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Current Colloquia & Seminars

  1. MT Research Seminar: Tameness and coincidence of dimensions in expansions of the real field

    Location: MSRI: Simons Auditorium
    Speakers: Chris Miller (Ohio State University)

    Philipp Hieronymi and I have recently established that if E is a boolean combination of open subsets of real euclidean n-space, and the expansion of the real field by E does not define the set of all integers, then the Lebesgue covering dimension of E is equal to its Assouad dimension (hence also to its Hausdorff and packing dimensions, and also to its upper Minkowski dimension if E is bounded). The proof is too technical to attempt in a seminar talk, but the result is surprisingly easy to prove for the case n=1. Indeed, I will prove the

    (possibly) stronger result that all reasonable (in a way that I will make precise) Lipschitz invariant metric dimensions then coincide on E.

    Updated on Apr 11, 2014 01:54 PM PDT
  2. Commutative Algebra and Algebraic Geometry

    Location: UC Berkeley, 939 Evans Hall
    Speakers: I. Martin Isaacs, François Loeser (Université de Paris VI (Pierre et Marie Curie))

    3:45 I. Martin Isaacs: Orbit sizes and an analog of the Alperin weight conjecture.

    Let G be a finite group acting on a finite vector space V. Then G also acts on the dual space of V, and by general principles, the numbers of orbits in these two actions are equal. Although the sizes of the orbits in these actions generally do not agree, there are, nevertheless, some subtle relationships among these orbit sizes. The proof of the relevant theorem is not hard, but it involves a formula that is formally identical to the still unproved Alperin weight conjecture, which will be explained.

    5:00 Francois Loeser: Monodromy and the Lefschetz fixed point formula
    In 2002, in joint work with Jan Denef, we gave a formula expressing the Lefschetz numbers of iterates of the monodromy in terms of arc spaces  using direct computation on a resolution. In this talk we shall present a different proof, relying on a Lefschetz fixed point formula and non-archimedean geometry. This is joint work with Ehud Hrushovski.
    Created on Apr 14, 2014 11:22 AM PDT
  3. Berkeley Model Theory Seminar: Pseudo Real Closed fields and NTP2

    Location: MSRI: Simons Auditorium
    Speakers: Samaria Montenegro-Guzman (Université de Paris VII (Denis Diderot))

    The notion of PAC fields has been generalized by Basarab and by Prestel to ordered fields. Prestel defines a field M to be Pseudo Real Closed field (PRC) if M is existentially closed (in the language of rings) in every regular extension L to which all orderings of M extend. Equivalently, if every absolutely irreducible variety defined over M that has a rational point in every real closure of M, has an M-rational point.

    In the first part of the talk I will present a short summary of the required preliminaries on pseudo real closed fields.The main theorem is a positive answer to the conjecture by A. Chernikov, I. Kaplan and P. Simon: If M is a PRC field, then Th(M) is NTP2 if and only if M is bounded.

    In the second part of the talk I will give a sketch of the proof.

    Updated on Apr 11, 2014 02:01 PM PDT
  4. Introduction to the middle K-theory of group rings and their relevance in topology, Part One: Introductory Talk

    Location: UC Berkeley, 740 Evans Hall
    Speakers: Wolfgang Lueck

    We give a basic introduction to the projective class group of a group ring and the Whitehead group of a group and discuss applications to topology such as Wall's finiteness obstruction, the s-Cobordism Theorem and topological rigidity.

    Created on Apr 14, 2014 11:17 AM PDT
  5. Berkeley Model Theory Seminar: Higher amalgamation and polygroupoids.

    Location: MSRI: Simons Auditorium
    Speakers: John Goodrick

    In simple theory, n-amalgamation is the property that any coherent, independent system of types indexed by proper subsets of {1, ..., n} has a consistent extension. For stable theories, there is a three-way connection (first discovered by Hrushovski) between 4-amalgamation of types, definable groupoids, and the splitting of certain finite covers.

    The present talk reports on joint work with Byunghan Kim and Alexei Kolesnikov which generalizes the equivalence of 4-amalgamation and eliminability of definable groupoids: in a stable theory, if n is minimal such that n-amalgamation fails, then in a mild expansion (adding a predicate for a Morley sequence) the theory interprets a homogeneous, locally finite structure which we call an (n-2)-ary polygroupoid that witnesses the failure of amalgamation. A 2-ary polygroupoid is an ordinary groupoid, and a k-ary polygroupoid has a k-ary "composition" operation which satisfies a generalized associativity law.

    Updated on Apr 11, 2014 02:06 PM PDT
  6. Algebraic K- and L-theory of groups rings and their applications to topology and geometry, Part II: Main Talk

    Location: UC Berkeley, 740 Evans Hall
    Speakers: Wolfgang Lueck

    We give an introduction to the K- and L-theoretic Farrell-Jones Conjecture and discuss its status. e.g, recently it has been proved for all lattices in almost connected Lie groups. We give a panorama of its large variety of applications, for instance to the Novikov Conjecvture about the homotopy invariance of higher signatures, the Borel Conjecture about the
    topological rigidity of aspherical manifolds and to hyperbolic groups with spheres as boundary. Finally we dicsuss some connections to equivariant homotopy and homology for proper actions of infinite groups.

    Created on Apr 14, 2014 11:19 AM PDT