Related papers: The Future of Set Theory
``The purpose of life is to obtain knowledge, use it to live with as much satisfaction as possible, and pass it on with improvements and modifications to the next generation.'' This may sound philosophical, and the interpretation of words…
We synthesize the reported results and recommendations of recent workshops and seminars that convened to discuss open questions within the important intersection of robotics, human-robot interaction, and spoken dialogue systems research.…
We discuss the connections between the failure of the axiom of choice in set theory, and certain model-theoretic structures with enough symmetry.
These lecture notes in Lie Groups are designed for a 1--semester third year or graduate course in mathematics, physics, engineering, chemistry or biology. This landmark theory of the 20th Century mathematics and physics gives a rigorous…
The opening of the meson factories twenty years ago provided nuclear physics with new beams, higher momentum transfers, and new opportunities for precision measurements. The resulting changes in nuclear physics were substantial, altering…
Given a class C of word languages, the C-separation problem asks for an algorithm that, given as input two regular languages, decides whether there exists a third language in C containing the first language, while being disjoint from the…
This paper provides a complete suite of axioms for a version of set theory that I call Explication. Explication borrows from the two most prominent existing systems of set theory. Explication starts with class variables. After several…
The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts…
Belief function theory provides a flexible way to combine information provided by different sources. This combination is usually followed by a decision making which can be handled by a range of decision rules. Some rules help to choose the…
"Math is not a spectator sport." "Lecturing is educational malpractice." Slogans like these rally some mathematicians to teach classes that feature "active learning", where lecturing is eschewed for student participation. Yet as much as I…
This is a lightly edited version of the talk given on September 30, 2020 to inaugurate the international seminar series {\it All Things EFT}. It reviews some of the early history of effective field theories, and concludes with a discussion…
Social media (SM) data provides a vast record of humanity's everyday thoughts, feelings, and actions at a resolution previously unimaginable. Because user behavior on SM is a reflection of events in the real world, researchers have realized…
There is growing acknowledgement within the software engineering community that a theory of software development is needed to integrate the myriad methodologies that are currently popular, some of which are based on opposing perspectives.…
Mathematicians manipulate sets with confidence almost every day, rarely making mistakes. Few of us, however, could accurately quote what are often referred to as "the" axioms of set theory. This suggests that we all carry around with us,…
Game Theory concepts have been successfully applied in a wide variety of domains over the past decade. Sports and games are one of the popular areas of game theory application owing to its merits and benefits in solving complex scenarios.…
Forecasting conversation derailment can be useful in real-world settings such as online content moderation, conflict resolution, and business negotiations. However, despite language models' success at identifying offensive speech present in…
These notes arose from three lectures on fusion system I gave at the University of Valencia in February 2023. We first consider fusion phenomena in classical group theory. Then we develop the abstract theory of fusion systems. Finally…
We closed the CHARM 2007 workshop with a lively panel discussion on the future of the field. This document presents a summary of the key points, and a lightly edited transcript of the discussion itself.
In this work, we develop a novel reasoning approach to enhance the performance of large language models (LLMs) in future occupation prediction. In this approach, a reason generator first derives a ``reason'' for a user using his/her past…
This set of lecture notes is an expanded version of a mini-course the author gave in March of 2025 for the program ``Representation Theory \& Noncommutative Geometry" at the Institut Henri Poincar\'e, Paris. The goal is to provide a survey…