Related papers: In the beginning: Langlands' doctoral thesis
This note develops some fundamental properties of resultants and related notions. It represents my own personal exploration of this domain, which I found more instructive than seeking answers in the standard literature. Consequently,…
These lecture notes were prepared for a special topics course in the Department of Statistics at the University of Washington, Seattle. They comprise the first eight chapters of a book currently in progress.
Lanczos-based methods have become standard tools for tasks involving matrix functions. Progress on these algorithms has been driven by several largely disjoint communities, resulting many innovative and important advancements which would…
The goal of this modern presentation, followed by an English translation from the German, is to make available some parts of Lie's very systematic mathematical thought which deserve to join the contemporary literature, and above all also,…
This is the extended write-up of a series of lectures on the duality between the Sine-Gordon model and the Thirring model. Prepared for the London Theory Institute (LonTI) - Fall 2022: a PhD-level mini-course, with exercises and a guide to…
These are slides for a talk given by the authors at the conference "Current developments and directions in the Langlands program" held in honor of Robert Langlands at the Northwestern University in May of 2008. The slides can be used as a…
A compendium for outsiders.
The recent proposal by Ben-Zvi, Sakellaridis and Venkatesh of a duality in the relative Langlands program, leads, via the process of quantization of Hamiltonian varieties, to a duality theory of branching problems. This often unexpectedly…
We present here our introduction to the contributed volume "Quantum Theory: Informational Foundations and Foils", Springer Netherlands (2016). It highlights recent trends in quantum foundations and offers an overview of the contributions…
This book is intended for teaching Signal Analysis methods and Inverse Problems theory. It is completely open access and will remain free. It is currently illustrated with examples that we have actually encountered in geophysics, but will…
A popular scientific contribution should not contradict any established facts and ought to be understandable. I complied with both these requirements and am offering a sufficiently full introduction to probability theory. Furthermore, I…
A dangerously brief history of the developments of the main ideas in economics, as observed by a physicist, is given. This was published in 'Econophysics of Stock and Other Markets', Eds. A. Chatterjee, B. K. Chakrabarti, New Economic…
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
This sequel to Derived Langlands II studies some PSH algebras and their numerical invariants, which generalise the epsilon factors of the local Langlands Programme. It also describes a conjectural Hopf algebra structure on the sum of the…
This paper has been withdrawn by the author; a revised version is part of the author's phd-thesis "Quasi-logarithmic structures" (Zurich, 2007).
This draft book offers a comprehensive and rigorous treatment of the mathematical principles underlying modern deep learning. The book spans core theoretical topics, from the approximation capabilities of deep neural networks, the theory…
These lecture notes provide an introduction to free probability theory, with a focus on tools and techniques useful in the study of large random matrices. Topics include freeness, free cumulants, additive and multiplicative free…
The following is an amalgamation of four preprints and some computer programs which together represent the current state of our investigations of higher order links. This investigation was motivated by questions discussed and raised in the…
These are lecture notes for a course I gave in mid-1990s for MSc students at the University of Bath. It presents an algorithm with singly exponential complexity for the existential theory of the reals, in the spirit of J. Renegar. The aim…