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:

- T. Pantev, B. Toen, M. Vaquie, G. Vezzosi, Shifted Symplectic Structures.
- D. Calaque, T. Pantev, B. Toen, M. Vaquie, G. Vezzosi, Shifted Poisson Structures and Deformation Quantization
- T. Pantev, G. Vezzosi, Symplectic and Poisson derived geometry and deformation quantization
- M. Kontsevich, Operads and Motives in Deformation Quantization
- P. Safronov, Braces and Poisson additivity
- V. Melani, P. Safronov, Derived coisotropic structures I: affine case
- V. Melani, P. Safronov, Derived coisotropic structures II: stacks and quantization
- C. Brav, V. Bussi, D. Dupont, D. Joyce, B. Szendroi, Symmetries and stabilization for sheaves of vanishing cycles
- J. Pridham, Deformation quantisation for unshifted symplectic structures on derived Artin stacks
- J. Pridham, Deformation quantisation for (-1)-shifted symplectic structures and vanishing cycles
- A. Preygel, Thom-Sebastiani & Duality for Matrix Factorizations
- K. Costello, O. Gwilliam, Factorization algebras in Quantum Field Theory
- J. Wallbridge, Derived smooth stacks and prequantum categories

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

- M. Kontsevich, Y. Manin, Gromov-Witten classes, Quantum Cohomology and Enumerative Geometry
- R. Pandharipande, R. P. Thomas, 13/2 ways of counting curves

On the Intrinsic Normal Cone approach

- K. Behrend, B. Fantechi, The intrinsic normal cone
- K. Behrend, Y. Manin, Stacks of Stable Maps and Gromov-Witten Invariants
- K. Behrend, Gromov-Witten invariants in algebraic geometry
- T. Schürg, B. Toën, G. Vezzosi, Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes
- N. Nabijou, Virtual Fundamental Classes in Gromov-Witten Theory

On the approach of J.Pardon

- J. PardonAn algebraic approach to virtual fundamental cycles on moduli spaces of pseudo-holomorphic curves
- J. Pardon Contact homology and virtual fundamental cycles

On Derived Differential Geometry

- Lurie, DAG V
- D. Spivak, Derived Smooth Manifolds
- D. Joyce, D-manifolds and d-orbifolds: a theory of derived differential geometry
- J. Wallbridge, Derived smooth stacks and prequantum categories
- A. Macpherson On the universal property of derived 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:

General

- J. Lurie Derived Algerbraic Geometry, and Spectral Algebraic Geometry (under construction)
- B. Toen, G. Vezzosi, Homotopical Algebraic Geometry II: geometric stacks and applications
- D. Gaitsgory and N. Rozenblyum A study in derived algebraic geometry

Infinity Categories

- M. Groth A short course on Infinity-categories
- J. Lurie Higher Topos Theory

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

- W. Gillam Simplicial Methods in Algebra and Algebraic Geometry
- J. Lurie Higher Algebra

Descent and Stacks

- J. Lurie, DAG VII
- J. Lurie, DAG V
- M. Porta, Comparison results for derived Deligne-Mumford stacks
- B. Toen, G. Vezzosi, Homotopical Algebraic Geometry II: geometric stacks and applications

Perfect Complexes

- T. Schürg, B. Toën, G. Vezzosi, Derived algebraic geometry, determinants of perfect complexes, and applications to obstruction theories for maps and complexes

Shifted Symplectic Structures and HKR Isomorphism

- B. Toen, G. Vezzosi, Algebres simpliciales S1 - ́equivariantes, theorie de Rham et theoremes HKR multiplicatifs
- D. Ben-Zvi, D. Nadler Loop Spaces and Connections
- T. Pantev, B. Toen, M. Vaquie, G. Vezzosi, Shifted Symplectic Structures.