Related papers: All what I wanted to know about Langlands program …
The present text is a collection of notes about differential geometry prepared to some extent as part of tutorials about topics and applications related to tensor calculus. They can be regarded as continuation to the previous notes on…
Benchmarks and leaderboards are how NLP most often communicates progress, but in the LLM era they are increasingly easy to misread. Scores can reflect benchmark-chasing, hidden evaluation choices, or accidental exposure to test content --…
Adaptive dimensionality reduction in high-dimensional problems is a key topic in statistics. The multiplicative gamma process takes a relevant step in this direction, but improved studies on its properties are required to ease…
We give an introduction to the "categorical" approach to the p-adic Langlands program, in both the "Banach" and "analytic" settings.
Computing educators and researchers have used programming process data to understand how programs are constructed and what sorts of problems students struggle with. Although such data shows promise for using it for feedback, fully automated…
We report on a first experiment about an email based course that connects learning Python basics and introductory probability theory. In the experiment 7 short sequences of homework were sent out to prospective mathematics teachers who did…
Motivated by the Langlands program in representation theory, number theory and geometry, the theory of representations of a reductive $p$-adic group over a coefficient ring different from the field of complex numbers has been widely…
Natural Language Processing offers new insights into language data across almost all disciplines and domains, and allows us to corroborate and/or challenge existing knowledge. The primary hurdles to widening participation in and use of…
As per organizers' request, my talk at the 11th Marcel Grossmann Conference consisted of two parts. In the first, I illustrated recent advances in loop quantum gravity through examples. In the second, I presented an overall assessment of…
Undergraduate research experiences hold many potential benefits. Students can learn about new areas opening up previously unknown paths in academia and industry. The hands-on experience often provides a deeper understanding of what science,…
Unlearning methods have the potential to improve the privacy and safety of large language models (LLMs) by removing sensitive or harmful information post hoc. The LLM unlearning research community has increasingly turned toward empirical…
In order to work with mathematical content in computer systems, it is necessary to represent it in formal languages. Ideally, these are supported by tools that verify the correctness of the content, allow computing with it, and produce…
While there are numerous linear algebra teaching tools, they tend to be focused on the basics, and not handle the more advanced aspects. This project aims to fill that gap, focusing specifically on methods like Strassen's fast matrix…
Transparent machine learning is introduced as an alternative form of machine learning, where both the model and the learning system are represented in source code form. The goal of this project is to enable direct human understanding of…
These informal notes discuss a few basic notions and examples, with emphasis on constructions that may be relevant for analysis on metric spaces.
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…
The goal of this project is to (i) accumulate annotated informal/formal mathematical corpora suitable for training semi-automated translation between informal and formal mathematics by statistical machine-translation methods, (ii) to…
These are notes for a very rapid introduction to the basics of exterior differential systems and their connection with what is now known as Lie theory, together with some typical and not-so-typical applications to illustrate their use.
Statistics is one of the most valuable of disciplines. Science is based on proof and it alone produces results, other approaches are not, and do not. Statistics is the only acceptable language of proof in science. Yet statistics is…
We discuss further around the generalized Langlands Program, by using $\infty$-categoricalization and $\infty$-analytic stackification.