Colloquium

from Monday
January 01, 2018 to Thursday
May 31, 2018
 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Seminar Analysis Student Seminar Capsule Research Talks Colloquium Commencement Ceremony Comprehensive Exams Dynamical Systems Seminar Equivalence Method and Exterior Differential Systems Seminar First and Second Year Student Seminar Friday Summer Meeting Geometric Analysis Learning Seminar Geometry/Topology Seminar Grad / Postdoc Professional Development Seminar Graduate Student Seminar Graduate Topology Seminar Grant Proposal Panel Hodge Theory, Moduli and Representation Theory Holiday Party Joint Columbia-CUNY-Stony Brook General Relativity Seminar Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Education Colloquium Mathematics Summer Camp Mini Course / Dynamics Learning Seminar Mini-School in Geometry Minicourse in Real Enumerative Geometry New Graduate Students NY General Relativity Seminar Postdoc Geometry/Dynamics Seminar Postdoc Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar Seminar in Topology and Symplectic Geometry Seminar on algebraic structures in physics Simons Colloquium Simons Lectures Series Singular metrics and direct images Special Algebra / Algebraic Geometry Seminar Special Analysis Seminar Special Colloquium Special Dynamics Seminar Special Geometry/Topology Seminar Special Lectures Special Seminar in Algebraic Geometry Special Topology Seminar Student Algebraic Geometry Seminar Student Gauge Theory Seminar Student Seminar on Differential Geometry and Analysis Summer Workshop in Topology and Geometry Symplectic Geometry Reading Seminar Symplectic Geometry Seminar Thesis Defense Topology and Symplectic Geometry / Math of Gauge Fields seminar Women in Mathematics Instructions for subscribing to Stony Brook Math Department Calendars

 ThursdayJanuary 25, 20184:00 PM - 5:00 PM Math Tower P-131 Frank Thorne, University of South Carolina An Analytic View of Arithmetic Statistics"Arithmetic statistics" is all about counting arithmetic objects: number fields, ideal class groups, Selmer groups of ellitpic curves, and so on. One common approach is to parametrize such objects in terms of lattice points in a vector space, up to an equivalence relation given by the action of a suitable group. One then counts the lattice points. I will give an overview of some work on this subject, from Gauss to contemporary work of Manjul Bhargava, myself, my host Bob Hough, and many others. I will concentrate on the analytic and quantitative side of the subject, and explain how refinements to our lattice point counting methods lead to improved results.

 ThursdayFebruary 01, 20184:00 PM - 5:00 PM Math Tower P-131 Xiuxiong Chen, Stony Brook University On constant scalar curvature Kaehler metricsInspired by the celebrated $C^0, C^2$ and $C^3$ a priori estimates of Calabi, Yau and others on Kaehler Einstein metrics, we present a report on a priori estimates on constant scalar curvature Kaehler metrics. With this estimate, we prove the Donaldson conjecture on geodesic stability and the well known properness conjecture on the Mabuchi energy functional. This is a joint work with Cheng JingRui from University of Wisconsin at Madison. This lecture is intended to be expository. This will be followed by a more technical lecture by Dr. Cheng Jingrui on Geometry/topology seminar (Feb. 6th).

 ThursdayFebruary 15, 20184:00 PM - 5:00 PM Math Tower P-131 Leonid Kovalev, Syracuse University Lipschitz geometry of finite subset spacesLet $X(n)$ be the set of all nonempty subsets of a metric space X with cardinality at most n. Equipped with the Hausdorff metric, $X(n)$ becomes a metric space of its own, a finite subset space of X. Such spaces have been studied since the 1931 paper of Borsuk and Ulam, mostly from the topological perspective. The investigation of their metric structure is more recent. The finite subset spaces form a natural chain of isometric embeddings: $X = X(1) ⊂ X(2) ⊂ X(3) ⊂ ...$ For example, when X is a circle, this chain describes a trefoil knot bounding a Möbius strip in the 3-sphere. For some classes of spaces these embedding split, even in the Lipschitz category. The existence of Lipschitz retractions $X(n) → X(n-1)$ generally corresponds to X being nonpositively curved, but the exact relationship is yet to be understood.

 ThursdayFebruary 22, 20184:00 PM - 5:00 PM Math Tower P-131 Nets Katz, Caltech Semialgebraic sets and the Kakeya ProblemIn joint work with Keith Rogers, we study the connection between the Kakeya problem and the highlights of the theory of semialgebraic sets such as Tarski's projection theorem and Gromov's algebraic lemma.

 ThursdayMarch 01, 20184:00 PM - 5:00 PM Math Tower P-131 Dzmitry Dudko, On the problem of local connectivity of the Mandelbrot set.The Mandelbrot set encodes how the dynamics of $z^2+c$ depends on $c$. In the 1980s A. Douady and J. Hubbard conjectured that the Mandelbrot set is locally connected -- the MLC conjecture. This conjecture would result in a simple abstract pinched disk'' model for the Mandelbrot set. Since the 1990s, local connectivity was established for a large class of parameters, but the full conjecture is still open. In the talk we will discuss recent developments in the area. Our main tool is Pacman renormalization'' responsible for self-similarity of the Mandelbrot set near its main cardioid. Based on a joint work with Misha Lyubich.

