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Colloquia & Seminars

  1. Special day in differential and difference algebra

    Location: MSRI: Simons Auditorium
    Speakers: Alexandru Buium (University of New Mexico), Lucia Di Vizio (Université Versailles/Saint Quentin-en-Yvelines), James Freitag (University of California, Berkeley), Charlotte Hardouin (Université de Toulouse III (Paul Sabatier)), Rahim Moosa (University of Waterloo), Thomas Scanlon (University of California, Berkeley), Michael Singer (North Carolina State University)

    9:30 - 10:20 am: Alexandru Buium (U. New Mexico) Curvature on the integers

    Abstract: The talk explains how one can introduce an arithmetic analogue of connection and curvature on principal bundles (over flat space). In the arithmetic  framework functions on manifolds are replaced by integer numbers, partial derivatives  are replaced by Fermat quotients with respect to different primes, and linear connections with values in classical Lie algebras are replaced by non-linear objects naturally attached to the corresponding classical groups.

    Our main results are vanishing/non-vanishing theorems for the curvatures of these connections. This is joint work in progress, with Malik Barrett.

    10:30 - 11:20 am: James Freitag (UC Berkeley) Superstability and central extensions of algebraic groups

    Abstract: Altinel and Cherlin proved that any perfect central extension of an algebraic group over an algebraically closed field which happens to be of finite Morley rank as a group is actually a finite central extension and is itself an algebraic group. We will prove a generalization of their result in the infinite rank setting with an additional hypothesis on the center of the group, while giving an example which shows the necessity of this hypothesis. The inspiration for the work comes from differential algebra; namely, this work answers a question of Cassidy and Singer in the (more general) setting of superstable groups.

    11:30 am - 12:20 pm: Rahim Moosa (U. Waterloo) Differential-algebraic tangent spaces and internality to the constants

    Abstract: Motivated on the one hand by phenomena in bimeromorphic geometry (so compact complex manifolds) and on the other by model-theoretic consideration arising from the study of the canonical base property, I asked some years ago whether the Kolchin tangent bundle of a finite dimensional differential-algebraic variety has the property that the restriction to any C-algebraic subvariety is C-algebraic. Here C is the field of constants in a saturated differentially closed field of characteristic zero, and C-algebraic means being generically in finite-to-finite correspondence with the C-points of an algebraic variety over C. Actually, one is interested not only in the Kolchin tangent bundle but also its higher order incarnations appearing in the work of Pillay and Ziegler. In recent work with Zoé Chatzidakis and Matthew Harrison-Trainor, we show that while the answer to the question as stated is no, an appropriate generic formulation has a positive answer. I will give motivations for the problem and discuss some aspects of its solution.

    2:00 - 2:50 pm: Thomas Scanlon (UC Berkeley) Algebraic differential equations from covering maps

    Abstract: We show as a consequence of two model theoretic theorems, elimination of imaginaries in differentially closed fields and the Peterzil-Starchenko GAGA theorem, that in wide generality for analytic covering maps π :U → X(C) of algebraic varieties that there are differential constructible functions χ defined on X which "nearly invert'' π in the same way in which the logarithmic derivative nearly inverts the exponential function.   As consequences we deduce the finite dimensionality of the Kolchin closure of the Hecke orbits of arbitrary points in moduli spaces of abelian varieties generalizing a theorem of Buium.

    3:00 - 3:20pm : Tea break

    3:20 -4:05pm: Michael Singer (U. North Carolina) Direct and Inverse Problems for Parameterized Linear Differential Equations

    Abstract: I will give an introduction to a Galois theory for differential equations of the form Y_x = A(x,t)Y where A(x,t) is an mxm matrix with entries that are functions of the principal variable x and the parameter t . The Galois groups in this theory are linear differential algebraic groups, that is, groups of mxm matrices whose entries are functions of t satisfying some fixed set of differential equations. This theory has been successfully used to decide when solutions of such equations satisfy additional differential equations with respect to the parameters and in particular questions of integrability. I will describe recent work of Minchenko, Ovchinnikov and myself concerning the direct problem calculating the Galois group of a given equation) and the inverse problem (which groups can occur as Galois groups).

    4:10 - 4:55pm: Lucia di Vizio (Versailles Saint Quentin) Linear Differential Equations with a discrete parameter: Theory

    5:00 - 5:45pm: Charlotte Hardouin (Toulouse) Linear Differential Equations with a discrete parameter: Applications

    Common abstract: We will discuss an analogous situation to the one described by M. Singer, apart from the fact that we consider a discrete parameter. In this case the theory produce a Galois group, which is a difference scheme and can be non-\sigma-reduced. We will explain how we get around this difficulty and the implications on the theory.

