Mini Course / Dynamics Learning Seminar

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

 WednesdayFebruary 07, 20182:30 PM - 3:30 PM Math Tower P-131 Dyi-Shing Ou, Stony Brook University Nonexistence of wandering domains for infinitely renormalizable : I Hénon mapsThe plan of the lectures is to prove the theorem: A strongly dissipative infinitely renormalizable Hénon-like map with stationary combinatorics does not have a wandering domain. I will focus on the case of the period-doubling combinatorics. After the proof, I will say a few words about extending the proof to other stationary combinatorics. The plan of the first talk is to cover the topics: 1. unimodal renormalization, 2. Hénon renormalization, 3. dynamics of an infinite period-doubling renormalizable Hénon map. We will begin to prove the theorem in the following talk.

 WednesdayFebruary 14, 20182:30 PM - 3:30 PM Math Tower P-131 Dyi-Shing Ou, Stony Brook University Nonexistence of wandering domains for infinitely renormalizable Henon maps: part IIIn this talk, we will prove the nonexistence of wandering domains for a strongly dissipative infinitely (period-doubling) renormalizable Henon-like map. I will classify the domain into two regions: the good region and the bad region. In the good region, the classical results from unimodal maps can be applied to Henon-like maps. In particular, if a wandering domain exists, the horizontal size of the elements in a rescaled orbit of the wandering domain (called the closest approach) expands at a definite rate. However, in the bad region, the Henon-like map behaves differently from a unimodal map and the property break down. I will show that the bad behavior can occur at most finitely many times in the rescaled orbit to conclude the theorem. After proving the theorem, I will give some remarks on my recent work of extending the proof to other stationary combinatorics.

 WednesdayFebruary 21, 20182:30 PM - 3:30 PM Math Tower P-131 Babak Modami, Stony Brook University Minimal nonuniquely ergodic foliations on surfaces: IMeasured foliations (laminations) on surfaces are well-known examples of dynamical systems in low dimension. The first return maps of measured foliations are interval exchange transformations which have been studied extensively. Measured foliations also determine the trajectories of Teichmüller and Weil-Petersson geodesics in the Teichmüller space. In this mini-course, I outline my joint work with Brock, Leininger and Rafi about construction of minimal nonuniquely ergodic laminations. This work was inspired by a construction of Gabai and the earlier work of Lenzhen-Leininger-Rafi where laminations are realized as the limits of sequences of curves on surfaces. An advantage of our method is explicit estimates for intersection numbers of the curves in sequences and the associated subsurface coefficients. These estimates are crucial to control the behavior of geodesics and determine their limit sets in the Thurston compactification of Teichmüller space (which won't be discussed in the minicourse).

 WednesdayFebruary 28, 20182:30 PM - 3:30 PM Math Tower P-131 Babak Modami, Stony Brook Minimal nonuniquely ergodic foliations on surfaces: IIMeasured foliations (laminations) on surfaces are well-known examples of dynamical systems in low dimension. The first return maps of measured foliations are interval exchange transformations which have been studied extensively. Measured foliations also determine the trajectories of Teichmüller and Weil-Petersson geodesics in the Teichmüller space. In this mini-course, I outline my joint work with Brock, Leininger and Rafi about construction of minimal nonuniquely ergodic laminations. This work was inspired by a construction of Gabai and the earlier work of Lenzhen-Leininger-Rafi where laminations are realized as the limits of sequences of curves on surfaces. An advantage of our method is explicit estimates for intersection numbers of the curves in sequences and the associated subsurface coefficients. These estimates are crucial to control the behavior of geodesics and determine their limit sets in the Thurston compactification of Teichmüller space (which won't be discussed in the minicourse).

 WednesdayMarch 07, 20182:30 PM - 3:30 PM Math Tower P-131 Michael Benedicks, KTH Royal Institute of Technology Attractors and sinks for Hénon mapsSince M. Hénon's fundamental computer experiment in 1976, it was a natural question whether the Hénon family of quadratic maps of the plane has parameters for which the corresponding maps has strange attractors (at least attractors that are not sinks). Hénon found numerically maps with sinks but also maps which seemed so have strange attractors. In the beginning of the 1990s Carleson and the speaker proved the existence of a positive Lebesgue measure of parameters with a strange attractor. We will review the construction in this proof and also indicate how one can find sinks, close to these parameters, even multiple coexisting sinks. The later is work in progress with Liviana Palmisano.

 WednesdayMarch 14, 20182:30 PM - 3:30 PM Math Tower P-131 Rostislav Grigorchuk, Texas A&M University Some rational multidimensional maps coming from self-similar groupsI will describe a non-standard method of getting multidimensional rational maps using self-similar groups. These maps are very different from the maps in general position and possess interesting properties. Then I will explain why study of dynamical properties of these maps is useful for solving spectral problems related to finite and infinite graphs and to groups. Also the KNS (Kesten-Von Neumann-Serre) spectral measures will be defined and discussed.

 WednesdayApril 11, 20182:30 PM - 3:30 PM Math Tower P-131 Dror Varolin, Stony Brook University Solution of the Cauchy-Riemann Equations with $L^2$ estimatesIn this three-lecture mini-school we will explain the technique introduced by Hormander to obtain solutions, with $L^2$ estimates, for the inhomogeneous Cauchy-Riemann equations. We will then demonstrate several applications of the theorem and of the technique of its proof, with a focus on the construction of subharmonic functions with certain properties. The background needed is relatively elementary, consisting only basic real and complex analysis, and a little bit of the formalism of differential forms on manifolds (though the latter is not absolutely necessary).

 WednesdayApril 25, 20182:30 PM - 3:30 PM Math Tower P-131 Dror Varolin, Stony Brook University Solution of the Cauchy-Riemann Equations with $L^2$ estimatesIn this three-lecture mini-school we will explain the technique introduced by Hormander to obtain solutions, with $L^2$ estimates, for the inhomogeneous Cauchy-Riemann equations. We will then demonstrate several applications of the theorem and of the technique of its proof, with a focus on the construction of subharmonic functions with certain properties. The background needed is relatively elementary, consisting only basic real and complex analysis, and a little bit of the formalism of differential forms on manifolds (though the latter is not absolutely necessary).

 WednesdayMay 02, 20182:30 PM - 3:30 PM Math Tower P-131 Dror Varolin, Stony Brook University Solution of the Cauchy-Riemann Equations with $L^2$ estimatesIn this three-lecture mini-school we will explain the technique introduced by Hormander to obtain solutions, with $L^2$ estimates, for the inhomogeneous Cauchy-Riemann equations. We will then demonstrate several applications of the theorem and of the technique of its proof, with a focus on the construction of subharmonic functions with certain properties. The background needed is relatively elementary, consisting only basic real and complex analysis, and a little bit of the formalism of differential forms on manifolds (though the latter is not absolutely necessary).

 WednesdayMay 09, 20182:30 PM - 3:30 PM Math Tower P-131 Hongming Nie, Indiana University TBATBA

 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