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PRODID:-//Département de mathématiques et applications - ECPv6.2.2//NONSGML v1.0//EN
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X-ORIGINAL-URL:https://www.math.ens.psl.eu
X-WR-CALDESC:évènements pour Département de mathématiques et applications
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X-PUBLISHED-TTL:PT1H
BEGIN:VTIMEZONE
TZID:Europe/Paris
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:20220327T010000
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BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20221030T010000
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END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220510T110000
DTEND;TZID=Europe/Paris:20220510T120000
DTSTAMP:20260525T095206
CREATED:20220502T094743Z
LAST-MODIFIED:20220502T094757Z
UID:15555-1652180400-1652184000@www.math.ens.psl.eu
SUMMARY:Euler equations via sparseness and local approximations
DESCRIPTION:We study Euler solutions via novel function spaces constructed using sparseness and local approximations. In particular\, we incorporate Tadmor’s scale of regularity spaces (2001) to our framework and applying interpolation/extrapolation methods we give a new approach to convergence of approximate Euler solutions. This is joint work with Mario Milman.
URL:https://www.math.ens.psl.eu/evenement/euler-equations-via-sparseness-and-local-approximations/
LOCATION:Jussieu —  salle 15-16-309\, 4 Place Jussieu\, Paris\, 75005\, France
CATEGORIES:Séminaire Analyse non linéaire et EDP
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220510T160000
DTEND;TZID=Europe/Paris:20220510T173000
DTSTAMP:20260525T095206
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
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220511T130000
DTEND;TZID=Europe/Paris:20220511T143000
DTSTAMP:20260525T095206
CREATED:20220309T154505Z
LAST-MODIFIED:20220509T072656Z
UID:15398-1652274000-1652279400@www.math.ens.psl.eu
SUMMARY:Un piano parfait ou une introduction aux mots sturmiens
DESCRIPTION:Olga Paris-Romaskevich\nUn piano parfait ou une introduction aux mots sturmiens\nPrenez le clavier d’un piano et écrivez (mentalement !) sur chacune de ses touches les mois de l’année\, en commençant par le mois janvier sur la note fa. Fa dièse serait annotée comme février\, puis sol comme mars\, etc. Vous bouclerez sans surprise\, comme il y a 12 notes dans une octave. Mais vous vous apercevrez que les cinq mois courts de l’année se retrouveront tous sur les notes noires. Dans cet exposé\, nous allons voir que cela ne pourrait pas être autrement et comment la configuration « de ce type » est unique. \n\n\nCet exposé est une introduction aux mots sturmiens\, et leur interprétation géométrique\, dynamique et combinatoire. Tout cela\, en suivant Bernoulli\, Markov\, Morse\, Hedlund\, Kontsevich…\n\n\n\n\n 
URL:https://www.math.ens.psl.eu/evenement/expose-dolga-paris-romaskevich/
LOCATION:amphi Galois NIR
CATEGORIES:ANNÉE 2021-2022,Séminaire Des mathématiques
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220512T113000
DTEND;TZID=Europe/Paris:20220512T123000
DTSTAMP:20260525T095206
CREATED:20220530T111420Z
LAST-MODIFIED:20220530T112029Z
UID:15615-1652355000-1652358600@www.math.ens.psl.eu
SUMMARY:Effective dynamics and critical scaling for Stochastic Gradient Descent in high dimensions -  Gerard Ben Arous (New York University)
DESCRIPTION:Gerard Ben Arous (New York University)\n \nTitle: Effective dynamics and critical scaling for Stochastic Gradient Descent in high dimensions\n \nAbstract: SGD in high dimension is a workhorse for high dimensional statistics and machine learning\, but understanding its behavior in high dimensions is not yet a simple task. We study here the limiting ‘effective’ dynamics of some summary statistics for SGD in high dimensions\, and find interesting and new regimes\, i.e. not the expected one given by the population gradient flow. We find that a new corrector term is needed and that the phase portrait of these dynamics is substantially different from what would be predicted using the classical approach including for simple tasks. (joint work with Reza Gheissari (UC Berkeley) and Aukosh Jagannath (Waterloo))