    Updated on Apr 18, 2014 09:01 AM PDT
  2. Eisenbud Seminar: Algebraic Geometry and Commutative Algebra

    Location: Evans 939
    Speakers: David Berlekamp, David Eisenbud (MSRI - Mathematical Sciences Research Institute)

    3:45: David Eisenbud: Assymptotic Boij-Soederberg theory and resolutions over complete intersections of quadrics

    I'll describe the cone of resolutions of high syzygies over a complete intersection of quadrics, and other related phenomena.

    5:00 David Berlekamp: Castelnuovo-Mumford regularity and log-canonical thresholds

    The regularity of an ideal is a measure of its computational complexity.  The log-canonical threshold is a measure of singularity.  Not surprisingly, these things are related - the log-canonical threshold of an ideal sheaf on projective space is (sharply) bounded below by the inverse of its regularity.  This and related bounds are worked out with multiplier ideals in recent work of Kuronya and Pintye.  I will attempt to explain what all of these words mean, and how this is done.  

    Created on Feb 10, 2014 08:42 AM PST
  3. Berkeley Topology Seminar: Part II: Main Talk - A variant of Rohlin's Theorem: on eta cubed

    Location: 3 Evans Hall
    Speakers: Michael Hill (University of Virginia)

    Rohlin's theorem on the signature of Spin 4-manifolds can be restated in terms of the connection between real and complex K-theory given by homotopy fixed points. This comes from a bordism result about Real manifolds versus unoriented manifolds, which in turn, comes from a C2-equivariant story. I'll describe a surprising analogue of this for
    larger cyclic 2 groups, showing that the element eta cubed is never detected! In particular, for any bordism theory orienting these generalizations of Real manifolds, the three torus is always a boundary.

    Created on Apr 17, 2014 04:55 PM PDT
  1. AT Research Seminar Pre-Talk: The Dold-Kan correspondence and commutative monoids

    Location: MSRI: Simons Auditorium
    Speakers: Birgit Richter (Universität Hamburg)

    Over a field in characteristic zero commutative dgas are well-behaved; otherwise they are not. For instance there isn't a
    right-induced model structure on them in the general case. I'll explain some of these issues and advertise symmetric sequences to repair that defect.

    Updated on Apr 17, 2014 04:57 PM PDT
  2. AT Research Seminar: An algebraic model for commutative HZ-algebras.

    Location: MSRI: Simons Auditorium
    Speakers: Birgit Richter (Universität Hamburg)

    Eilenberg-Mac Lane spectra represent singular cohomology and they allow for rather algebraic considerations in stable homotopy theory. Shipley proved that there is a Quillen equivalence between algebras over the Eilenberg-Mac Lane spectrum of the integers, HZ, and differential graded rings. I'll talk about ongoing work with her where we aim at extending her result to commutative HZ-algebras. This builds on a Dold-Kan type theorem for commutative monoids in symmetric sequences.

    Updated on Apr 17, 2014 04:58 PM PDT
  3. AT Postdoc Seminar: The Mirror Symmetry Conjecture and Cobordisms

    Location: MSRI: Baker Board Room
    Speakers: Hiro Tanaka (Harvard University)

    This talk--aimed for a general audience of neither topologists nor model theorists--will discuss applications of cobordisms to Kontsevich's mirror symmetry conjecture. We'll begin by stating a rough version of the
    conjecture, which builds a bridge between symplectic geometry on one hand, and on the other hand, algebraic geometry over the complex numbers. We then discuss how the theory of cobordisms, which studies when two manifolds can be the boundary of another manifold, sheds light on how to generalize the mirror symmetry conjecture, while giving us information about objects in symplectic geometry. (For example, two Lagrangians related by a compact cobordism are equivalent in the Fukaya category.)

    Updated on Apr 17, 2014 05:00 PM PDT
  4. Logic Colloquium: The Differential Field of Transseries

    Location: UC Berkeley, 60 Evans Hall
    Speakers: Lou van den Dries (University of Illinois at Urbana-Champaign)

    Transseries originated some 25 years ago, mainly in Ecalle's work, but also independently in the study of Tarski's problem on the field of reals with exponentiation. Some 20 years ago I formulated some conjectures about the differential field of transseries, and started exploring its model-theoretic properties, first jointly with Matthias Aschenbrenner, and a few years later also in collaboration with Joris van der Hoeven. Around 2011 we finally saw a clear path towards a proof, sharpening the conjectures in the meantime. In the last few weeks we finished the job, with one proviso: as part of a division of labor and for lack of time, some final details have only been checked by some of us, but not yet by all three of us. In any case, I will motivate these conjectures, and give an account of their status.

