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X-WR-CALNAME:Département de mathématiques et applications
X-ORIGINAL-URL:https://www.math.ens.psl.eu
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TZID:Europe/Paris
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DTSTART:20170326T010000
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DTSTART:20171029T010000
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DTSTART;TZID=Europe/Paris:20170210T110000
DTEND;TZID=Europe/Paris:20170210T110000
DTSTAMP:20260412T024915
CREATED:20170210T100000Z
LAST-MODIFIED:20211104T102528Z
UID:8341-1486724400-1486724400@www.math.ens.psl.eu
SUMMARY:Geometric invariants that are encoded in the Newton polygon
DESCRIPTION:Let k be a field and let P be a lattice polygon\, i.e. the convex hull in R^2 of finitely many non-collinear points of Z^2. Let C/k be the algebraic curve defined by a sufficiently generic Laurent polynomial that is supported on P. A result due to Khovanskii states that the geometric genus of C equals the number of Z^2-valued points that are contained in the interior of P. In this talk we will give an overview of various other curve invariants that can be told by looking at the combinatorics of P\, such as the gonality\, the Clifford index\, the Clifford dimension\, the scrollar invariants associated to a gonality pencil\, and in some special cases the canonical graded Betti numbers. This will cover joint work with Filip Cools\, Jeroen Demeyer and Alexander Lemmens.
URL:https://www.math.ens.psl.eu/evenement/geometric-invariants-that-are-encoded-in-the-newton-polygon/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
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BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170210T141500
DTEND;TZID=Europe/Paris:20170210T141500
DTSTAMP:20260412T024915
CREATED:20170210T131500Z
LAST-MODIFIED:20211104T102727Z
UID:8342-1486736100-1486736100@www.math.ens.psl.eu
SUMMARY:Determining finite simple images of finitely presented groups
DESCRIPTION:I will discuss joint work with Martin Bridson and Martin Liebeck which addresses the question: for which collections of finite simple groups does there exist an algorithm that determines the images of an arbitrary finitely presented group that lie in the collection? We prove both positive and negative results. For a collection of finite simple groups that contains infinitely many alternating groups\, or contains classical groups of unbounded dimensions\, we prove that there is no such algorithm. On the other hand\, for a collection of simple groups of fixed Lie type we obtain positive results by using the model theory of finite fields.
URL:https://www.math.ens.psl.eu/evenement/determining-finite-simple-images-of-finitely-presented-groups/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Paris:20170210T160000
DTEND;TZID=Europe/Paris:20170210T160000
DTSTAMP:20260412T024915
CREATED:20170210T150000Z
LAST-MODIFIED:20211104T102728Z
UID:8343-1486742400-1486742400@www.math.ens.psl.eu
SUMMARY:Cell Decomposition for P-minimal structures: a story
DESCRIPTION:P-minimality is a concept that was developed by Haskell and Macpherson as a p-adic equivalent for o-minimality. For o-minimality\, the cell decomposition theorem is probably one of the most powerful tools\, so it is quite a natural question to ask for a p-adic equivalent of this.In this talk I would like to give an overview of the development of cell decomposition in the p-adic context\, with an emphasis on how questions regarding the existence of definable skolem functions have complicated things. The idea of p-adic cell decomposition was first developed by Denef\, for p-adic semi-algebraic structures\, as a tool to answer certain questions regarding quantifier elimination\, rationality and p-adic integration. This first version eventually resulted in a cell decomposition theorem for P-minimal structures. This theorem\, proven by Mourgues\, was however dependent on the existence of definable Skolem functions. The second part of the talk will focus a bit more on Skolem functions\, and sketch a generalized version of the Denef-Mourgues theorem that does not rely on the existence of such functions\, by introducing a notion of clustered cells. We will explain the notion\, give an informal sketch of the proof\, and compare with other versions of cell decomposition.
URL:https://www.math.ens.psl.eu/evenement/cell-decomposition-for-p-minimal-structures-a-story/
LOCATION:ENS Salle W
CATEGORIES:Séminaire Géométrie et théorie des modèles
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