URL:https://www.math.ens.psl.eu/evenement/learning-to-predict-complex-outputs-a-kernel-view-gerard-ben-arous-new-york-university/
LOCATION:Amphi Jaurès (29 Rue d’Ulm)
CATEGORIES:Séminaire Data de l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220513T110000
DTEND;TZID=Europe/Paris:20220513T123000
DTSTAMP:20260525T095206
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:20260525T095206
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:20260525T095206
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:20220517T093000
DTEND;TZID=Europe/Paris:20220517T123000
DTSTAMP:20260525T095206
CREATED:20211109T065054Z
LAST-MODIFIED:20220502T095016Z
UID:14481-1652779800-1652790600@www.math.ens.psl.eu
SUMMARY:Formes normales et EDPs hamiltoniennes
DESCRIPTION:Les solutions de petites amplitudes d’équations aux dérivées partielle nonlinéaires dispersives sur un compact sans bord (par exemple un tore ou une sphère) sont soumises à deux effets concurrents : \n\nla dispersion des ondes\, conséquence du fait que les ondes planes solutions de la partie linéaire de l’équation voyagent avec des vitesses différentes (les ondes s’éloignent les unes des autres)\nla compacité du domaine qui incite à l’interaction via la non-linéarité (les ondes sont amenées à se revoir souvent !).\n\nQui gagne ? La dynamique en temps long va-t-elle vers la stabilité ou la turbulence ? Nous essaierons de répondre (partiellement) à ces questions à travers des méthodes de formes normales dans le cadre des EDPs Hamiltoniennes. \nDans la première partie\, je donnerai un aperçu du théorème de forme normale de Birkhoff en dimension finie qui permet d’établir\, sous certaines conditions de non résonances\, la stabilité sur des temps longs d’un point d’équilibre elliptique. J’expliquerai comment le passage d’un tel résultat en dimension infinie conduit à des résultats de stabilité pour des EDPs hamiltoniennes\, en particulier l’équation de Schrödinger non linéaire. \nDans la seconde partie\, je donnerai les résultats récents obtenus avec Joackim Bernier concernant la stabilité en faible régularité.
URL:https://www.math.ens.psl.eu/evenement/formes-normales-et-edps-hamiltoniennes/
LOCATION:Jussieu —  salle 15-16-309\, 4 Place Jussieu\, Paris\, 75005\, France
CATEGORIES:Séminaire Analyse non linéaire et EDP
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220524T110000
DTEND;TZID=Europe/Paris:20220524T120000
DTSTAMP:20260525T095206
CREATED:20220530T095159Z
LAST-MODIFIED:20220530T095159Z
UID:15609-1653390000-1653393600@www.math.ens.psl.eu
SUMMARY:Gabriel Peyré: Introduction au transport optimal.
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/gabriel-peyre-introduction-au-transport-optimal/
LOCATION:DMA Salle W
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220531T110000
DTEND;TZID=Europe/Paris:20220531T120000
DTSTAMP:20260525T095206
CREATED:20220530T095052Z
LAST-MODIFIED:20220530T095052Z
UID:15607-1653994800-1653998400@www.math.ens.psl.eu
SUMMARY:Carlo Mariconda: Le problème classique du calcul des variations: nouveaux résultats sur les conditions nécessaires\, la régularité des minima et des suites minimisantes.
DESCRIPTION:
URL:https://www.math.ens.psl.eu/evenement/carlo-mariconda-le-probleme-classique-du-calcul-des-variations-nouveaux-resultats-sur-les-conditions-necessaires-la-regularite-des-minima-et-des-suites-minimisantes/
LOCATION:ENS – salle W\, 45 rue d'Ulm\, Paris\, 75005\, France
CATEGORIES:Séminaire informel de probabilités
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20220531T160000
DTEND;TZID=Europe/Paris:20220531T170000
DTSTAMP:20260525T095206
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
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