Related papers: On the Reduction and Evaluation of Generalized Pol…
We describe a theoretical and effective algorithm which enables us to prove that rather general hypergeometric series and integrals can be decomposed as linear combinations of multiple zeta values, with rational coefficients.
This article, which grew out of my lecture at the conference "Analysis and Applications: A Conference in Honor of Elias M. Stein" in May 2011, is intended to give an overview on a collection of results which have been obtained jointly with…
This article is a survey of conjectures and results on reductive algebraic groups having good reduction at a suitable set of discrete valuations of the base field. Until recently, this subject has received relatively little attention, but…
We study when low coordinate degree functions (LCDF) -- linear combinations of functions depending on small subsets of entries of a vector -- can hypothesis test between high-dimensional probability measures. These functions are a…
We propose a novel training objective for GPs constructed using lower-dimensional linear projections of the data, referred to as \emph{projected likelihood} (PL). We provide a closed-form expression for the information loss related to the…
The generalized Hamming weights (GHWs) of linear codes are fundamental parameters, the knowledge of which is of great interest in many applications. However, to determine the GHWs of linear codes is difficult in general. In this paper, we…
During the past decade, nine papers have obtained increasingly strong consequences from the assumption that boolean or bounded-query hierarchies collapse. The final four papers of this nine-paper progression actually achieve downward…
Randomized parallel algorithms for many fundamental problems achieve optimal linear work in expectation, but upgrading this guarantee to hold with high probability (whp) remains a recurring theoretical challenge. In this paper, we address…
This is a collection of discussions of `Riemann manifold Langevin and Hamiltonian Monte Carlo methods" by Girolami and Calderhead, to appear in the Journal of the Royal Statistical Society, Series B.
The problem of reduction of multisymplectic manifolds by the action of Lie groups is stated and discussed, as a previous step to give a fully covariant scheme of reduction for classical field theories with symmetries.
We study the set of generalized principal $\mathfrak{g}$-logarithms of any matrix belonging to a connected SVD-closed subgroup $G$ of $U_n$, with Lie algebra $\mathfrak{g}$. This set is a non-empty disjoint union of a finite number of…
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,…
These are the notes of my lectures at the 1996 European Congress of Mathematicians. {} Polynomials appear in mathematics frequently, and we all know from experience that low degree polynomials are easier to deal with than high degree ones.…
As machine learning becomes more and more available to the general public, theoretical questions are turning into pressing practical issues. Possibly, one of the most relevant concerns is the assessment of our confidence in trusting machine…
We introduce uniparametric and multiparametric quantisations of the general linear supergroup, in the form of "quantised function algebras", both in a formal setting - yielding "quantum formal series Hopf superalgebras", a` la Drinfeld -…
Large language models (LLMs) perform well on multi-hop reasoning, yet how they internally compose multiple facts remains unclear. Recent work proposes \emph{hop-aligned circuit hypothesis}, suggesting that bridge entities are computed…
I briefly review the current theoretical description of Standard Model processes relevant for the LHC, and the tools that are used in the corresponding phenomenological applications. I discuss in particular the recent theoretical progress…
The generalized Hamming weight of linear codes is a natural generalization of the minimum Hamming distance. They convey the structural information of a linear code and determine its performance in various applications, and have become one…
A comprehensive study is performed of general massive, tensor, two-loop Feynman diagrams with two and three external legs. Reduction to generalized scalar functions is discussed. Integral representations, supporting the same class of…
Harmonic polylogarithms $\H(\vec{a};x)$, a generalization of Nielsen's polylogarithms ${S}_{n,p}(x)$, appear frequently in analytic calculations of radiative corrections in quantum field theory. We present an algorithm for the numerical…