The AROMATH seminar will usually happen on Tuesday at 10h30-11h30 every two weeks, except for a few deviations.
The presentations will typically take place at Inria Sophia Antipolis, Byron Blanc 106, and also online.
To join online, at https://cutt.ly/aromath or with a web browser at https://cutt.ly/aromath-web
use meeting ID: 828 5859 7791, passcode: 123
Events in March–August 2024
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- Rémi Prebet (LIP6, CNRS - Sorbonne Université) - Connectivity in real algebraic sets: algorithms and applications
Rémi Prebet (LIP6, CNRS - Sorbonne Université) - Connectivity in real algebraic sets: algorithms and applications Rémi Prebet (LIP6, CNRS - Sorbonne Université) - Connectivity in real algebraic sets: algorithms and applications
14h30-15h30
11 March 2024Computational real algebraic geometry is a field at the interface of mathematics and computer science, that deals with algorithmic problems on real solution sets (which are basic semi-algebraic sets) to systems of polynomial constraints with real coefficients. I will first show how classical subroutines of this field, such as computing one point in each connected component or deciding connectivity queries, can be used to solve challenging problems in robotics, such as cuspidality decisions. Then, I will present new algorithmic improvements to the problem of answering connectivity queries in real algebraic sets by using the notion of roadmaps, which allows to reduce such problems to the case of connectivity queries over real algebraic curves. Throughout the talk, we will pay close attention to the complexity of the algorithms under consideration. This talk gathers joint works with D.Chablat, N.Islam, A.Poteaux, M.Safey El Din, D.Salunkhe, É.Schost and P.Wenger.
Salle Byron Blanc (Y106), Inria -
- Elisa Lorenzo Garcia (Université de Neuchâtel et Université de Rennes 1) - Types de réduction de quartiques planes à partir de leurs octades de Cayley et de leurs invariants
Elisa Lorenzo Garcia (Université de Neuchâtel et Université de Rennes 1) - Types de réduction de quartiques planes à partir de leurs octades de Cayley et de leurs invariants Elisa Lorenzo Garcia (Université de Neuchâtel et Université de Rennes 1) - Types de réduction de quartiques planes à partir de leurs octades de Cayley et de leurs invariants
10h30-12h
12 March 2024Travail en collaboration avec R. van Bommel, J. Docking, V. Dokchitser et R. Lercier.
Dans cet exposé, je présenterai une caractérisation conjecturale (reposant sur un grand nombre d’expériences numériques et quelques résultats théoriques) de la réduction stable des quartiques planes sur des corps locaux en termes de leurs octades de Cayley. Il en découle des critères p-adiques permettant d'identifier efficacement le type de réduction stable parmi les 42 types possibles. Ces critères s'inscrivent dans la lignée de la nouvelle machinerie des « cluster pictures» pour les courbes hyperelliptiques.
Dans un second temps, des critères (pas conjecturels mais partiels) sont fournis pour déterminer le type de réduction en termes des valuations des invariants de Dixmier-Ohno des quartiques planes.
Je commencerai avec une introduction et une motivation détaillées sur le sujet et j’accompagnerai mon exposé de plusieurs exemples.
https://arxiv.org/abs/2309.17381
https://arxiv.org/abs/2401.13902Salle Byron Blanc (Y106), Inria -
- Lucas Gamertsfelder (Inria d'UNICA) - LP Based Bounds for Cesaro and Abel Limits of the Optimal Values in Non-Ergodic Stochastic Systems
Lucas Gamertsfelder (Inria d'UNICA) - LP Based Bounds for Cesaro and Abel Limits of the Optimal Values in Non-Ergodic Stochastic Systems Lucas Gamertsfelder (Inria d'UNICA) - LP Based Bounds for Cesaro and Abel Limits of the Optimal Values in Non-Ergodic Stochastic Systems
14:00-15:30
2 April 2024In this work, we study asymptotic properties of problems of control of stochastic discrete time systems with time averaging and time discounting optimality criteria, and we establish that the Cesaro and Abel limits of the optimal values in such problems can be evaluated with the help of a certain infinite-dimensional linear programming (IDLP) problem and its dual.
Salle Byron Blanc (Y106), Inria -
- Enrico Savi (Université Côte d'Azur) - The Q-algebraicity problem in real algebraic geometry
Enrico Savi (Université Côte d'Azur) - The Q-algebraicity problem in real algebraic geometry Enrico Savi (Université Côte d'Azur) - The Q-algebraicity problem in real algebraic geometry
10h30-12h
29 May 2024In 2020, Parusi´nski and Rond proved that every algebraic set V subset R^n is homeomor-
phic to a Qr-algebraic set V' subset R^n, where Qr denotes the field of real algebraic numbers. Latter
very general result motivates the following open problem:
Q-algebraicity problem: (Parusinski, 2022) Is every algebraic set V subset R^n homeomorphic
to some Q-algebraic set V' subset R^m, with m >= n?
The aim of the talk is to introduce above open problem and to explain how our new approxi-
mation techniques over Q allowed us to provide some classes of real algebraic sets that positively
answer the Q-algebraicity problem.Salle Byron Blanc (Y106), Inria -
- Daniele Taufer (Univ. K. Leuven) - Natural apolar schemes across algebra, geometry, and computations
Daniele Taufer (Univ. K. Leuven) - Natural apolar schemes across algebra, geometry, and computations Daniele Taufer (Univ. K. Leuven) - Natural apolar schemes across algebra, geometry, and computations
10h30-12h
4 June 2024Natural apolar schemes across algebra, geometry, and computations
Abstract: Symmetric order-d tensors (equiv. homogeneous degree-d polynomials) admit infinitely many additive decompositions by means of possibly simpler components.
To each such decomposition, one can canonically associate a zero-dimensional scheme that remembers the core geometrical information about the starting decomposition.
In this talk, we will discuss how to abstractly define and explicitly construct such geometrical objects.
On the theoretical side, we will observe that these schemes enjoy beautiful algebraic properties that are still a field of open research.
Computationally, these features may be exploited to investigate (additive) symmetric tensor decomposition, and we will look at examples of such applications.
This is based on a joint work with A. Bernardi and A. Oneto.Salle Byron Blanc (Y106), Inria -
- Adam Parusiński (UniCA) - Arc-wise analytic triviality
Adam Parusiński (UniCA) - Arc-wise analytic triviality Adam Parusiński (UniCA) - Arc-wise analytic triviality
14h-15h
18 June 2024Arc-wise analytic stratification of real and complex analytic spaces was introduced a few years ago
for the proof of Whitney’s fibering conjecture. It satisfies a strong local triviality property, namely is
locally trivial along each stratum by a trivialization that preserves the real analytic arcs. Its construction is based on Zariski’s algebro-geometric equisingularity.
In this talk I present several applications and discuss related open problems.Salle Byron Blanc (Y106), Inria
