Related papers: The Tate conjecture over finite fields (AIM talk)
These lectures give a brief introduction to the Computer Algebra systems Reduce and Maple. The aim is to provide a systematic survey of most important commands and concepts. In particular, this includes a discussion of simplification…
I gave a rambling talk about gravity and its many mysteries at Chen-Ning Yang's 85th Birthday Celebration held in November 2007. I don't have any answers.
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.
These are the notes of some lectures given by the author for a workshop held at TIFR, Mumbai in December, 2011, giving an exposition of the Deligne-Lusztig theory.
In this paper, we survey some recent results on the Artin conjecture and discuss some aspects for the Artin conjecture.
We consider the estimation of small probabilities or other risk quantities associated with rare but catastrophic events. In the model-based literature, much of the focus has been devoted to efficient Monte Carlo computation or analytical…
These are the lecture notes of a set of lectures delivered at the 1995 Trieste summer school in June. I review some recent work on duality in four dimensional Maxwell theory on arbitrary four manifolds, as well as a new set of topological…
We show how powerful algorithms recently developed for counting lattice points and computing volumes of convex polyhedra can be used to compute probabilities of a wide variety of events of interest in social choice theory. Several…
Submanifolds of finite type were introduced by the author during the late 1970s. The first results on this subject were collected in author's books [26,29]. In 1991, a list of twelve open problems and three conjectures on finite type…
This survey is based on lectures given by the authors during the program "Noncommutative algebraic geometry and representation theory" at the MSRI, Berkeley, in the spring of 2013. It covers the recent work of the authors on noncommutative…
The lattice definition of the two-dimensional topological quantum field theory [Fukuma, {\em et al}, Commun.~Math.~Phys.\ {\bf 161}, 157 (1994)] is generalized to arbitrary (not necessarily orientable) compact surfaces. It is shown that…
Effective field theories consistent with quantum gravity obey surprising finiteness constraints, appearing in several distinct but interconnected forms. In this work we develop a framework that unifies these observations by proposing that…
I use an instrumental approach to investigate some commonly made claims about interpretations of quantum mechanics, especially those that pertain questions of locality. The here presented investigation builds on a recently proposed taxonomy…
In July of 2021, the Santa Fe Institute hosted a workshop on evolutionary computation as part of its Foundations of Intelligence in Natural and Artificial Systems project. This project seeks to advance the field of artificial intelligence…
In 1987, Mazur and Tate stated conjectures which, in some cases, resemble the classical Birch-Swinnerton-Dyer conjecture and its $p$-adic analog. We study experimentally three conjectures stated by Mazur and Tate using SageMath. Our…
Talk presented at the XXVI International Conference on High Energy Physics, Dallas, Texas, August, 12, 1992.
This article, intended for a general mathematical audience, is an informal review of some of the many interesting links which have developed between quantum cohomology and "classical" mathematics. It is based on a talk given at the Autumn…
The aim of this note is threefold: first, to present a few relevant facts about the way in which the technique of enriching contractive mappings was introduced; secondly, to expose the main contributions in the area of enriched mappings…
The purpose of this paper is to continue studying the properties of $\gamma$-regular open sets introduced and explored in [6]. The concept of $\gamma$-closed spaces have also been defined and discussed.
The Eighth International Conference on Applied Category Theory took place at the University of Florida on June 2-6 2025. The conference consisted of 2 plenary invited talks, 28 contributed talks, an online community meeting, a general…