Colloquium

from Thursday
June 01, 2017 to Sunday
December 31, 2017
 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis 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 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

 ThursdaySeptember 14, 20174:00 PM - 5:00 PM Math Tower P-131 Brian Lawrence, Columbia University Diophantine Problems and $p$-adic AnalysisMordell's Conjecture (now Faltings' Theorem) establishes a surprising link between geometry and number theory: a curve of genus at least two has only finitely many rational points. We show how $p$-adic analysis can prove finiteness results in number theory. The speaker and A. Venkatesh hope to use these ideas to give a new proof of Faltings' Theorem.

 ThursdaySeptember 21, 20174:00 PM - 5:00 PM Math Tower P-131 Misha Skolnikov, Princeton University A new approach to the largest eigenvalues of random matricesI will discuss a new method for the study of fluctuations of the largest eigenvalues in various random symmetric matrix ensembles. In addition to striking mathematical features, these arise naturally in the principal component analysis of sample covariance matrices from high-dimensional data. The new approach is based on the moment method for tridiagonal random matrices and strong invariance principles for random walks and their local times. Based on joint works with Vadim Gorin and Pierre Yves Gaudreau Lamarre.

 ThursdaySeptember 28, 20174:00 PM - 5:00 PM SCGP Rm 102 Nick Trefethen, NYU Random functions, random ODEs, and ChebfunWhat is a random function? What is noise? The standard answers are nonsmooth, defined pointwise via the Wiener process and Brownian motion. In the Chebfun project, we have found it more natural to work with smooth random functions defined by finite Fourier series with random coefficients. The length of the series is determined by a wavelength parameter $λ$. Integrals give smooth random walks, which approach Brownian paths as $λ→ 0$, and smooth random ODEs, which approach stochastic DEs of the Stratonovich variety. Numerical explorations become very easy in this framework. There are plenty of conceptual challenges in this subject, starting with the fact that white noise has infinite amplitude and infinite energy, a paradox that goes back two different ways to Einstein in 1905.

 ThursdayOctober 05, 20174:00 PM - 5:00 PM Math Tower P-131 Lionel Levine, Cornell University Will this avalanche go on forever?In the abelian sandpile model on the d-dimensional lattice Z^d, each site that has at least 2d grains of sand gives one grain of sand to each of its 2d nearest neighbors. An "avalanche" is what happens when you iterate this move. In https://arxiv.org/abs/1508.00161 Hannah Cairns proved that for d=3 the question in the title is algorithmically undecidable: it is as hard as the halting problem! This infinite unclimbable peak is surrounded by appealing finite peaks: What about d=2? What if the initial configuration of sand is random? I’ll tell you about the “mod 1 harmonic functions” Bob Hough and Daniel Jerison and I used to prove in https://arxiv.org/abs/1703.00827 that certain avalanches go on forever.

 ThursdayOctober 19, 20174:00 PM - 5:00 PM Math Tower P-131 Alex Gamburd, CUNY Graduate Center Arithmetic and Dynamics on Markoff-Hurwitz VarietiesMarkoff triples are integer solutions of the equation $x^2+y^2+z^2=3xyz$ which arose in Markoff's spectacular and fundamental work (1879) on diophantine approximation and has been henceforth ubiquitous in a tremendous variety of different fields in mathematics and beyond. After reviewing some of these, we will discuss joint work with Bourgain and Sarnak on the connectedness of the set of solutions of the Markoff equation modulo primes under the action of the group generated by Vieta involutions, showing, in particular, that for almost all primes the induced graph is connected. Similar results for composite moduli enable us to establish certain new arithmetical properties of Markoff numbers, for instance the fact that almost all of them are composite. Time permitting, we will also discuss recent joint work with Magee and Ronan on the asymptotic formula for integer points on Markoff-Hurwitz surfaces $x_1^2+x_2^2 + \dots + x_n^2 = x_1 x_2 \dots x_n$, giving an interpretation for the exponent of growth in terms of certain conformal measure on the projective space.

 ThursdayOctober 26, 20174:00 PM - 5:30 PM SCGP 102 Peter Kronheimer, Harvard University Simon Donaldson's Mathematics: A RetrospectiveThis talk will provide a personal perspective on some of Simon Donaldson's many important contributions to the geometry and topology of manifolds.

 ThursdayNovember 02, 20174:00 PM - 5:00 PM Math Tower P-131 Simon Marshall, University of Wisconsin, and the Neil Chriss and Natasha Herron Chriss Founders' Circle Member, IAS The asymptotic size of (arithmetic) eigenfunctionsConsider an L^2-normalized Laplace eigenfunction f with large eigenvalue on a compact Riemannian manifold. A well-studied question in harmonic analysis, called the sup-norm problem, asks for the best bound on the pointwise norm of f that one can give in terms of its eigenvalue. This is particularly interesting when the manifold is negatively curved, as the gap between what we expect and can prove is quite large. I will survey some results on the sup-norm problem in negative curvature that one can obtain by specializing to the case of eigenfunctions with extra arithmetic properties, called Hecke-Maass forms. I will also describe connections between the sup-norm problem for Hecke-Maass forms and the subconvexity problem for L-functions. Some of these results will be work of myself and Farrell Brumley.

 WednesdayDecember 06, 20172:30 PM - 3:30 PM Math Tower P-131 Dorian Goldfeld, Columbia University Super-positivity of L-functionsL-functions are ubiquitous in number theory. Their coefficients and special values encode the most important number theoretic and geometric invariants. An L-function is said to be super-positive if all its derivatives at a real number $s ≥ 1/2$ are non-negative. In this talk we discuss how super-positivity can arise, how it relates to the generalized Riemann hypothesis and the Birch-Swinnerton-Dyer conjecture, and why it can be shown that a positive proportion of primitive self-dual L-functions in a suitable family have the super-positivity property.

 Show events for: All Events AGNES Algebraic geometry seminar Algebraic models in geometry seminar Am.Math.Soc. (AMS) Chapter Seminar Analysis 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 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