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Within the past five years derived geometry has become a central tool in the mathematics of quantum field theory. Even more recently, shifted Poisson structures (generalizing those of classical mechanics) and their quantization have found application in both mathematics and quantum fields and strings. This conference will allow for the review of recent advances in derived geometry and applications thereof to various moduli spaces by leading experts. In addition, the conference seeks to facilitate the expansion of these techniques into the realm of supersymmetric gauge theory in dimensions three and four.
- Dima Arinkin, University of Wisconsin
- Oren Ben-Bassat, University of Haifa
- Christopher Brav, National Research University Higher School of Economics
- Damien Calaque, IMAG, University of Montpellier 2
- Andrei Caldararu, University of Wisconsin
- David Gepner, Purdue University
- Julien Grivaux, Aix-Marseille Université
- Rune Haugseng, Max Planck Institute of Mathematics
- Benjamin Hennion, Max Planck Institute of Mathematics
- Dominic Joyce, Oxford University
- Mauro Porta, Institut de Mathematiques Jussieu
- Nick Rozenblyum, University of Chicago
- Pavel Safronov, Oxford University
- Theodore Spaide, University of Vienna
- David Treumann, Boston College
- Michel Vaquie, Universite Paul Sabatier
- Dima Arinkin, University of Wisconsin
- Oren Ben-Bassat, University of Haifa
- Christopher Brav, National Research University Higher School of Economics
- Alexander Braverman, Perimeter Institute & University of Toronto
- Damien Calaque, IMAG, University of Montpellier 2
- Andrei Caldararu, University of Wisconsin
- Kevin Costello, Perimeter Institute
- Chris Dodd, Perimeter Institute
- Chris Elliott, Northwestern University
- David Gepner, Purdue University
- Ryan Grady, Perimeter Institute
- Julien Grivaux, Aix-Marseille Université
- Rune Haugseng, Max Planck Institute of Mathematics
- Benjamin Hennion, Max Planck Institute of Mathematics
- Dominic Joyce, Oxford University
- Mykola Matviichuk, University of Toronto
- Tony Pantev, University of Pennsylvania
- Mauro Porta, Institut de Mathematiques Jussieu
- Nick Rozenblyum, University of Chicago
- Pavel Safronov, Oxford University
- Theodore Spaide, University of Vienna
- David Treumann, Boston College
- Michel Vaquie, Universite Paul Sabatier
- Philsang Yoo, Northwestern University
Monday, April 18, 2016
Time |
Event |
Location |
9:00 – 9:30am |
Registration |
Reception |
9:30 – 9:35am |
Welcome and Opening Remarks |
Alice Room |
9:35 – 10:30am |
Michel Vaquie, University Paul Sabatier |
Alice Room |
10:30 – 11:00am |
Coffee Break |
Bistro – 1^{st} Floor |
11:00 – 12:00pm |
Mauro Porta, Institut de Mathematiques Jussieu |
Alice Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2^{nd} Floor |
2:00 – 3:00pm |
Dominic Joyce, Oxford University |
Alice Room |
3:00 – 3:30pm |
Coffee Break |
Bistro – 1^{st} Floor |
3:30pm – 4:30pm |
Tony Pantev, University of Pennsylvania |
Alice Room |
Tuesday, April 19, 2016
Time |
Event |
Location |
9:30 – 10:30am |
Andrei Caldararu, University of Wisconsin |
Alice Room |
10:30 – 11:00am |
Coffee Break |
Bistro – 1^{st} Floor |
11:00 – 12:00pm |
Dima Arinkin, University of Wisconsin |
Alice Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2^{nd} Floor |
2:00 – 3:00pm |
Ted Spaide, University of Vienna |
Alice Room |
3:00 – 3:30pm |
Coffee Break |
Bistro – 1^{st} Floor |
3:30pm – 4:30pm |
David Treumann, Boston College |
Alice Room |
Wednesday, April 20, 2016
Time |
Event |
Location |
9:30 – 10:30am |
Christopher Brav, Higher School of Economics (Moscow) |
Alice Room |
10:30 – 11:00am |
Coffee Break |
Bistro – 1^{st} Floor |
11:00 – 12:00pm |
Julien Grivaux, Aix-Marseille Université |
Alice Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2^{nd} Floor |
2:00 – 3:30pm |
Colloquium |
Time Room |
3:30 – 4:00pm |
Coffee Break |
Bistro – 1^{st} Floor |
5:30pm |
Banquet |
Bistro – 2^{nd} Floor |
Thursday, April 21, 2016
Time |
Event |
Location |
9:30 – 10:30am |
David Gepner, Purdue University |
Alice Room |
10:30 – 11:00am |
Coffee Break |
Bistro – 1^{st} Floor |
11:00 – 12:00pm |
Rune Haugseng, Max Planck Institute |
Alice Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2^{nd} Floor |
2:00 – 3:00pm |
Benjamin Hennion, Max Planck Institute |
Alice Room |
3:00 – 3:15pm |
Conference Photo |
TBA |
3:15 – 4:15pm |
Coffee Break |
Bistro – 1^{st} Floor |
4:15pm |
Collaboration |
Alice Room |
Friday, April 22, 2016
Time |
Event |
Location |
9:30 – 10:30am |
Nick Rozenbluym, University of Chicago |
Alice Room |
10:30 – 11:00am |
Coffee Break |
Bistro – 1^{st} Floor |
11:00 – 12:00pm |
Pavel Safronov, Oxford University |
Alice Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2^{nd} Floor |
2:00 – 3:00pm |
Oren Ben-Bassat, University of Hafia |
Alice Room |
3:00 – 3:10pm |
Wrap-up and Good-bye |
Alice Room |
Dima Arinkin, University of Wisconsin
Singular support of categories
In many situations, geometric objects on a space have some kind of singular support, which refines the usual support. For instance, for smooth X, the singular support of a D-module (or a perverse sheaf) on X is as a conical subset of the cotangent bundle; similarly, for quasi-smooth X, the singular support of a coherent sheaf on X is a conical subset of the cohomologically shifted cotangent bundle. I would like to describe a higher categorical version of this notion.
