CONFERENCE
Symmetry, Stability, and interactions with Computation
Symétrie, stabilité et interactions algorithmiques
13 – 17 November 2023
Scientific Committee
Comité scientifique
Harm Derksen (University of Michigan)
Jan Draisma (Eindhoven University of Technology)
Gabriele Nebe (Aachen University)
Marie-Françoise Roy (Université Rennes)
Michael F. Singer (North Carolina State University)
Organizing Committee
Comité d’organisation
Saugata Basu (Purdue University)
Evelyne Hubert (INRIA Sophia Antipolis)
Philippe Moustrou (Université de Toulouse – Jean Jaurès)
Cordian Riener (The Arctic University of Norway)
Study of symmetry as a structural property of algebraic structures is one of the fundamental pillars of the developments of modern mathematics, most prominently beginning with the work of Abel and Galois. In the language of algebra, symmetry is the invariance of an object or a property by some action of a group. The presence of symmetries can lead to a possible reduction of algorithmic complexity and preserving and applying symmetry is an intellectual and practical necessity but form a challenge to computational methods and their implementation.
This meeting aims at creating new interactions between several different current trends in the general area of study of symmetries. The overall goal of this meeting will be to study the recent progress in quantitative and algorithmic questions in which symmetry plays an important role and bring recent developments which bridge mathematics and computer science and the open problems in this area to the attention of a wider mathematical audience. The following three areas, their mutual interactions, as well as interactions with other areas will be the primary focus of the conference:
(a) symmetry in real algebraic geometry,
(b) preserving and exploiting symmetry in algebraic computations, and
(c) symmetry in the study of polynomial rings with an infinite number of variables.
Our goal is to bring out the fundamental connections and foundational concepts that relate these different areas and thus we aim to provide new guiding principles in further development.
L’étude des symétries en tant que propriété structurelle des objets algébriques, apparaissant déjà dans les travaux d’Abel et Galois, est devenue l’un des piliers fondamentaux dans les développements des mathématiques modernes. D’un point de vue algébrique, une symétrie se traduit par l’invariance d’un objet ou d’une propriété par une certaine action de groupe. La présence de symétries peut permettre d’espérer une réduction de complexité algorithmique, si bien que comprendre, préserver, et tirer avantage des symétries deviennent, au-delà de questions théoriques passionnantes, des enjeux pratiques cruciaux pour les méthodes de calcul et leur implémentation.
Ce rassemblement a pour ambition de créer de nouvelles interactions entre différentes directions de recherche dans le domaine des symétries. Son enjeu premier est de mettre en lumière les avancées récentes sur des questions algorithmiques et quantitatives mettant en jeu les symétries, en présentant résultats modernes et problèmes ouverts à l’interface entre mathématiques et informatique à un plus large public. Les trois thèmes suivants, leurs interactions mutuelles comme celles avec d’autres domaines mathématiques, seront au coeur du programme :
(a) Symétries en géométrie algébrique réelle,
(b) Préserver et tirer avantage des symétries dans les calculs algébriques, et
(c) Symétries dans un contexte infini.
Notre but au travers de cette conférence est de faire émerger des connexions fondamentales et des principes généraux communs entre ces différents domaines, ouvrant des pistes vers de nouveaux développements.
SPEAKERS
Bram Bekker (Delft University of Technology) Semidefinite programming bounds for distance-avoiding set problems on compact spaces
Greg Blekherman (Georgia Tech) Traces of Matrix Powers and Symmetric Polynomials
Emmanuel Briand (University of Sevilla) TBA
Michel Brion (Université Grenoble Alpes) Symmetry groups of projective algebraic varieties
Daniel Brosch (University of Klagenfurt) Flag Sums of Squares for Sidorenko’s Conjecture
Peter Burgisser (Technical University of Berlin) The zonoid algebra and random intersections in symmetric spaces
Sebastian Debus (University of Magdeburg) Specht ideals
Fernando De Oliveira Filho (Delft University of Technology) The integrality gap of the MAXCUT semidefinite programming formulation
Jan Draisma (University of Bern) Strength and symmetry
Sarah Eggleston (University of Osnabrück) Reach of Segre-Veronese manifolds
Evelyne Hubert (INRIA Sophia Antipolis) Algorithms to compute fundamental invariants and equivariants
Martin Jalard (Université Côte d’Azur) An algebraically independant generating set for the orthogonal action with Seshadri Slice lemma
Trevor Karn (University of Minnesota) Exploring Permutation Actions
Khazhgali Kozhasov (Friedrich Schiller University Jena) Are odd powers of psd forms sos?
Mario Kummer (Technical University of Dresden) Fourier quasicrystals
Nando Leijenhorst (Delft University of Technology) The second step of the Lasserre hierarchy for energy minimization
Aida Maraj (University of Michigan) Algebraic Approaches to Colored Gaussian Graphical Models
Tobias Metzlaff (Technical University of Kaiserslautern) Symmetry in Trigonometric Optimization
Fatemeh Mohammadi (Catholic University of Leuven) TBA
Ali Mohammad Nezhad (University of North Carolina at Chapel Hill) An improved effective Lojasiewicz inequality and its applications
Hans Munthe-Kaas (Arctic University of Norway) Connection Algebras
Uwe Nagel (University of Kentucky) Alexander Duals of Symmetric Simplicial Complexes and Stanley-Reisner Ideals
Thu Hien Nguyen (Julius Maximilian University of Würzburg) Some simple conditions for entire functions to have only real zeros
Daniel Perrucci (University of Buenos Aires) Zero sets of real multi-affine hypersurfaces
Sven Polak (Tilburg University) Symmetry reduction to optimize a graph-based polynomial from queuing theory
Claudiu Raicu (University of Notre Dame) Stable cohomology of line bundles on flag varieties
Victor Reiner (University of Minnesota) Stirling numbers and Koszul algebras with symmetry
Mohab Safey El Din (Sorbonne Université) Enhanced real root finding algorithms for symmetric invariant polynomial systems
Leonie Scheeren (Aachen University) Conjugate weight enumerators and invariant theory
Tim Seynnaeve (Catholic University of Leuven) Signature Tensors of Paths and Their Representation Theory
Markus Szymik (The University of Sheffield) Symmetries and stable homology computations
Josué Tonelli-Cueto (John Hopkins University) Learning with symmetries and quasisymmetries
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