Analysis 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

 ThursdayJanuary 25, 20182:30 PM P-131 Leonid Kovalev, Syracuse University Metrically removable setsA compact subset K of Euclidean space R^n is called metrically removable if any two points a,b of its complement can be joined by a curve that is disjoint from K and has length arbitrarily close to |a-b|. Every set of zero (n-1)-dimensional measure is metrically removable, but not conversely. Metrically removable sets can even have positive n-dimensional measure. I will describe some properties of metrically removable sets and outline a proof of the following fact: totally disconnected sets of finite (n-1)-dimensional measure are metrically removable. This answers a question raised by Hakobyan and Herron in 2008. Joint work with Sergei Kalmykov and Tapio Rajala.

 FridayJanuary 26, 201811:00 AM - 12:00 AM P-131 Frank Thorne, South Carolina Levels of Distribution for Prehomogeneous Vector SpacesThis will be a continuation of Thursday's talk, where I will explain multiple approaches to the lattice point counting problem. The quantitatively strongest estimates all involve Fourier analysis in some guise, which turns out to have nice interplay with the action of the group.

 ThursdayFebruary 15, 20182:30 PM P-131 Max Engelstein, MIT An Epiperimetric approach to singular points in the Alt-Caffarelli functionalWe prove a uniqueness of blowups result for isolated singular points in the free boundary of minimizers to the Alt-Caffarelli functional. The key tool is a (log-)epiperimetric inequality, which we prove by means of two Fourier expansions (one on the function and one on its free boundary). If time allows we will also explain how this approach can be adapted to (re)prove old and new regularity results for area-minimizing hypersurfaces.

 ThursdayMarch 01, 20182:30 PM - 03:30 AM P-131 Ewain Gwynne, MIT Tutte embeddings of random planar maps via random walk in inhomogeneous random environmentsWe prove that the Tutte embeddings (a.k.a. harmonic/barycentric embeddings) of certain random planar maps converge to $γ$-Liouville quantum gravity ($γ$-LQG). Specifically, we treat mated-CRT maps, which are discretized matings of correlated continuum random trees, and $γ$ ranges from $0$ to $2$ as one varies the correlation parameter. We also show that the associated space-filling path on the embedded map converges to space-filling SLE$_{\kappa}$ for $\kappa =16/γ^2$ (in the annealed sense) and that the embedded random walk converges to Brownian motion (in the quenched sense). This constitutes the first proof that discrete conformal embeddings of random planar maps converge to LQG. To accomplish this, we establish a very general quenched invariance principle for random walk in a two-dimensional random environments in which the length scale is allowed to vary from place to place, so that the environment is only translation invariance modulo scaling. This result contains a number of existing results concerning random walk in random environments, and we expect that it will be useful in other settings as well, including other random environments related to random planar maps and LQG. Based on joint work with Jason Miller and Scott Sheffield.

 ThursdayMarch 08, 20182:30 PM P-131 CANCELED- Harrison Pugh, Stony Brook University Algebraic Structures on Currents

 ThursdayMarch 29, 20182:30 PM P-131 Silvia Ghinassi, Stony Brook University Sufficient conditions for $C^{1,α}$ rectifiabilityWe provide sufficient conditions for a set or measure in $\mathbb{R}^n$ to be $C^{1,α}$ $d$-rectifiable, with $α ∈ [0,1]$. The conditions use a Bishop-Jones type square function and all statements are quantitative in that the $C^{1,α}$ constants depend on such a function. Key tools for the proof come from Guy David and Tatiana Toro's parametrization of Reifenberg flat sets (with holes) in the Hölder and Lipschitz categories.

 ThursdayApril 12, 20182:30 PM P-131 Beibei Liu, UC Davis Geometric finiteness in negatively pinched Hadamard manifoldsWe generalize Bonahon’s characterization of geometrically infinite torsion-free discrete subgroups of PSL(2, C) to geometrically infinite discrete torsion-free subgroups $Γ$ of isometries of negatively pinched Hadamard manifolds $X$. We then generalize a theorem of Bishop to prove that every such geometrically infinite isometry subgroup $Γ$ has a set of nonconical limit points with cardinality of continuum.

 ThursdayApril 19, 20182:30 PM P-131 Chris Green, Macquarie University, Australia Using the Schottky-Klein prime function to solve problems in multiply connected domains.The Schottky-Klein prime function is a special transcendental function which plays a central role in problems involving multiply connected domains (i.e. domains with multiple boundary components). Despite this, it has been scarcely used by pure and applied mathematicians since it was originally written down (independently by both Schottky and Klein towards the end of the 19th century). It turns out this function can be used to solve many mathematical problems set in multiply connected domains, exactly or in closed-form. In this talk, we will present the solutions to three different problems where it has been advantageous to employ the Schottky-Klein prime function and its associated function theory in order to construct closed-form analytical solutions.

 FridayApril 20, 201811:00 AM P-131 Evita Nestoridi, Princeton University Optimal strong stationary times for random walks on the chambers of a hyperplane arrangement.The Bidigare-Hanlon-Rockmore random walk on the chambers of real hyperplane arrangements is a Markov chain that generalizes famous examples, such as the Tsetlin library and riffle shuffles. We will introduce lower bounds for the separation distance and a strong stationary time, which allow for the first time to study cutoff for hyperplane arrangement walks under certain conditions. We will also discuss how the method for the lower bound can be used to prove a uniform lower bound for the mixing time of Glauber dynamics on a monotone system, such as the Ising model.

 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