Related papers: A survey of Gersten's conjecture
The use of ensembles of neural networks (NNs) for the quantification of predictive uncertainty is widespread. However, the current justification is intuitive rather than analytical. This work proposes one minor modification to the normal…
Elements of supergeometry are an ingredient in many contemporary classical and quantum field models involving odd fields. For instance, this is the case of SUSY field theory, BRST theory, supergravity. Addressing to theoreticians, these…
In this article we discuss Bousfield localization, beginning with definitions in terms of mapping spaces and working up to a discussion of how they can be constructed when we have access to the small object argument. We also discuss…
In this survey, we give a short overview of the recent progress on the multidimensional L2 conjecture. It can also serve as an introduction to the subject.
This is an overview of our series of papers on the modular generalized Springer correspondence. It is an expansion of a lecture given by the second author in the Fifth Conference of the Tsinghua Sanya International Mathematics Forum, Sanya,…
In this note we give a summary of [arXiv:2401.14449] in which we proposed a proof of the weak gravity conjecture in perturbative string theory. While the WGC is well established, checked in many examples, and many of the ingredients we use…
In this note, we review the recent developments in the string field theory in the temporal gauge. (Based on a talk presented by N.I. in the workshop {\it Quantum Field Theory, Integrable Models and Beyond}, Yukawa Institute for Theoretical…
Some class of sums which naturally include the sums of powers of integers is considered. A number of conjectures concerning a representation of these sums is made.
We prove a `Weierstrass Preparation Theorem' and develop an explicit descent formalism in the context of Whitehead groups of non-commutative Iwasawa algebras. We use these results to describe the precise connection between the main…
These are lecture notes compiled for a short lecture series at the 2023 Condensed Matter Summer School at the University of Minnesota. They are designed to be conversational and fun, and not to take the place of review articles that do a…
This is a revised version of NT0505521, a translation of our Japanese expository article that was published under the title `{\it An overview of sieve methods}' in the second issue of the 52nd volume of Sugaku, the Mathematical Society of…
In this paper we present a new proof of a proposition presented in the article: Complexes of tournaments, directionality filtrations and persistent homology. This paper is part of Joaqu\'in Casta\~neda's undergraduate thesis.
We provide an overview of recent work which aims to understand patterns of vanishing Yukawa couplings that arise in models of particle physics derived from string theory. These patterns are seemingly linked to a plethora of different…
We present the proofs of the conjectures mentioned in the paper published in the proceedings of the 2024 AAAI conference [1], and discovered by the decomposition methods presented in the same paper.
A brief review of the motivation and the present status of Fractional Superstring is presented. Talk at ``Strings 93'', Berkeley, May 1993.
These lectures discuss recent advances on syzygies on algebraic curves, especially concerning the Green, the Prym-Green and the Green-Lazarsfeld Secant Conjectures. The methods used are largely geometric and variational, with a special…
We prove that the BRST complex of a topological conformal field theory is a homotopy Gerstenhaber algebra, as conjectured by Lian and Zuckerman in 1992. We also suggest a refinement of the original conjecture for topological vertex operator…
These are lecture notes that are based on the lectures from a class I taught on the topic of Randomized Linear Algebra (RLA) at UC Berkeley during the Fall 2013 semester.
For a compact and convex window, Mecke described a process of tessellations which arise from cell divisions in discrete time. At each time step, one of the existing cells is selected according to an equally-likely law. Independently, a line…
These are the expanded and detailed notes of the lectures given by the authors during the school and workshop entitled "Liaison and Related Topics," held at the Politecnico di Torino during the period October 1-5, 2001. In these notes we…