DS - Causal Inference in Machine Learning" at the Center for Data Science, New York University in Spring, 2024. This course was created to target master's and PhD level…

Lecture notes for an introductory course in elementary particles.

In this talk I explain in brief the motivations behind undertaking a study of the LHC-ILC interplay. I will give information about the activities of the LHC-LC study group as well as the study group document. I will illustrate the scope of…

These are lecture notes on causal set theory prepared in Jan. 2002 for a Summer School in Valdivia, Chile. In some places, they are more complete, in others much less so, regrettably. An extensive set of references and a glossary of terms…

Thanks to Hrushovski-Loeser's work on motivic Milnor fibers, we give a model-theoretic proof for the motivic Thom-Sebastiani theorem in the case of regular functions. Moreover, slightly extending of Hrushovski-Loeser's construction adjusted…

In this paper we prove a version of Deligne's conjecture for potentially automorphic motives, twisted by certain algebraic Hecke characters. The Hecke characters are chosen in such a way that we can use automorphic methods in the context of…

In this article, we study a family of motives $\mathrm{M}_{n+1}^k$ associated with the symmetric power of Kloosterman sheaves, as constructed by Fres\'an, Sabbah, and Yu. They demonstrated that for $n=1$, the motivic $L$-functions of…

I have developed a pedagogy and textbook for teaching logic centered on what I call "logical worldviews". A logical worldview examines the close connection between philosophical commitments and the logical principles and method for a…

Lecture notes on selected topics in the theory of gravitation.