BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Département de mathématiques et applications - ECPv6.2.2//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
X-WR-CALNAME:Département de mathématiques et applications
X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
REFRESH-INTERVAL;VALUE=DURATION:PT1H
X-Robots-Tag:noindex
X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Europe/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20220327T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20221030T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220510T160000
DTEND;TZID=Europe/Paris:20220510T173000
DTSTAMP:20260405T185806
CREATED:20220502T091359Z
LAST-MODIFIED:20220502T115516Z
UID:15549-1652198400-1652203800@www.math.ens.psl.eu
SUMMARY:Existential theories of henselian fields\, parameters welcome
DESCRIPTION:The first-order theories of local fields of positive characteristic\, i.e. fields of Laurent series over finite fields\, are far less well understood than their characteristic zero analogues: the fields of real\, complex and p-adic numbers. On the other hand\, the existential theory of an equicharacteristic henselian valued field in the language of valued fields is controlled by the existential theory of its residue field. One is decidable if and only if the other is decidable. When we add a parameter to the language\, things get more complicated. Denef and Schoutens gave an algorithm\, assuming resolution of singularities\, to decide the existential theory of rings like Fp[[t]]\, with the parameter t in the language. I will discuss their algorithm and present a new result (from ongoing work\, with Dittmann and Fehm) that weakens the hypothesis to a form of local uniformization\, and which works in greater generality.
URL:https://www.math.ens.psl.eu/evenement/tba-12/
LOCATION:Sophie Germain salle 1016
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220513T110000
DTEND;TZID=Europe/Paris:20220513T123000
DTSTAMP:20260405T185806
CREATED:20220421T115851Z
LAST-MODIFIED:20220503T103102Z
UID:15539-1652439600-1652445000@www.math.ens.psl.eu
SUMMARY:Complexity of l-adic sheaves
DESCRIPTION:To a complex of l-adic sheaves on a quasi-projective variety one associate an integer\, its complexity. The main result on the complexity is that it is continuous with tensor product\, pullback and pushforward\, providing effective version of the constructibility theorems in l-adic cohomology. Another key feature is that the complexity bounds the dimensions of the cohomology groups of the complex. This can be used to prove equidistribution results for exponential sums over finite fields. This is due to Will Sawin\, written up in collaboration with Javier Fresán and Emmanuel Kowalski.
URL:https://www.math.ens.psl.eu/evenement/complexity-of-l-adic-sheaves/
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220513T141500
DTEND;TZID=Europe/Paris:20220513T154500
DTSTAMP:20260405T185806
CREATED:20220421T120028Z
LAST-MODIFIED:20220503T103029Z
UID:15542-1652451300-1652456700@www.math.ens.psl.eu
SUMMARY:Skew-invariant curves and algebraic independence
DESCRIPTION:A σ-variety over a difference field (K\,σ) is a pair (X\,φ) consisting of an algebraic variety X over K and φ:X → X^σ is a regular map from X to its transform Xσ under σ. A subvariety Y ⊆ X is skew-invariant if φ(Y) ⊆ Y^σ. In earlier work with Alice Medvedev we gave a procedure to describe skew-invariant varieties of σ-varieties of the form (𝔸^n\,φ) where φ(x_1\,…\,x_n) = (P_1(x_1)\,…\,P_n(x_n)). The most important case\, from which the others may be deduced\, is that of n = 2. In the present work we give a sharper description of the skew-invariant curves in the case where P_2 = P_1^τ for some other automorphism of K which commutes with σ. Specifically\, if P in K[x] is a polynomial of degree greater than one which is not eventually skew-conjugate to a monomial or ± Chebyshev (i.e. P is “nonexceptional”) then skew-invariant curves in (𝔸^2\,(P\,P^τ)) are horizontal\, vertical\, or skew-twists: described by equations of the form y = α^{σ^n} ∘ P^{σ^{n-1}} ∘ ⋅⋅⋅ ∘ P^σ ∘ P(x) or x = β^{σ{-1}}∘ P^{τ σ^{-n-2}}∘ P^{τ σ^{-n-3}}∘ ⋅⋅⋅ ∘ P^τ(y) where P = α ∘ β and P^τ = α^{σ^{n+1}}∘ β^{σ^n}} for some integer n.