 ThursdayApril 05, 20184:00 PM - 5:00 PM SCGP Auditorium 103 John Milnor, Stony Brook University Points on a Circle: from Pappus to ThurstonA soft introduction to the easiest examples of Deligne-Mumford compactifications.

 ThursdayApril 12, 20184:00 PM - 5:00 PM SCGP-102 Piotr Sulkowski, University of Warsaw (Poland) & Caltech Categorification in mathematical physics workshop Colloquium: Knots-quivers correspondenceI will present a surprising relation between knot invariants and quiver representation theory, motivated by various string theory constructions. Consequences of this relation include the proof of one of the famous integrality conjectures of BPS invariants (i.e. Labastida-Marino-Ooguri-Vafa conjecture for symmetric representations), explicit (and unknown before) formulas for colored HOMFLY-PT polynomials for various knots, new viewpoint on knot homologies, a novel type of categorification, new dualities between quivers, solutions to certain combinatorial problems, and many others.

 ThursdayApril 19, 20184:00 PM - 5:00 PM Math Tower P-131 Percy Deift, NYU Courant Universality in numerical computation with random data. Case studies and analytical results.The speaker will discuss various universality aspects of numerical computations using standard algorithms. These aspects include empirical observations, rigorous results, and some speculations about computation in a broader sense. Joint with C.Pfrang, G.Menon, S.Olver and Thomas Trogdon.

 ThursdayApril 26, 20184:00 PM - 5:00 PM Math Tower P-131 Mohammed Abouzaid, Columbia University Mirror symmetry, loop spaces, and immersed LagrangiansA compelling approach to mirror symmetry, initiated by Strominger-Yau-Zaslow and Fukaya, is to associate to a symplectic manifold with a Lagrangian torus fibration a mirror space consisting of the space of objects of the Fukaya category supported on the fibres with multiplicity one. In the simplest setting of the cotangent bundle of the torus, the mirror correspondence thus amounts to the natural identification between the group ring of the fundamental group and Laurent polynomials. I will begin by explaining how one can globalise this argument to yield a proof of homological mirror symmetry for manifolds admitting non-singular Lagrangian fibrations. Then I will explain how the main obstruction to generalise this proof is to formulate an appropriate notion of loop space for singular Lagrangians. Finally, I will sketch a construction that plays the role of the loop space for immersed Lagrangians, and indicate how this should suffice to prove mirror symmetry for examples arising from toric degenerations.

 ThursdayMay 03, 20182:30 PM - 3:30 PM Math Tower P-131 Chris Bishop, Stony Brook University Snowflakes and TreesThis is a short survey of various results involving (mostly planar) harmonic measure, ranging roughly from Makarov's theorems of the 1980's to the present, but focusing mostly on topics related to "balancing" harmonic measure on two sides of a common boundary. We touch on topics like Brownian motion, conformal maps, circle homeomorphisms, dessins d'enfants, transcendental dynamics, wandering domains and European history.

 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis Seminar Analysis Student Seminar Capsule Research Talks Colloquium Commencement Ceremony Comprehensive Exams Dynamical Systems Seminar Equivalence Method and Exterior Differential Systems Seminar First and Second Year Student Seminar Friday Summer Meeting Geometric Analysis Learning Seminar Geometry/Topology Seminar Grad / Postdoc Professional Development Seminar Graduate Student Seminar Graduate Topology Seminar Grant Proposal Panel Hodge Theory, Moduli and Representation Theory Holiday Party Joint Columbia-CUNY-Stony Brook General Relativity Seminar Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Education Colloquium Mathematics Summer Camp Mini Course / Dynamics Learning Seminar Mini-School in Geometry Minicourse in Real Enumerative Geometry New Graduate Students NY General Relativity Seminar Postdoc Geometry/Dynamics Seminar Postdoc Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar Seminar in Topology and Symplectic Geometry Seminar on algebraic structures in physics Simons Colloquium Simons Lectures Series Singular metrics and direct images Special Algebra / Algebraic Geometry Seminar Special Analysis Seminar Special Colloquium Special Dynamics Seminar Special Geometry/Topology Seminar Special Lectures Special Seminar in Algebraic Geometry Special Topology Seminar Student Algebraic Geometry Seminar Student Gauge Theory Seminar Student Seminar on Differential Geometry and Analysis Summer Workshop in Topology and Geometry Symplectic Geometry Reading Seminar Symplectic Geometry Seminar Thesis Defense Topology and Symplectic Geometry / Math of Gauge Fields seminar Women in Mathematics Instructions for subscribing to Stony Brook Math Department Calendars