Analysis Student 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

 WednesdayJanuary 31, 20184:00 PM Math Tower 5-127 Jack Burkart, Stony Brook University Intro to Brownian MotionAfter a quick introduction, we'll define and discuss what we need to know about Gaussian random variables. From there, we will define what Brownian motion is, and give a construction of Brownian motion on an interval.

 WednesdayFebruary 07, 20184:00 PM Math Tower 5-127 Jack Burkart, Stony Brook University Construction of Brownian MotionWe will start by addressing some of the questions asked in the last talk. After that and a quick review, we will construct Brownian motion on an interval.

 WednesdayFebruary 14, 20184:00 PM Math Tower 5-127 Matthew Dannenberg, Stony Brook University Basic Properties of Brownian MotionWe discuss the basic properties of Brownian motion, including scaling and inversion relationships, Holder continuity, and nowhere differentiability.

 WednesdayFebruary 21, 20184:00 PM Math Tower 5-127 Ben Sokolowsky, Stony Brook University Reflection and Conformal InvarianceWe will discuss stopping times and the strong Markov property of Brownian motion, proving a reflection principle along the way. Time permitting we will also discuss the conformal invariance of Brownian motion.

 WednesdayFebruary 28, 20184:00 PM Math Tower 5-127 Silvia Ghinassi, Stony Brook University Dimension Results for Brownian MotionAfter recalling a few definitions and basic facts regarding Hausdorff and Minkowski dimensions, we state and prove dimension results for the graph and the image of Brownian motion with the help of Frostman's lemma. We will state and understand dimension doubling results for d-dimensional Brownian motion, for $d ≥ 2$. Finally, if time allows, we will discuss in detail area of planar Brownian motion.

 WednesdayMarch 07, 20184:00 PM Math Tower 5-127 Jack Burkart, Stony Brook University The Zeros of Brownian MotionWe show that the zero set of Brownian motion almost surely has dimension equal to 1/2

 WednesdayApril 04, 20184:00 PM Math Tower 5-127 Matt Dannenberg, Stony Brook University The Universality of Brownian MotionWe will discuss sections 7.2-7.4 in Bishop-Peres, including material on the Law of the Iterated Logarithm, Skorokhod's representation of random variables by Brownian Motion with a certain stopping time, and Donsker's invariance principle, which allows us to view Brownian motion as the limit of many simple, discrete random walks.

 WednesdayApril 11, 20184:00 PM Math Tower 5-127 Ben Sokolowsky and Jack Burkart, Stony Brook University Probabilistic View of Harmonic FunctionsFollowing 7.5-7.7 in Bishop-Peres, we will develop the theory of harmonic functions in Euclidean space using the ideas using Brownian motion. Applications include the transience of Brownian motion in dimensions 3 and higher and the solution of the Dirichlet problem for domains satisfying the Poincare cone condition.

 WednesdayApril 18, 20184:00 PM Math Tower 5-127 Mu Zhao, Stony Brook University MartingalesWe'll define and construct the conditional expectation of a random variable, and discuss its basic features. Then we'll discuss and define martingales.

 WednesdayApril 25, 20184:00 PM Math Tower 5-127 Jack Burkart, Stony Brook University Kakutani's Theorem on Harmonic MeasureGiven a domain in the complex plane and a sufficiently nice subset of its boundary, the harmonic measure is the solution of the Dirichlet problem with boundary data given by the indicator function. It's a central topic in analysis that touches complex analysis, geometric measure theory, and harmonic analysis. In this lecture, we'll carefully define harmonic measure and prove Kakutani's theorem, which says that the harmonic measure of a subset evaluated at a point coincides with the probability that Brownian motion starting at that point first hits the boundary at this subset.

 MondayMay 07, 20182:30 PM Math Tower 5-127 Matt Dannenberg, Stony Brook University Intro to Stochastic CalculusWe'll define what it means to integrate with respect to a stochastic process, such as Brownian motion. This gives us a formal way of understanding systems that behave randomly. After that, we will state a few of the main theorems and applications of this idea.

 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