URL:https://www.math.ens.psl.eu/evenement/skew-invariant-curves-and-algebraic-independence/
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220513T160000
DTEND;TZID=Europe/Paris:20220513T173000
DTSTAMP:20260405T185806
CREATED:20220503T102922Z
LAST-MODIFIED:20220503T102922Z
UID:15562-1652457600-1652463000@www.math.ens.psl.eu
SUMMARY:Sharp o-minimality: towards an arithmetically tame geometry
DESCRIPTION:Over the last 15 years a remarkable link between o-minimality and algebraic/arithmetic geometry has been unfolding following the discovery of Pila-Wilkie’s counting theorem and its applications around unlikely intersections\, functional transcendence etc. While the counting theorem is nearly optimal in general\, Wilkie has conjectured a much sharper form in the structure R_exp. There is a folklore expectation that such sharper bounds should hold in structures « coming from geometry »\, but for lack of a general formalism explicit conjectures have been made only for specific structures.\nI will describe a refinement of the standard o-minimality theory aimed at capturing the finer « arithmetic tameness » that we expect to see in structures coming from geometry. After presenting the general framework I will discuss my result with Vorobjov showing that the restricted Pfaffian structure is sharply o-minimal\, and how this was used in our recent work with Novikov and Zack to prove Wilkie’s conjecture for the restricted Pfaffian structure and for Wilkie’s original case of R_exp. I will also discuss some conjectures on the construction of larger sharply o-minimal structures\, and some partial results in this direction. Finally I will explain the crucial role played by these results in my recent work with Schmidt and Yafaev on Galois orbit lower bounds for CM points in general Shimura varieties\, and subsequently in the recent resolution of general André-Oort conjecture by Pila-Shankar-Tsimerman-(Esnault-Groechenig).
URL:https://www.math.ens.psl.eu/evenement/sharp-o-minimality-towards-an-arithmetically-tame-geometry/
LOCATION:Salle W (ENS) et Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220531T160000
DTEND;TZID=Europe/Paris:20220531T170000
DTSTAMP:20260405T185806
CREATED:20220502T091657Z
LAST-MODIFIED:20220502T091657Z
UID:15552-1654012800-1654016400@www.math.ens.psl.eu
SUMMARY:Le théorème du corps gauche de Zilber / Zilber's Skew-Field Theorem (joint with Frank Wagner)
DESCRIPTION:Le théorème du corps est l’observation qu’un groupe de rang de Morley fini connexe\, résoluble\, et non nilpotent\, interprète un corps infini. Par d’autres résultats classiques\, le corps est commutatif et même algébriquement clos.\nLe théorème du corps est souvent vu comme corollaire du «théorème d’engendrement par des indécomposables» mais c’est une erreur car il en est indépendant. Il a quelques variantes\, des théorèmes de linéarisation d’actions de groupes.\nJe donnerai un énoncé qui généralise naturellement tous les résultats «à la Zilber». C’est un résultat de linéarisation de bimodules\, dans un contexte plus général que les théories de rang de Morley fini. En général on interprète un corps gauche.\nPrérequis : notion de définissabilité ; «lemme de Schur» en théorie des représentations (l’anneau des endomorphismes qui commutent avec une représentation irréductible est en fait un corps gauche). \nZilber’s Field Theorem ZFT is the observation that a connected\, soluble\, non-nilpotent group of finite Morley rank interprets an infinite field. By other classical results\, the field is commutative indeed\, and even algebraically closed.\nThe ZFT is often seen as a corollary to Zilber’s `indecomposable generation theorem’; but it actually is independent from it. The ZFT has a couple of variants\, linearisation results for definable group actions.\nI shall give a theorem which generalises naturally all results `à la Zilber’. It is a tool that can linearise bimodule actions\, in a broader context than theories of finite Morley rank. In general it produces a definable skew-field.\nPrerequisites: definable sets; `Schur’s lemma’ from representation theory (the ring of endomorphisms commuting with an irreducible representation\, actually is a skew-field).
URL:https://www.math.ens.psl.eu/evenement/le-theoreme-du-corps-gauche-de-zilber-zilbers-skew-field-theorem-joint-with-frank-wagner/
LOCATION:Sophie Germain salle 1016.
CATEGORIES:Théorie des Modèles et Groupes
END:VEVENT
END:VCALENDAR