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Algebra and geometry of link homology Lecture notes from the IHES 2021 Summer School

Related publications (29)

Mean value theorems for collections of lattices with a prescribed group of symmetries

Euclidean lattices are mathematical objects of increasing interest in the fields of cryptography and error-correcting codes. This doctoral thesis is a study on high-dimensional lattices with the motivation to understand how efficient they are in terms of b ...

EPFL2024

Koopman-based Data-driven Robust Control of Nonlinear Systems Using Integral Quadratic Constraints

Alireza Karimi, Mert Eyuboglu

This paper introduces a novel method for data-driven robust control of nonlinear systems based on the Koopman operator, utilizing Integral Quadratic Constraints (IQCs). The Koopman operator theory facilitates the linear representation of nonlinear system d ...

2024

BPS invariants from p-adic integrals

Dimitri Stelio Wyss, Francesca Carocci, Giulio Orecchia

We define p-adic BPS or pBPS invariants for moduli spaces M-beta,M-chi of one-dimensional sheaves on del Pezzo and K3 surfaces by means of integration over a non-archimedean local field F. Our definition relies on a canonical measure mu can on the F-analyt ...

Cambridge Univ Press2024

Price Discrimination with Robust Beliefs

Thomas Alois Weber, Jun Han

This paper considers the problem of second-degree price discrimination when the type distribution is unknown or imperfectly specified by means of an ambiguity set. As robustness measure we use a performance index, equivalent to relative regret, which quant ...

2023

Arithmetic and geometric deformations of threefolds

Fabio Bernasconi, Stefano Filipazzi

We show that mixed-characteristic and equicharacteristic small deformations of 3-dimensional canonical (resp., terminal) singularities with perfect residue field of characteristic p>5 are canonical (resp., terminal). We discuss applications to arithmetic a ...

Wiley2023

4M: Massively Multimodal Masked Modeling

Amir Roshan Zamir, Roman Christian Bachmann, Shuqing Teresa Yeo, David Mizrahi, Oguzhan Fatih Kar

Current machine learning models for vision are often highly specialized and limited to a single modality and task. In contrast, recent large language models exhibit a wide range of capabilities, hinting at a possibility for similarly versatile models in co ...

Neural Information Processing Systems (Nips)2023

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

On the projectivity of some moduli spaces of varieties

Quentin Arthur Frantisek Posva

This thesis is constituted of one article and three preprints that I wrote during my PhD thesis. Their common theme is the moduli theory of algebraic varieties. In the first article I study the Chow--Mumford line bundle for families of uniformly K-stable F ...

EPFL2022

Learning V1 Simple Cells with Vector Representation of Local Content and Matrix Representation of Local Motion

Yufan Ren, Siyuan Huang

This paper proposes a representational model for image pairs such as consecutive video frames that are related by local pixel displacements, in the hope that the model may shed light on motion perception in primary visual cortex (V1). The model couples the ...

ASSOC ADVANCEMENT ARTIFICIAL INTELLIGENCE2022

Reduced representations of complexes, signals, and multifiltrations

Celia Camille Hacker

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

From Undercomplete to Sparse Overcomplete Autoencoders to Improve LF-MMI Speech Recognition

Hervé Bourlard, Selen Hande Kabil

Starting from a strong Lattice-Free Maximum Mutual Information (LF-MMI) baseline system, we explore different autoencoder configurations to enhance Mel-Frequency Cepstral Coefficients (MFCC) features. Autoencoders are expected to generate new MFCC features ...

ISCA-INT SPEECH COMMUNICATION ASSOC2022

Graph Representation Learning with Optimal Transport: Analysis and Applications

Effrosyni Simou

In several machine learning settings, the data of interest are well described by graphs. Examples include data pertaining to transportation networks or social networks. Further, biological data, such as proteins or molecules, lend themselves well to graph- ...

EPFL2022

Quand les artistes font forme en habitant ensemble. Usages, présences, imaginaires

Mathilde Coline Chénin

Taking root within a historical and transversal perspective of communities of artists at work, and of the relationship that they nourish with the places that host their creative activity, the present research intends to bring to light the grammars of "the ...

EPFL2022

Reduced order modelling of nonaffine problems on parameterized NURBS multipatch geometries

Annalisa Buffa, Pablo Antolin Sanchez, Margarita Chasapi

This contribution explores the combined capabilities of reduced basis methods and IsoGeometric Analysis (IGA) in the context of parameterized partial differential equations. The introduction of IGA enables a unified simulation framework based on a single g ...

2022

Local invertibility and sensitivity of atomic structure-feature mappings

Michele Ceriotti, Sergey Pozdnyakov

Background: The increasingly common applications of machine-learning schemes to atomic-scale simulations have triggered efforts to better understand the mathematical properties of the mapping between the Cartesian coordinates of the atoms and the variety o ...

2021

Serre-Tate theory for Calabi-Yau varieties

Maciej Emilian Zdanowicz

Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...

WALTER DE GRUYTER GMBH2021

Home, Spatial Familiarity And Routines In Mobility Behaviours

Marc-Edouard Baptiste Grégoire Schultheiss

This research explores the unreasoned influences of locational behaviour – i.e. locational habits – in Activity- Travel-Behaviour (ATB). In particular, the interrelations between Activity Space characteristics and mobility patterns. In a wider research eff ...

2021

Global Frobenius liftability I

Maciej Emilian Zdanowicz

We formulate a conjecture characterizing smooth projective varieties in positive characteristic whose Frobenius morphism can be lifted modulo p(2)-we expect that such varieties, after a finite stale cover, admit a toric fibration over an ordinary abelian v ...

2021

On The Singular Set In The Thin Obstacle Problem: Higher-Order Blow-Ups And The Very Thin Obstacle Problem

Xavier Fernandez-Real Girona

We consider the singular set in the thin obstacle problem with weight vertical bar x(n +1)vertical bar(a) for a epsilon (-1, 1), which arises as the local extension of the obstacle problem for the fractional Laplacian (a nonlocal problem). We develop a ref ...

MATHEMATICAL SCIENCE PUBL2021

Irvsp: To obtain irreducible representations of electronic states in the VASP

Quansheng Wu, Ziyi Wang

We present an open-source program irvsp, to compute irreducible representations of electronic states for all 230 space groups with an interface to the Vienna ab-initio Simulation Package. This code is fed with plane-wave-based wavefunctions (e.g. WAVECAR) ...

ELSEVIER2021