Related papers: In the beginning: Langlands' doctoral thesis
This survey aims to provide a guide to the literature on topological 4-manifolds. Foundational theorems on 4-manifolds are stated, especially in the topological category. Precise references are given, with indications of the strategies…
In this technical paper we introduce the Tensor Network Theory (TNT) library -- an open-source software project aimed at providing a platform for rapidly developing robust, easy to use and highly optimised code for TNT calculations. The…
10 years ago or so Bill Helton introduced me to some mathematical problems arising from semidefinite programming. This paper is a partial account of what was and what is happening with one of these problems, including many open questions…
We review the theory of martingales as applied to stochastic thermodynamics and stochastic processes in physics more generally.
I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.
A long-term research proposal on the algebraic structure, the representations and the possible applications of paraparticle algebras is structured in three modules: The first part stems from an attempt to classify the inequivalent gradings…
This unpublished paper is a copy (completed by a development of section 5 and by minor corrections) of the article with the same title published in: Complex Analysis and Digital Geometry, Proceedings from the Kiselmanfest, 2006, Acta…
We study (relative) $\mathcal K$-Mittag-Leffler modules as was done in the author's habilitation thesis, rephrase old, unpublished results in terms of definable subcategories, and present newer ones, culminating in a characterization of…
A sketch of some of the fundamental notions related to the nature of knowledge is offered, with special focus on the role of mathematics and my own opinions. No single idea exposed here is entirely original; indeed, this topic has been…
The "Millennium Prize Problems" have a place in the history of mathematics. Here we tell some little-known anecdotes from the perspective of the planner of that project. These stories are far from their end; more likely they are just at…
This PhD thesis investigates the societal impact of machine learning (ML). ML increasingly informs consequential decisions and recommendations, significantly affecting many aspects of our lives. As these data-driven systems are often…
The aim of this paper is to alter the abstract definition of the program of the theoretical programming model which has been developed at Eotvos Lorand University for many years in order to investigate methods that support designing correct…
Discussion of "Likelihood Inference for Models with Unobservables: Another View" by Youngjo Lee and John A. Nelder [arXiv:1010.0303]
Discussion of "Likelihood Inference for Models with Unobservables: Another View" by Youngjo Lee and John A. Nelder [arXiv:1010.0303]
This is an extended version of notes prepared for the talk at the conference "Rajchman-Zygmund-Marcinkiewicz 2000" based on recent works of the authors.
We discuss further around the generalized Langlands Program, by using $\infty$-categoricalization and $\infty$-analytic stackification.
This is a survey of known algorithms in algebraic topology with a focus on finite simplicial complexes and, in particular, simplicial manifolds. Wherever possible an elementary approach is chosen. This way the text may also serve as a…
In the ML fairness literature, there have been few investigations through the viewpoint of philosophy, a lens that encourages the critical evaluation of basic assumptions. The purpose of this paper is to use three ideas from the philosophy…
These are lecture notes that arose from a representation theory course given by the first author to the remaining six authors in March 2004 within the framework of the Clay Mathematics Institute Research Academy for high school students,…
This paper has been withdrawn, not because of any errors (that we know of), but because rather than presenting our material as a series of 3 papers, as we originally intended, we have now combined them into one long paper, which is "A…