    Created on Apr 22, 2014 12:04 PM PDT
  5. MT Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Updated on Apr 18, 2014 12:49 PM PDT
  6. MSRI/Evans Lecture: The (un)reasonable effectiveness of model theory in mathematics

    Location: 60 Evans Hall
    Speakers: Carol Wood (Wesleyan University)

    The talk will be built around  examples of how model theory informs our understanding in areas of mathematics such as algebra, number theory, algebraic geometry and analysis. The model theory behind these applications includes concepts such as compactness, definability, stability and o-minimality. However, we assume  no special expertise in model theory, but rather aim  to illustrate the kinds  of  mathematical questions for which a model theoretical perspective has proven to be useful.

    Updated on Apr 15, 2014 11:58 AM PDT
  7. Conformal Field Theory

    Location: MSRI: Baker Board Room
    Created on Feb 19, 2014 08:18 AM PST
  8. Eisenbud Seminar: Algebraic Geometry and Commutative Algebra

    Location: Evans 939

    Speaker: Zvi Rosen (UC Berkeley)
    Title:   Computing Algebraic Matroids

    Abstract: Algebraic matroids characterize the combinatorial structure of an algebraic variety. By decorating the matroid with circuit polynomials and base degrees, we capture even more information about the variety and its coordinate projections.  In this talk, we will introduce algebraic matroids, discuss algorithms for their computation, and present some motivating examples.


    Speaker: Noah Giansiracusa (UC Berkeley)
    Title:  Equations of Tropical Varieties

    Abstract: I'll discuss joint work with J.H. Giansiracusa (Swansea) in which we study scheme theory over the tropical semiring T, using the notion of semiring schemes provided by Toen-Vaquie, Durov, or Lorscheid. We define tropical hypersurfaces in this setting and a tropicalization functor that sends closed subschemes of a toric variety over a field with non-archimedean valuation to closed subschemes of the corresponding toric variety over T. Upon passing to the set of \mathbb{T}-valued points this yields Kajiwara-Payne's extended tropicalization functor. We prove that the Hilbert polynomial of any projective subscheme is preserved by our tropicalization functor, so the scheme-theoretic foundations developed here reveal a hidden flatness in the degeneration sending a variety to its tropical skeleton.

    Created on Feb 10, 2014 08:42 AM PST
  9. AT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Feb 14, 2014 08:56 AM PST
  10. MT Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Created on Feb 06, 2014 09:23 AM PST
  11. AT Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Speakers: Vesna Stojanoska (Massachusetts Institute of Technology)
    Created on Feb 07, 2014 09:36 AM PST
  12. Conformal Field Theory

    Location: MSRI: Baker Board Room
    Created on Feb 19, 2014 08:18 AM PST
  13. AT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Feb 14, 2014 08:57 AM PST
  14. MT Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Created on Feb 06, 2014 09:23 AM PST
  15. AT Postdoc Seminar

    Location: MSRI: Simons Auditorium
    Speakers: Joseph Hirsh (Massachusetts Institute of Technology)
    Created on Feb 07, 2014 09:37 AM PST
  16. AT Seminar

    Location: MSRI: Simons Auditorium
    Speakers: Alexei Kitaev (Kavli Institute for Theoretical Physics)
    Created on Apr 14, 2014 09:17 AM PDT
  17. Conformal Field Theory

    Location: MSRI: Baker Board Room
    Created on Feb 19, 2014 08:23 AM PST
  18. AT Research Seminar

    Location: MSRI: Baker Board Room
    Created on Feb 14, 2014 08:57 AM PST
  19. Conformal Field Theory

    Location: MSRI: Baker Board Room
    Created on Feb 19, 2014 08:24 AM PST
  20. AT Research Seminar

    Location: MSRI: Simons Auditorium
    Created on Feb 14, 2014 08:58 AM PST

Past Seminars

  1. Seminar MT Postdoc Seminar

    Created on Feb 06, 2014 09:21 AM PST
There are more then 30 past seminars. Please go to Past seminars to see all past seminars.