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X-WR-CALNAME:Département de mathématiques et applications
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DTSTART:20200329T010000
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DTSTART;TZID=Europe/Paris:20201112T103000
DTEND;TZID=Europe/Paris:20201112T115000
DTSTAMP:20260407T190613
CREATED:20201112T093000Z
LAST-MODIFIED:20211104T121624Z
UID:14111-1605177000-1605181800@www.math.ens.psl.eu
SUMMARY:Cohomology of algebraic varieties over non-archimedean fields
DESCRIPTION:I will report on a joint work with Mário Edmundo and Jinhe Ye in which we introduced a sheaf cohomology theory for algebraic varieties over non-archimedean fields based on Hrushovski-Loeser spaces. After informally framing our main results with respect to classical statements\, I will discuss some details of our construction and the main difficulties arising in this new context. If time allows\, I will further explain how our results allow us to recover results of V. Berkovich on the sheaf cohomology of the analytification of an algebraic variety over a rank 1 complete non-archimedean field.
URL:https://www.math.ens.psl.eu/evenement/cohomology-of-algebraic-varieties-over-non-archimedean-fields-2/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201113T090000
DTEND;TZID=Europe/Paris:20201113T102000
DTSTAMP:20260407T190613
CREATED:20201113T080000Z
LAST-MODIFIED:20211104T141207Z
UID:8558-1605258000-1605262800@www.math.ens.psl.eu
SUMMARY:The étale-open topology
DESCRIPTION:Fix an abstract field K. For each K-variety V\, we will define an étale-open topology on the set V(K) of rational points of V. This notion uniformly recovers (1) the Zariski topology on V(K) when K is algebraically closed\, (2) the analytic topology on V(K) when K is the real numbers\, (3) the valuation topology on V(K) when K is almost any henselian field. On pseudo-finite fields\, the étale-open topology seems to be new\, and has some interesting properties.The étale-open topology is mostly of interest when K is large (also known as ample). On non-large fields\, the étale-open topology is discrete. In fact\, this property characterizes largeness. Using this\, one can recover some well-known facts about large fields\, and classify the model-theoretically stable large fields. It may be possible to push these arguments towards a classification of NIP large fields. Joint work with Chieu-Minh Tran\, Erik Walsberg\, and Jinhe Ye.
URL:https://www.math.ens.psl.eu/evenement/the-etale-open-topology/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201113T103000
DTEND;TZID=Europe/Paris:20201113T115000
DTSTAMP:20260407T190613
CREATED:20201113T093000Z
LAST-MODIFIED:20211104T141149Z
UID:8559-1605263400-1605268200@www.math.ens.psl.eu
SUMMARY:Belles paires of valued fields and analytification
DESCRIPTION:In their work\, Hrushovski and Loeser proposed the space V̂ of generically stable types concentrating on V to study the homotopy type of the Berkovich analytification of V. An important feature of V̂ is that it is canonically identified as a projective limit of definable sets in ACVF\, which grants them tools from model theory. In this talk\, we will give a brief introduction to this object and present an alternative approach to internalize various spaces of definable types\, motivated by Poizat’s work on belles paires of stable theories. Several results of interest to model theorists will also be discussed. Particularly\, we recover the space V̂ is strict pro-definable and we propose a model-theoretic counterpart Ṽ of Huber’s analytification. Time permitting\, we will discuss some comparison and lifting results between V̂ and Ṽ. This is a joint project with Pablo Cubides Kovacsics and Martin Hils.
URL:https://www.math.ens.psl.eu/evenement/belles-paires-of-valued-fields-and-analytification/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201124T140000
DTEND;TZID=Europe/Paris:20201124T170000
DTSTAMP:20260407T190613
CREATED:20201124T130000Z
LAST-MODIFIED:20211104T134624Z
UID:8561-1606226400-1606237200@www.math.ens.psl.eu
SUMMARY:Après-midi de théorie de groupes
DESCRIPTION:https://us02web.zoom.us/j/83180342864The password is answer to the following question: What is the degree of the standard Cayely graph on 107 generators?14.00-14.45 Alessandro Sisto (Heriot-Watt)\, Cubulation of hulls and bicombings15.00-15.45 Thomas Haettel (Montpellier)\, The coarse Helly property\, hierarchical hyperbolicity and semihyperbolicity16.15-17.00 Mark Hagen (Bristol)\, Wallspaces\, the Behrstock inequality\, and l_1 metrics onasymptotic cones
URL:https://www.math.ens.psl.eu/evenement/apres-midi-de-theorie-de-groupes-10/
LOCATION:Zoom: https://us02web.zoom.us/j/83180342864
CATEGORIES:Séminaire de théorie des groupes à l’ENS
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20201127T090000
DTEND;TZID=Europe/Paris:20201127T100000
DTSTAMP:20260407T190613
CREATED:20201127T080000Z
LAST-MODIFIED:20211104T141134Z
UID:8562-1606467600-1606471200@www.math.ens.psl.eu
SUMMARY:The étale-open topology (suite)
DESCRIPTION:Fix an abstract field K. For each K-variety V\, we will define an “étale-open” topology on the set V(K) of rational points of V. This notion uniformly recovers (1) the Zariski topology on V(K) when K is algebraically closed\, (2) the analytic topology on V(K) when K is the real numbers\, (3) the valuation topology on V(K) when K is almost any henselian field. On pseudo-finite fields\, the étale-open topology seems to be new\, and has some interesting properties.\nThe étale-open topology is mostly of interest when Kis large (also known as ample). On non-large fields\, theétale-open topology is discrete. In fact\, this propertycharacterizes largeness. Using this\, one can recover some well-knownfacts about large fields\, and classify the model-theoretically stablelarge fields. It may be possible to push these arguments towards aclassification of NIP large fields. Joint work with Chieu-Minh Tran\, Erik Walsberg\, and Jinhe Ye.
URL:https://www.math.ens.psl.eu/evenement/the-etale-open-topology-suite/
LOCATION:Zoom
CATEGORIES:Séminaire Géométrie et théorie des modèles
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