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Algèbre et géométrie

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Aujourd'hui

Un après-midi de sous-groupes aleatoires invariants ou stationaires

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ZOOM: https://us02web.zoom.us/j/81548053762 ID: 815 4805 3762 Mot de passe: G est un Graphe de Cayley du groupe libre à 107 générateurs. Quel est le degré de ce graphe? Tapez le numéro à trois chiffres comme un mot de passe. 15.00 - 15.45    Tsachik Gelander (Weizmann Institute), "Stationary random discrete subgroups of semisimple Lie groups" 16.00 - 16.45     Matthieu Joseph (ENS Lyon), "Allosteric actions of surface groups" 17.15 - 18.00     Yair Hartman (Ben Gurion University), "Intersectional Invariant Random Subgroups" Vous pourrez trouver les résumés sur le site du séminaire: […]

Groups definable in partial differential fields with an automorphism

Sophie Germain salle 1016.

This is a joint work with Ronald Bustamante Medina and Zoé Chatzidakis. In this talk we are interested in differential and difference fields from the model-theoretic point of view. A differential field is a field with a set of commuting derivations and a difference-differential field is a differential field equipped with an automorphism which commutes with the derivations. Cassidy studied definable groups in differentially closed fields, in particular she studied Zariski dense definable subgroups of simple algebraic groups and showed that they are isomorphic to the rational points of an […]

Léonard Pille-Schneider, raconte-moi les espaces hybrides !

En salle W au DMA, ou sur Zoom

Soit X=(X_t) une famille de variétés algébriques complexes paramétrée par le disque épointé, dont les équations ont une singularité méromorphe en t=0. Le but de cet exposé est d'expliquer comment associer à cette famille un espace dit hybride, permettant de voir les variétés complexes X_t dégénérer vers l'espace analytique non-archimédien obtenu en interprétant X comme une variété algébrique sur le corps des séries de Laurent. Je donnerai aussi des applications géométriques de cette construction.

The Kemperman inverse problem

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Let G be a connected locally compact group with a left Haar measure μ, and let A,B ⊆ G be nonempty and compact. Assume further that G is unimodular, i.e., μ is also the right Haar measure; this holds, e.g., when G is compact, a nilpotent Lie group, or a semisimple Lie group. In 1964, Kemperman showed that μ(AB) ≥ min {μ(A)+μ(B), μ(G)} . The Kemperman inverse problem (proposed by Griesmer, Kemperman, and Tao) asks when the equality happens or nearly happens. I will discuss the recent solution of this […]

Not Pfaffian

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This talk describes the connection between /strong minimality/ of the differential equation satisfied by an complex analytic function and the real and imaginary parts of the function being /Pfaffian/. The talk will not assume the audience knows these notions previously, and will attempt to motivate why each of them are important notions in various areas. The connection we give, combined with a theorem of Freitag and Scanlon (2017) provides the answer to a question of Binyamini and Novikov (2017). We also answer a question of Bianconi (2016). We give what […]

NIPn fields part 2: random hypergraphs and NIPn CHIPS transfer

salle 1016 Sophie Germain

A core question in the model theory of fields is to understand how combinatorial patterns and algebraic properties interact. The study of NIPn fields, which can't express the edge relation of random n-hypergraph, is linked to henselianity. In this talk, we use Chernikov and Hils conditions to obtain transfer in some situations, that is, under some algebraic assumptions, it is enough to know that the residue field of a henselian valued field is NIPn in order to known that it is itself NIPn, and we discuss consequences on hypothetical strictly […]

Existentially closed measure-preserving actions of free groups

Sophie Germain salle 1016.

I will discuss a joint work with Alexander Berenstein and Ward Henson, in which we show that the theory of probability algebras with two automorphisms has a model completion, which moreover has quantifier elimination and is stable. We also exhibit two non-isomorphic (but approximately isomorphic) models of the model completion. More generally, we give a sufficient set of conditions for the axiomatizability (in continuous logic) of the existentially closed actions of a free group on a separably categorical, stable structure. I will also mention a number of open questions.

Najib Idrissi, raconte-moi les opérades !

En salle W au DMA, ou sur Zoom

Les opérades sont des objets qui gouvernent des catégories d'algèbres au sens large — par exemple, les algèbres associatives, les algèbres commutatives, ou les algèbres de Lie — qui sont habituellement définies par « opérations génératrices et relations ». Le but de cet exposé est d'introduire la théorie des opérades avec des exemples, et en particulier l'exemple fondateur des opérades des petits disques. J'expliquerai comment les opérades des petits disques permettent d'obtenir des invariants des variétés de deux façons duales : le calcul des plongements et l'homologie de factorisation.

Un après-midi de théorie des groupes

14:00-17:00 Salle W

Le séminaire sera dans salle W et retransmis sur Zoom : ZOOM: https://us02web.zoom.us/j/82070470538 ID: 820 7047 0538 Mot de passe: G est un Graphe de Cayley du groupe libre à 107 générateurs. Quel est le degré de ce graphe? Tapez le numéro à trois chiffres comme un mot de passe. 14.00 - 14.45 Marcin Sabok  (McGill University), "Hyperfiniteness at hyperbolic boundries" 15.00 - 15.45 Juan Paucar (Jussieu), "Coarse embeddings between locally compact groups and quantitative measured equivalence" 16.00 - 16.45 Josh Frisch (ENS), "Characteristic Measures and Minimal Subdynamics" Vous pourrez […]

Curve-excluding fields

salle 1016 Sophie Germain

Consider the class of fields with Char(K)=0 and x^4+y^4=1 has only 4 solutions in K, we show that this class has a model companion, which we denote by curve-excluding fields. Curve-excluding fields provides (counter)examples to various questions. Model theoretically, they are model complete and TP_2. Field theoretically, they are not large and unbounded. We will discuss other aspects such as decidability of such fields. This is joint work with Will Johnson and Erik Walsberg.

Interdefinability and compatibility in certain o-minimal expansions of the real field

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Let us say that a real function f is o-minimal if the expansion (R,f) of the real field by f is o-minimal. A function g is definable from f if g is definable in (R,f). Two o-minimal functions are compatible if there exists an o-minimal expansion M of the real field in which they are both definable. I will discuss the o-minimality, the interdefinability and the compatibility of two special functions, Euler's Gamma and Riemann's Zeta, restricted to the reals. If time allows it, I will present a general technique […]

Tameness beyond o-minimality (in expansions of the real ordered additive group)

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In his influential paper “Tameness in expansions of the real field” from the early 2000s, Chris Miller wrote: “ What might it mean for a first-order expansion of the field of real numbers to be tame or well behaved? In recent years, much attention has been paid by model theorists and real-analytic geometers to the o-minimal setting: expansions of the real field in which every definable set has finitely many connected components. But there are expansions of the real field that define sets with infinitely many connected components, yet are […]