A perspective on derived analytic geometry
I will present a 'categorical' way of doing analytic geometry in which analytic geometry is seen as a precise analogue of algebraic geometry.
Our approach works for both complex analytic geometry and p-adic analytic geometry in a uniform way. I will focus on the idea of an 'open set' as used in various geometrical theories and how it is characterized
Derived coisotropic structures
I will define coisotropic structures in the setting of shifted Poisson geometry in two ways and show their equivalence. The interplay between the definitions allows one to produce nontrivial statements. I will also describe some examples of coisotropic structures. This is a report on joint work with V. Melani.
AKSZ quantization of shifted Poisson structures
One of the key constructions in the PTVV theory of shifted symplectic structures is the construction, via transgression, of a shifted symplectic structure on the derived mapping stack from an oriented manifold to a shifted symplectic stack vastly generalizing the AKSZ construction (which was formulated in the context of super manifolds). I will explain local-to-global approach to this construction, which also generalizes the construction to shifted Poisson structures and shows that the AKSZ/PTVV construction is compatible with quantization in a strong sense.
Formal loop spaces
Formal loop spaces are algebraic analogs to smooth loops. They were introduced and studied extensively in the 2000' by Kapranov and Vasserot for their link to chiral algebras.
In this talk, we will introduced higher dimensional analogs of K. and V. formal loop spaces. We will show how derived methods allow such a definition. We will then study their tangent complexes: even though formal loop spaces are "of infinite dimension", their tangent has enough structure so that we can speak of symplectic forms on them.
Free linear BV-quantization as an infinity-functor
I will describe a functorial construction of the free BV-quantization of chain complexes equipped with antisymmetric forms of degree 1 in the context of infinity-categories. This is joint work with Owen Gwilliam.
On the stable homotopy theory of stacks and elliptic cohomology
In this talk, we'll discuss what it means to be a cohomology theory for topological stacks, using a notion of local symmetric monoidal inversion of objects in families. While the general setup is abstract, it specializes to many cases of interest, including Schwede's global spectra. We will then go on to discuss various examples with particular emphasis on elliptic cohomology. It turns out that TMF sees more objects as dualizable (or even invertible) than one might naively expect.
Derived symplectic geometry and classical Chern-Simons theory
In this talk we will review various point-of-views on classical Chern-Simons theory and moduli of flat connections. We will explain how derived symplectic geomletry (after
Pantev-Toën-Vaquié-Vezzosi) somehow reconciles all of these. If time permits, we will discuss a bit the quantization problem.
Towards a general description of derived self-intersections
Thanks to a result of Arinkin and Cāldāru, the derived self-intersection of a closed smooth subscheme of an ambiant scheme (over a field of characteristic zero) is a formal object if and only if the conormal bundle of the subscheme extends to a locally free sheaf at the first order. In this talk, we will explain a program as well as new results in order to describe these derived self-intersections in the non-formal case.
Relative non-commutative Calabi-Yau structures and shifted Lagrangians
We give a definition of relative Calabi-Yau structure on a dg functor f: A --> B, discussing a examples coming from algebraic geometry, homotopy theory, and representation theory. When A=0, this returns the usual definition of Calabi-Yau structure on a smooth dg category B.
The Maslov cycle and the J-homomorphism
Let L be an exact Lagrangian submanifold of a cotangent bundle T^* M. If a topological obstruction vanishes, a local system of R-modules on L determines a constructible sheaf of R-modules on M -- this is the Nadler-Zaslow construction. I will discuss a variant of this construction that avoids Floer theory, and that allows R to be a ring spectrum. The talk is based on joint work with Xin Jin.
Pages
Scientific Organizers:
- Damien Calaque, IMAG, University of Montpellier 2
- Kevin Costello, Perimeter Institute
- Ryan Grady, Perimeter Institute
- Tony Pantev, University of Pennsylvania