
Special day in differential and difference algebra
Location: MSRI: Simons Auditorium Speakers: Alexandru Buium (University of New Mexico), Lucia Di Vizio (Université Versailles/Saint QuentinenYvelines), 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 nonlinear objects naturally attached to the corresponding classical groups.
Our main results are vanishing/nonvanishing 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) Differentialalgebraic 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 modeltheoretic consideration arising from the study of the canonical base property, I asked some years ago whether the Kolchin tangent bundle of a finite dimensional differentialalgebraic variety has the property that the restriction to any Calgebraic subvariety is Calgebraic. Here C is the field of constants in a saturated differentially closed field of characteristic zero, and Calgebraic means being generically in finitetofinite correspondence with the Cpoints 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 HarrisonTrainor, 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 PeterzilStarchenko 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\sigmareduced. We will explain how we get around this difficulty and the implications on the theory.
Updated on Apr 18, 2014 09:01 AM PDT 
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 BoijSoederberg 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: CastelnuovoMumford regularity and logcanonical thresholds
The regularity of an ideal is a measure of its computational complexity. The logcanonical threshold is a measure of singularity. Not surprisingly, these things are related  the logcanonical 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 
Berkeley Topology Seminar: Part I: Introductory Talk Equivariant Homotopy and Mackey Functors
Location: 740 Evans Hall Speakers: Michael Hill (University of Virginia)I'll describe the computational tools needed to understand the proof of the results in the main talk.
Created on Apr 17, 2014 04:52 PM PDT 
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 4manifolds can be restated in terms of the connection between real and complex Ktheory given by homotopy fixed points. This comes from a bordism result about Real manifolds versus unoriented manifolds, which in turn, comes from a C2equivariant 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

AT Research Seminar PreTalk: The DoldKan correspondence and commutative monoids
Location: MSRI: Simons Auditorium Speakers: Birgit Richter (Universität Hamburg)Over a field in characteristic zero commutative dgas are wellbehaved; otherwise they are not. For instance there isn't a
rightinduced 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 
AT Research Seminar: An algebraic model for commutative HZalgebras.
Location: MSRI: Simons Auditorium Speakers: Birgit Richter (Universität Hamburg)EilenbergMac 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 EilenbergMac 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 HZalgebras. This builds on a DoldKan type theorem for commutative monoids in symmetric sequences.
Updated on Apr 17, 2014 04:58 PM PDT 
AT Postdoc Seminar: The Mirror Symmetry Conjecture and Cobordisms
Location: MSRI: Baker Board Room Speakers: Hiro Tanaka (Harvard University)This talkaimed for a general audience of neither topologists nor model theoristswill 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 
Logic Colloquium: The Differential Field of Transseries
Location: UC Berkeley, 60 Evans Hall Speakers: Lou van den Dries (University of Illinois at UrbanaChampaign)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 modeltheoretic 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 
MT Postdoc Seminar
Location: MSRI: Simons AuditoriumUpdated on Apr 18, 2014 12:49 PM PDT 
Alegbraic Topology Open Problems / Work in Progress Seminar
Location: MSRI: Simons AuditoriumCreated on Jan 30, 2014 08:23 AM PST 
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 ominimality. 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 
Conformal Field Theory
Location: MSRI: Baker Board RoomCreated on Feb 19, 2014 08:18 AM PST 
Model Theory, Arithmetic Geometry and Number Theory Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 04, 2014 09:06 AM PST 
Model Theory, Arithmetic Geometry and Number Theory Seminar
Location: MSRI: Simons AuditoriumUpdated on Mar 24, 2014 11:20 AM PDT 
Eisenbud Seminar: Algebraic Geometry and Commutative Algebra
Location: Evans 9393:45pm
Speaker: Zvi Rosen (UC Berkeley)
Title: Computing Algebraic MatroidsAbstract: 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.
