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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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DTSTART:20200329T010000
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DTSTART:20201025T010000
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DTSTART;TZID=Europe/Paris:20201016T090000
DTEND;TZID=Europe/Paris:20201016T102000
DTSTAMP:20260407T204906
CREATED:20201016T070000Z
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UID:8556-1602838800-1602843600@www.math.ens.psl.eu
SUMMARY:Complex Cellular Structures
DESCRIPTION:Real semialgebraic sets admit so-called cellular decomposition\, i.e. representation as a union of convenient semialgebraic images of standard cubes.\nThe Gromov-Yomdin Lemma (later generalized by Pila and Wilkie) proves that the maps could be chosen of C^r-smooth norm at most one\, and the number of such maps is uniformly bounded for finite-dimensional families. This number was not effectively bounded by Yomdin or Gromov\, but itnecessarily grows as r ? ?.\nIt turns out there is a natural obstruction to a naive holomorphic complexification of this result related to the natural hyperbolic metric of complex holomorphic sets.\nWe prove a lemma about holomorphic functions in annulii\, a quantitative version of the great Picard theorem. This lemma allowed us to construct an effective holomorphic version of the cellular decomposition results in all dimensions\, with explicit polynomial bounds on complexity for families of complex (sub)analytic and semialgebraic sets.\nAs the first corollary we get an effective version of Yomdin-Gromov Lemma with polynomial bounds on the complexity\, thus proving a long-standing Yomdin conjecture about tail entropy of analytic maps.Further connection to diophantine applications will be explained in Gal’s talk.
URL:https://www.math.ens.psl.eu/evenement/complex-cellular-structures/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201016T103000
DTEND;TZID=Europe/Paris:20201016T115000
DTSTAMP:20260407T204906
CREATED:20201016T083000Z
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UID:8557-1602844200-1602849000@www.math.ens.psl.eu
SUMMARY:Tame geometry and diophantine approximation
DESCRIPTION:Tame geometry is the study of structures where the definable sets admit finite complexity. Around 15 years ago Pila and Wilkie discovered a deep connection between tame geometry and diophantine approximation\, in the form of asymptotic estimates on the number of rational points in a tame set (as a function of height). This later led to deep applications in diophantine geometry\, functional transcendence and Hodge theory.I will describe some conjectures and a long-term project around a more effective form of tame geometry\, suited for improving the quality of the diophantine approximation results and their applications. I will try to outline some of the pieces that are already available\, and how they should conjecturally fit together. Finally I will survey some applications of the existing results around the Manin-Mumford conjecture\, the Andre-Oort conjecture\, Galois-orbit lower bounds in Shimura varieties\, unlikely intersections in group schemes\, and some other directions (time permitting).
URL:https://www.math.ens.psl.eu/evenement/tame-geometry-and-diophantine-approximation/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201027T090000
DTEND;TZID=Europe/Paris:20201027T120000
DTSTAMP:20260407T204906
CREATED:20201027T080000Z
LAST-MODIFIED:20211104T134742Z
UID:8560-1603789200-1603800000@www.math.ens.psl.eu
SUMMARY:Une matinée de théorie de groupes
DESCRIPTION:https://us02web.zoom.us/j/86850693514The password is answer to the following question: What is the degree of the standard Cayely graph on 107 generators?09.00-09.45 Koji Fujiwara (Kyoto)\, The rates of growth in a hyperbolic group10.00-10.45 Macarena Arenas (Cambridge)\, Linear isoperimetric functions for surfaces in hyperbolic groups11.15-12.00 Indira Chatterji (Nice)\, Tangent bundles on hyperbolic spaces and proper actions on Lp spaces
URL:https://www.math.ens.psl.eu/evenement/une-matinee-de-theorie-de-groupes/
LOCATION:Zoom: https://us02web.zoom.us/j/86850693514
CATEGORIES:Séminaire de théorie des groupes à l’ENS
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