BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Département de mathématiques et applications - ECPv6.2.2//NONSGML v1.0//EN
CALSCALE:GREGORIAN
METHOD:PUBLISH
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:20180325T010000
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:20181028T010000
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180119T110000
DTEND;TZID=Europe/Paris:20180119T110000
DTSTAMP:20260408T115925
CREATED:20180119T100000Z
LAST-MODIFIED:20211104T105937Z
UID:8441-1516359600-1516359600@www.math.ens.psl.eu
SUMMARY:Spectral gap and definability
DESCRIPTION:Originating in the theory of unitary group representations\, the notion of spectral gap has played a huge role in many of the deep results in the theory of von Neumann algebras in the last couple of decades. Recently\, with my collaborators\, we are slowly understanding the model-theoretic significance of spectral gap\, in particular its connection with definability. In this talk\, I will discuss a few of our recent observations in this direction and speculate on some further possible developments. I will assume no knowledge of von Neumann algebras nor continuous logic. Various parts of this work are joint with Bradd Hart\, Thomas Sinclair\, and Henry Towsner.
URL:https://www.math.ens.psl.eu/evenement/spectral-gap-and-definability/
LOCATION:Amphitheatre Hermite IHP
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180119T141500
DTEND;TZID=Europe/Paris:20180119T141500
DTSTAMP:20260408T115925
CREATED:20180119T131500Z
LAST-MODIFIED:20211104T105936Z
UID:8439-1516371300-1516371300@www.math.ens.psl.eu
SUMMARY:Effective Chabauty and the Cursed Curve
DESCRIPTION:The Chabauty method often allows one to find the rational points on curves of genus at least 2 over the rationals\, but has a lot of limitations. On a theoretical level\, the Mordell-Weil rank of the Jacobian of the curve has to be strictly smaller than its genus. In practice\, even when this condition is satisfied\, the relevant Coleman integrals can usually only be computed for hyperelliptic curves. We will report on recent work of ours (with different combinations of collaborators) on extending the method to more general curves. In particular\, we will show how one can use an extension of the Chabauty method by Kim to find the rational points on the split Cartan modular curve of level 13\, which is also known as the cursed curve. The talk will be aimed at non-specialists with an interest in number theory.
URL:https://www.math.ens.psl.eu/evenement/effective-chabauty-and-the-cursed-curve/
LOCATION:Institut Henri Poincaré amphi Hermite
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20180119T160000
DTEND;TZID=Europe/Paris:20180119T160000
DTSTAMP:20260408T115925
CREATED:20180119T150000Z
LAST-MODIFIED:20211104T105937Z
UID:8440-1516377600-1516377600@www.math.ens.psl.eu
SUMMARY:Blurred Complex Exponentiation
DESCRIPTION:Zilber conjectured that the complex field equipped with the exponential function is quasiminimal: every definable subset of the complex numbers is countable or co-countable. If true\, it would mean that the geometry of solution sets of complex exponential-polynomial equations and their projections is somewhat like algebraic geometry. If false\, it is likely that the real field is definable and there may be no reasonable geometric theory of these definable sets.I will report on some progress towards the conjecture\, including a proof when the exponential function is replaced by the approximate version given by exists q\,r in Q [y = e^{x+q+2pi i r}]. This set is the graph of the exponential function blurred by the group exp(Q + 2 pi i Q). We can also blur by a larger subgroup and prove a stronger version of the theorem. Not only do we get quasiminimality but the resulting structure is isomorphic to the analogous blurring of Zilber’s exponential field and to a reduct of a differentially closed field. Reference: Jonathan Kirby\, Blurred Complex Exponentiation\, arXiv:1705.04574
URL:https://www.math.ens.psl.eu/evenement/blurred-complex-exponentiation/
LOCATION:Amphitheatre Hermite IHP
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
END:VCALENDAR