5:00pm
Speaker: Noah Giansiracusa (UC Berkeley)
Title: Equations of Tropical VarietiesAbstract: 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 ToenVaquie, 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 nonarchimedean valuation to closed subschemes of the corresponding toric variety over T. Upon passing to the set of \mathbb{T}valued points this yields KajiwaraPayne's extended tropicalization functor. We prove that the Hilbert polynomial of any projective subscheme is preserved by our tropicalization functor, so the schemetheoretic 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 
AT Research Seminar PreTalk
Location: MSRI: Simons AuditoriumUpdated on Mar 06, 2014 02:41 PM PST 
AT Research Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 14, 2014 08:56 AM PST 
MT Postdoc Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 06, 2014 09:23 AM PST 
AT Postdoc Seminar
Location: MSRI: Simons Auditorium Speakers: Vesna Stojanoska (Massachusetts Institute of Technology)Created on Feb 07, 2014 09:36 AM PST 
Alegbraic Topology Open Problems / Work in Progress Seminar
Location: MSRI: Simons AuditoriumCreated on Jan 30, 2014 08:23 AM PST 
Conformal Field Theory
Location: MSRI: Baker Board RoomCreated on Feb 19, 2014 08:18 AM PST 
Model Theory, Arithmetic Geometry and Number Theory Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 04, 2014 09:06 AM PST 
Model Theory, Arithmetic Geometry and Number Theory Seminar
Location: MSRI: Simons AuditoriumUpdated on Mar 24, 2014 11:23 AM PDT 
Eisenbud Seminar: Algebraic Geometry and Commutative Algebra
Location: Evans 939Created on Feb 10, 2014 08:43 AM PST 
AT Research Seminar PreTalk
Location: MSRI: Simons AuditoriumUpdated on Mar 06, 2014 02:44 PM PST 
AT Research Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 14, 2014 08:57 AM PST 
MT Postdoc Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 06, 2014 09:23 AM PST 
AT Postdoc Seminar
Location: MSRI: Simons Auditorium Speakers: Joseph Hirsh (Massachusetts Institute of Technology)Created on Feb 07, 2014 09:37 AM PST 
AT Seminar
Location: MSRI: Simons Auditorium Speakers: Alexei Kitaev (Kavli Institute for Theoretical Physics)Created on Apr 14, 2014 09:17 AM PDT 
Alegbraic Topology Open Problems / Work in Progress Seminar
Location: MSRI: Baker Board RoomCreated on Jan 30, 2014 08:22 AM PST 
Conformal Field Theory
Location: MSRI: Baker Board RoomCreated on Feb 19, 2014 08:23 AM PST 
Model Theory, Arithmetic Geometry and Number Theory Seminar
Location: MSRI: Baker Board RoomCreated on Feb 04, 2014 09:05 AM PST 
Model Theory, Arithmetic Geometry and Number Theory Seminar
Location: MSRI: Baker Board RoomUpdated on Mar 24, 2014 11:31 AM PDT 
Eisenbud Seminar: Algebraic Geometry and Commutative Algebra
Location: Evans 939Created on Feb 10, 2014 08:43 AM PST 
AT Research Seminar PreTalk
Location: MSRI: Baker Board RoomUpdated on Mar 11, 2014 03:18 PM PDT 
AT Research Seminar
Location: MSRI: Baker Board RoomCreated on Feb 14, 2014 08:57 AM PST 
Alegbraic Topology Open Problems / Work in Progress Seminar
Location: MSRI: Simons AuditoriumCreated on Jan 30, 2014 08:20 AM PST 
Conformal Field Theory
Location: MSRI: Baker Board RoomCreated on Feb 19, 2014 08:24 AM PST 
Model Theory, Arithmetic Geometry and Number Theory Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 04, 2014 08:54 AM PST 
Model Theory, Arithmetic Geometry and Number Theory Seminar
Location: MSRI: Simons AuditoriumUpdated on Mar 24, 2014 11:32 AM PDT 
Eisenbud Seminar: Algebraic Geometry and Commutative Algebra
Location: Evans 939Created on Feb 10, 2014 08:44 AM PST 
AT Research Seminar PreTalk
Location: MSRI: Simons AuditoriumUpdated on Mar 06, 2014 02:51 PM PST 
AT Research Seminar
Location: MSRI: Simons AuditoriumCreated on Feb 14, 2014 08:58 AM PST
Past Seminars

Seminar MSRI/Evans Lecture: A journey through motivic integration
Updated on Apr 11, 2014 03:43 PM PDT 
Seminar Conformal Field Theory
Created on Feb 19, 2014 08:18 AM PST 
Seminar AT Open Problems/Work in Progress Seminar: Problems arising from an interface between homotopy theory and knot theory.
