Equivalence Method and Exterior Differential Systems 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 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

 FridayFebruary 09, 20181:30 PM - 2:30 PM P-131 Aaron Mazel-Gee, USC The geometry of the cyclotomic traceAlgebraic $K$-theory -- the analog of topological $K$-theory for varieties and schemes -- is a deep and far-reaching invariant, but it is notoriously difficult to compute. To date, the primary means of understanding $K$-theory is through its cyclotomic trace'' map $K → TC$ to topological cyclic homology. This map is usually advertised as an analog of the Chern character, but this is something of a misnomer: $TC$ is a further refinement of any flavor of de Rham cohomology (even topological'', i.e.\! built from $THH$), though this discrepancy disappears rationally. However, despite the enormous success of so-called trace methods'' in $K$-theory computations, the algebro-geometric nature of $TC$ has remained mysterious. In this talk, I will describe a new construction of $TC$ that affords a precise interpretation of the cyclotomic trace at the level of derived algebraic geometry, which is based on nothing but universal properties (coming from Goodwillie calculus) and the geometry of 1-manifolds (via factorization homology). This is joint work with David Ayala and Nick Rozenblyum.

 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