from Tuesday
January 01, 2019 to Friday
May 31, 2019
 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 and Art Symposium for Tony Phillips Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Department Gathering 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 Representation Theory Student Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar SCGP Seminars 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 Differential 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 30, 20191:00 PM - 2:00 PM Math Tower P-131 Ying Hong Tham, Stony Brook University Character varietiesGiven a closed surface $S$ and a Lie group $G$, one defines the character variety to be roughly the space of representations of $π_1(S)$ in $G$. This space has connections to geometry, topology, physics, combinatorics, knot theory, and many other fields. In this talk, we will discuss some of these connections and develop some properties of the character variety.

 WednesdayFebruary 06, 20191:00 PM - 2:00 PM Math Tower P-131 Yi Wang, Stony Brook University Flat connections on Riemann surfacesI will explain how to identify the moduli space of flat connections, which is a differential geometric object, with corresponding moduli spaces in topological and holomorphic contexts. The key example we will focus on is Jacobian variety of a Riemann surface. In general, when the structure group is unitary, this is a theorem of Narasimhan and Seshadri, generalized by Donaldson-Uhlenbeck-Yau; When the structure group is complex reductive, this is Donaldson-Corlette's theorem on harmonic metrics and Hitchin-Simpson's theorem on Higgs bundles.

 WednesdayFebruary 13, 20191:00 PM - 2:00 PM Math Tower P-131 Matthew Dannenberg, Stony Brook University KAM Theory and the Collapse of Integrable DynamicsMany simple models in physics and symplectic geometry exhibit an algebraic property called (Liouville) complete integrability. This algebraic property gives rise to rich topological structure and simple dynamics, yet itself vanishes under small perturbations of the model. KAM Theory provides a mechanism to show that, despite this loss, the topological and dynamical structures persist on an extremely large set. In this talk I'll discuss what makes an integrable system so nice, show how to obtain the large set of persistence, and hint at the onset of chaos beyond KAM Tori.

 WednesdayFebruary 20, 20191:00 PM - 2:00 PM Math Tower P-131 Taras Kolomatski, Stony Brook University An Infinite Quantum Ramsey TheoremNik Weaver (2015) showed an intriguing non-commutative version of the classical Ramsey's theorem on graphs: Let $\mathcal{V}$ be a subspace of $M_n(\mathbb{C})$ which contains the identity matrix and is stable under the formation of Hermitian conjugates. If $n$ is sufficiently large, then there is a rank $k$ orthogonal projection such that $\dim (P\mathcal{V}P)$ is $1$ or $k^2$. These are the minimal and maximal possibilities for this dimension, and in these cases such a projection is called a quantum $k-$anticlique or quantum $k-$clique, respectively. Weaver further showed that both the classical and quantum Ramsey's theorems are special cases of a general Ramsey theorem on \textit{quantum graphs}, which are modelled on such matrix spaces with the additional algebraic structure of being a bimodule of some matrix $*-$algebra. Investigation of such objects was initially motivated by quantum information theory, in which quantum graphs provided an analogue of the confusability graph in classical communication over a noisy channel. Weaver's work follows a long list of results successfully generalising classical results to this context, such as the definition of quantum Shannon capacity by Duan, Severini and Winter (2013). In this talk, I will look at salient examples that demonstrate the difference between the classical and quantum contexts, sketch Weaver's results, and describe the process by which we successfully adapted Weaver's work demonstrate a quantum analogue of the classical infinite Ramsey's theorem in Kennedy, Kolomatski, Spivak (2017). Working in this infinite dimensional setting required functional analysis, and invited plenty of delightful nuance in topological considerations.

 WednesdayFebruary 27, 20191:00 PM - 2:00 PM Math Tower P-131 Diljit Singh, Stony Brook University An Introduction to Additive Number TheoryWe will give an overview of certain questions in the field, interesting connections to other topics in math, and important theorems. The talk will be flexible and we can focus on topics of the audiences choosing.

 WednesdayMarch 06, 20191:00 PM - 2:00 PM Math Tower P-131 Jiahao Hu, Stony Brook University Formal groups, complex manifolds and elliptic curvesA (commutative) formal group law on a ring R is a formal power series f(x,y) with coefficients in R satisfying the axioms that define a group and f(x,y)=f(y,x). A stably almost complex manifold X is a smooth (real) manifold with its tangent bundle TX being stably almost complex, that is after direct summing with a finite rank trivial bundle it becomes a complex vector bundle. An elliptic curve E is a genus 1 Riemann surface. I will introduce a very surprising connection among these three objects, and explain what it means by saying "signature and A-hat genus correspond to degenerate elliptic curves".

 WednesdayMarch 13, 20191:00 PM - 2:00 PM Math Tower P-131 Shamuel Auyeung, Stony Brook University Morse Theory and Hamiltonian Floer HomologyOne rendition of Arnold's famous conjecture is the following: The number of 1-periodic solutions of a nondegenerate time-dependent Hamiltonian system on a compact symplectic manifold $(M,ω)$ is greater than or equal to $\sum_k dim(H_k(M; \mathbb{Z}_2))$. The goal of this talk is to tell a story of Arnold's conjecture, beginning with Morse theory and ending with an answer to the conjecture by way of an infinite dimensional Morse theory variant: Floer theory. Along the way, I'll define what we need to understand the conjecture itself and also introduce the main players: well-chosen functions and their critical points, vector fields and their trajectories, transversality and compactness.

 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 and Art Symposium for Tony Phillips Math Club Math Day 2016 Math in Jeans Mathematical Writing Seminar Mathematics Department Gathering 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 Representation Theory Student Seminar RTG Colloquium RTG Seminar RTG Student Geometry Seminar SCGP Seminars 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 Differential 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