Updated on Apr 17, 2014 04:34 PM PDT 
Seminar Unlikely intersections in semiabelian schemes.
Created on Apr 11, 2014 02:11 PM PDT 
Seminar AT Research Seminar: The classification of Taylor towers for functors from based spaces to spectra
Updated on Apr 14, 2014 11:20 AM PDT 
Seminar AT Research Seminar PreTalk: Module structures on Goodwillie derivatives
Updated on Apr 14, 2014 10:50 AM PDT 
Seminar Algebraic K and Ltheory of groups rings and their applications to topology and geometry, Part II: Main Talk
Created on Apr 14, 2014 11:19 AM PDT 
Seminar Berkeley Model Theory Seminar: Higher amalgamation and polygroupoids.
Updated on Apr 11, 2014 02:06 PM PDT 
Seminar Introduction to the middle Ktheory of group rings and their relevance in topology, Part One: Introductory Talk
Created on Apr 14, 2014 11:17 AM PDT 
Seminar Berkeley Model Theory Seminar: Pseudo Real Closed fields and NTP2
Updated on Apr 11, 2014 02:01 PM PDT 
Seminar Finite Structures Seminar
Created on Apr 09, 2014 03:24 PM PDT 
Seminar Commutative Algebra and Algebraic Geometry
Created on Apr 14, 2014 11:22 AM PDT 
Seminar MT Research Seminar: Tameness and coincidence of dimensions in expansions of the real field
Updated on Apr 11, 2014 01:54 PM PDT 
Seminar MT Research Seminar: Torsion free groups definable in ominimal structures.
Updated on Apr 11, 2014 01:38 PM PDT 
Seminar Conformal Field Theory
Created on Feb 19, 2014 08:16 AM PST 
Seminar Alegbraic Topology Open Problems / Work in Progress Seminar
Created on Jan 30, 2014 08:24 AM PST 
Seminar UC Berkeley Model Theory Seminar: Locally definable groups as covers of definable groups.
Created on Apr 04, 2014 10:01 AM PDT 
Seminar MT Research Seminar: The Finite Submodel Property and Definability in Classes of Finite Structures.
Updated on Apr 04, 2014 12:57 PM PDT 
Seminar MT Research Seminar: On the fundamental complexity of simple theories
Updated on Apr 04, 2014 09:47 AM PDT 
Seminar MSRI/Evans Lecture: Sullivan's conjecture and applications to arithmetic
Updated on Apr 01, 2014 03:43 PM PDT 
Seminar Conformal Field Theory
Created on Feb 19, 2014 08:15 AM PST 
Seminar Problem Sessions in Model Theory
Created on Mar 27, 2014 11:58 AM PDT 
Seminar AT Postdoc Seminar: Galois equivariance and stable motivic homotopy theory
Updated on Mar 28, 2014 01:16 PM PDT 
Seminar MT Postdoc Seminar
Created on Feb 06, 2014 09:21 AM PST 
Seminar AT Research Seminar: Compactified string topology
Updated on Mar 28, 2014 12:07 PM PDT 
Seminar AT Research Seminar PreTalk: Introduction to string topology and to combinatorial models for the moduli space of Riemann surfaces
Updated on Mar 28, 2014 11:41 AM PDT 
Seminar UC Berkeley Topology Seminar: On a nilpotence conjecture of J.P. May
Created on Mar 28, 2014 11:25 AM PDT 
Seminar UC Berkeley Topology Seminar Intro talk: Prerequisites on ring spectra and nilpotence
Updated on Mar 28, 2014 10:37 AM PDT 
Seminar MSRI/Evans Lecture: Bounding the density of rational points on trascendental hypersurfaces via model theory
Updated on Mar 28, 2014 09:53 AM PDT 
Seminar MT Research Seminar: Towards a Z/ell analogue of Bogomolov's birational anabelian geometry.
Updated on Mar 28, 2014 09:40 AM PDT