Benedict Morrissey

In summer 2017 the DAG learning seminar is going over shifted Poisson and symplectic geometry, and quantization. There may also be a brief session in August on applications to algebraic topology (Chromatic homotopy theory, Elliptic Cohomology,...). Now that Mauro is gone I guess I'm organizing the seminar. Notes to appear.

The Talk Schedule is:

  • Derived Differential Calculus, Formal Localization and Poisson structures (M-), 14th June.
  • Quantization and Quantization of Coisotropic structures (M-), 15th June.
  • Quantization of -1 -shifted structures, Darboux forms, and the perverse sheaf of vanishing cycles (SJ), 16th June.

A list of useful references is given by:

The Derived Algebraic Geometry Seminar is a learning seminar in Spring 2017 (continuing from Spring 2016), run by Mauro Porta. The goal of the Spring 2017 Seminar is to apply the knowledge of derived geometry from the previous semester to problems in enumerative geometry. In particular a quasismooth derived stack endows its truncation with a perfect obstruction theory, and a (-1)-shifted symplectic structure gives rise to a symmetric obstruction theory.

The seminar meets in 4N30 on Monday at 12 Noon to 1:30PM. Typed (alpha release) notes are available here.

The Talk Schedule has been:

  • Axiomatic Gromov-Witten Invariants (Matei), Tuesday 17th January.
  • Obstruction Theories and GW Invariants (M-), Thursday 2nd February, Part II on 6th February.
  • Artin-Lurie Representability and Mapping Stacks (Matei), 13th Febuary.
  • Reduced Structure for Stable Maps to K3-surfaces (M-), 20th February.
  • DT Theory and Stable Pairs (SJ), 27th February.
  • Discussion session on J.Pardon's approach to Virtual Fundamental Classes
  • An introduction to derived differential geometry (SJ)
  • An interpretation of J. Pardon's approach in Derived differential or algebraic geometry (M-), 3rd April
  • More on Derived Differential Geometry (DM Stacks in derived differential geometry) (Matei), 10th April
  • Further Derived Differential Geometry and derived cobordism (SJ), 17th April
  • Derived Symplectic Reduction, and charts for derived cobordism (M-), 24th April

A list of useful references is given by:

On Enumerative Geometry

On the Intrinsic Normal Cone approach

On the approach of J.Pardon

On Derived Differential Geometry

The notes (Taken by Matei and I) for the first seminar of the Derived Algebraic Geometry seminar can be found here.

Problems (by Mauro) with some solutions (Sukjoo, Matei and I) can be found here.

The Talk Schedule was:

  • Infinity Categories (Mauro)
  • Derived Affines (M-)
  • Stable Infinity Categories (Michael)
  • Cotangent Complex (SJ)
  • Square Zero Extensions(Matei)
  • Perfect Complexes (M-)
  • Descent (Antonjio)
  • Geometric Stacks and Gluing (Mauro)
  • The Stack Perf (SJ)
  • D-modules (M-)
  • HKR Isomorphism and Shifted Symplectic Structures (Matei)

A list of useful references is given by:


Infinity Categories

Algebra in CDGA's/SCR's/E infinity rings

Descent and Stacks

Perfect Complexes

Shifted Symplectic Structures and HKR Isomorphism