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Publications associées (28)

K3 surfaces, cyclotomic polynomials and orthogonal groups

Eva Bayer Fluckiger

Let X be a complex projective K3 surface and let T-X be its transcendental lattice; the characteristic polynomials of isometries of T-X induced by automorphisms of X are powers of cyclotomic polynomials. Which powers of cyclotomic polynomials occur? The ai ...

Springer Int Publ Ag2024

Multiplicity-free Representations of Algebraic Groups

Donna Testerman, Martin W. Liebeck

Let K be an algebraically closed field of characteristic zero, and let G be a connected reductive algebraic group over K. We address the problem of classifying triples (G, H, V ), where H is a proper connected subgroup of G, and V is a finitedimensional ir ...

Amer Mathematical Soc2024

Spectral Estimators for High-Dimensional Matrix Inference

Farzad Pourkamali

A key challenge across many disciplines is to extract meaningful information from data which is often obscured by noise. These datasets are typically represented as large matrices. Given the current trend of ever-increasing data volumes, with datasets grow ...

EPFL2024

The multivariate Serre conjecture ring

Luc Guyot

It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension

Academic Press Inc Elsevier Science2023

Linear Complexity Self-Attention With 3rd Order Polynomials

Filippos Kokkinos, Grigorios Chrysos

Self-attention mechanisms and non-local blocks have become crucial building blocks for state-of-the-art neural architectures thanks to their unparalleled ability in capturing long-range dependencies in the input. However their cost is quadratic with the nu ...

Ieee Computer Soc2023

From Kernel Methods to Neural Networks: A Unifying Variational Formulation

Michaël Unser

The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator L\documentclass[12pt]{ ...

Springer2023

Certification of Bottleneck Task Assignment With Shortest Path Criteria

Maryam Kamgarpour, Tony Alan Wood

Minimising the longest travel distance for a group of mobile robots with interchangeable goals requires knowledge of the shortest length paths between all robots and goal destinations. Determining the exact length of the shortest paths in an environment wi ...

2023

A NEW PROOF OF THE ERDOS-KAC CENTRAL LIMIT THEOREM

Thomas Mountford, Michael Cranston

In this paper we use the Riemann zeta distribution to give a new proof of the Erdos-Kac Central Limit Theorem. That is, if zeta(s) = Sigma(n >= 1) (1)(s)(n) , s > 1, then we consider the random variable X-s with P(X-s = n) = (1) (zeta) ( ...

Amer Mathematical Soc2023

Lattice packings through division algebras

Nihar Prakash Gargava

In this text, we will show the existence of lattice packings in a family of dimensions by employing division algebras. This construction is a generalization of Venkatesh's lattice packing result Venkatesh (Int Math Res Notices 2013(7): 1628-1642, 2013). In ...

SPRINGER HEIDELBERG2023

A Determinantal Identity for the Permanent of a Rank 2 Matrix

Adam Wade Marcus

We prove an identity relating the permanent of a rank 2 matrix and the determinants of its Hadamard powers. When viewed in the right way, the resulting formula looks strikingly similar to an identity of Carlitz and Levine, suggesting the possibility that t ...

TAYLOR & FRANCIS INC2022

Multiplicity-free representations of algebraic groups II

Donna Testerman, Martin W. Liebeck

We continue our work, started in [9], on the program of classifying triples (X, Y, V), where X, Yare simple algebraic groups over an algebraically closed field of characteristic zero with X < Y, and Vis an irreducible module for Y such that the restriction ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Eigenvalue multiplicities of group elements in irreducible representations of simple linear algebraic groups

Ana-Maria Retegan

Let k be an algebraically closed field of arbitrary characteristic, let G be a simple simply connected linear algebraic group and let V be a rational irreducible tensor-indecomposable finite-dimensional kG-module. For an element g of G we denote by $V_{g}( ...

EPFL2022

Coxeter Combinatorics For Sum Formulas In The Representation Theory Of Algebraic Groups

Jonathan Gruber

Let G be a simple algebraic group over an algebraically closed field F of characteristic p >= h, the Coxeter number of G. We observe an easy 'recursion formula' for computing the Jantzen sum formula of a Weyl module with p-regular highest weight. We also d ...

AMER MATHEMATICAL SOC2022

Fast deterministic and randomized algorithms for low-rank approximation, matrix functions, and trace estimation

Alice Cortinovis

In this thesis we propose and analyze algorithms for some numerical linear algebra tasks: finding low-rank approximations of matrices, computing matrix functions, and estimating the trace of matrices. In the first part, we consider algorithms for building ...

EPFL2022

From Trees to Barcodes and Back Again: A Combinatorial, Probabilistic and Geometric Study of a Topological Inverse Problem

Adélie Eliane Garin

In this thesis, we investigate the inverse problem of trees and barcodes from a combinatorial, geometric, probabilistic and statistical point of view. Computing the persistent homology of a merge tree yields a barcode B. Reconstructing a tree from B invol ...

EPFL2022

Generic direct summands of tensor products for simple algebraic groups and quantum groups at roots of unity

Jonathan Gruber

Let G be either a simple linear algebraic group over an algebraically closed field of characteristic l>0 or a quantum group at an l-th root of unity. The category Rep(G) of finite-dimensional G-modules is non-semisimple. In this thesis, we develop new tech ...

EPFL2022

Quadrature-free immersed isogeometric analysis

Pablo Antolin Sanchez, Thibaut Hirschler

This paper presents a novel method for solving partial differential equations on three-dimensional CAD geometries by means of immersed isogeometric discretizations that do not require quadrature schemes. It relies on a newly developed technique for the eva ...

SPRINGER2022

Formula Normalizations in Verification

Viktor Kuncak, Mario Bucev, Simon Guilloud, Dragana Milovancevic

We propose a new approach for normalization and simplification of logical formulas. Our approach is based on algorithms for lattice-like structures. Specifically, we present two efficient algorithms for computing a normal form and deciding the word problem ...

2023

A PCP Theorem for Interactive Proofs and Applications

Alessandro Chiesa

The celebrated PCP Theorem states that any language in NP can be decided via a verifier that reads O(1) bits from a polynomially long proof. Interactive oracle proofs (IOP), a generalization of PCPs, allow the verifier to interact with the prover for multi ...

SPRINGER INTERNATIONAL PUBLISHING AG2022

Optimal denoising of rotationally invariant rectangular matrices

Florent Gérard Krzakala, Lenka Zdeborová, Emanuele Troiani, Vittorio Erba

In this manuscript we consider denoising of large rectangular matrices: given a noisy observation of a signal matrix, what is the best way of recovering the signal matrix itself? For Gaussian noise and rotationally-invariant signal priors, we completely ch ...

2022

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