Geometry/Topology Seminar

from Friday
June 01, 2018 to Monday
December 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 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

 TuesdaySeptember 25, 20184:00 PM - 5:30 PM Math Tower P-131 Benjamin McMillan, Stony Brook University Conservation laws and Monge-Ampère parabolic equationsIn this talk I will describe how the geometry of an arbitrary parabolic second order equation governs the behavior of its conservation laws, and conversely, how the existence of a conservation law puts strong geometric restrictions on a parabolic equation. In particular, the class of Monge-Ampère parabolic equations is very non-generic, but I will nonetheless describe how the only parabolic equations with at least one conservation law are those of Monge-Ampere type.

 TuesdayOctober 02, 20184:00 PM - 5:30 PM Math Tower P-131 Eric Woolgar, University of Alberta Formal power series solutions of the Bach equationConformal gravity is an alternative to Einstein gravity in 4 dimensions, obtained by replacing the Einstein equation by the Bach equation, which has many more solutions. Maldacena has proposed that the theories are equivalent, provided one imposes certain boundary and physical conditions to remove the additional solutions of the Bach equation. We test this idea. Following the method laid out by Fefferman and Graham for the Einstein equation, we expand asymptotically hyperbolic solutions of the Bach equation in power series about conformal infinity, so as to identify the free data and find those data that yield Einstein metrics. There are infinitely many free data, reflecting the conformal invariance of the 4-dimensional Bach equation, but even if we choose to break conformal invariance by imposing a constant-scalar-curvature condition, the so-called mass aspect tensor remains freely specifiable. In dimensions greater than 4, there are many different generalizations of the Bach tensor, most of which are not well-suited to the Fefferman-Graham method. We choose a well-suited definition and find that the free data separate into two pairs of data, reflecting the separation of data for the Einstein equation into "Dirichlet" and "Neumann" data. This talk is based on joint work with Aghil Alaee.

 TuesdayOctober 23, 20184:00 PM - 5:30 PM Math Tower P-131 Xujia Chen, Stony Brook University Kontsevich-type recursions for counts of real curvesKontsevich's recursion, proved by Ruan-Tian in the early 90s, enumerates rational curves in complex surfaces. Welschinger defined invariant signed counts of real rational curves in real surfaces (complex surfaces with a conjugation) in 2003. Solomon interpreted Welschinger's invariants as holomorphic disk counts in 2006 and proposed Kontsevich-type recursions for them in 2007, along with an outline for adapting Ruan-Tian's homotopy style argument to the real setting. For many symplectic fourfolds, these recursions determine all invariants from basic inputs. We establish Solomon's recursions by re-interpreting his disk counts as degrees of relatively oriented pseudocycles from moduli spaces of stable real maps and lifting cobordisms from Deligne-Mumford moduli spaces of stable real curves.

 TuesdayOctober 30, 20184:00 PM - 5:30 PM Math Tower P-131 Yang Li, Imperial College Dirichlet problem for maximal graphs of higher codimensionMaximal submanifolds in Lorentzian type ambient spaces are the formal analogues of minimal submanifolds in Euclidean spaces, which arise naturally in adiabatic problems for G2 manifolds. We obtain general existence and uniqueness results for the Dirichlet problem of graphical maximal submanifolds in any codimension, which stand in sharp contrast to the analogous problem for graphical minimal submanifolds.

 TuesdayNovember 06, 20184:00 PM - 5:30 PM Math Tower P-131 Ruobing Zhang, Stony Brook University Compactness and bubbling phenomena of Bach-flat manifoldsThis talk centers on the regularity and structure theory of Bach-flat 4-manifolds. We will introduce some recent study of the $σ_2$-curvature equation on Bach-flat 4-manifolds. Specifically, we are interested in the limiting behavior of the solutions and also characterizing the bubble limits of the blowing-up solutions. This is joint work with Alice Chang and Paul Yang.

 TuesdayNovember 13, 20184:00 PM - 5:30 PM Math Tower P-131 Demetre Kazaras, Stony Brook University PSC bordism and the periodic eta-invariantIn this talk, we will study spin manifolds equipped with metrics of positive scalar curvature (psc) and infinite-cyclic covers. Considering the Dirac operator on the cover, one may define a periodic eta-invariant. By establishing an index theorem for end-periodic operators, Mrowka-Ruberman-Saveliev have shown that this invariant can distinguish path components in the moduli space of psc metrics. In this talk we go further, using a minimal hypersurface method to show that the periodic eta-invariant can distinguish psc-bordism classes in dimensions less than 7.

 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