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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 – 1st Floor |
11:00 – 12:00pm |
Mauro Porta, Institut de Mathematiques Jussieu |
Alice Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2nd Floor |
2:00 – 3:00pm |
Dominic Joyce, Oxford University |
Alice Room |
3:00 – 3:30pm |
Coffee Break |
Bistro – 1st 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 – 1st Floor |
11:00 – 12:00pm |
Dima Arinkin, University of Wisconsin |
Alice Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2nd Floor |
2:00 – 3:00pm |
Ted Spaide, University of Vienna |
Alice Room |
3:00 – 3:30pm |
Coffee Break |
Bistro – 1st 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 – 1st Floor |
11:00 – 12:00pm |
Julien Grivaux, Aix-Marseille Université |
Alice Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2nd Floor |
2:00 – 3:30pm |
Colloquium |
Time Room |
3:30 – 4:00pm |
Coffee Break |
Bistro – 1st Floor |
5:30pm |
Banquet |
Bistro – 2nd 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 – 1st Floor |
11:00 – 12:00pm |
Rune Haugseng, Max Planck Institute |
Alice Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2nd 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 – 1st 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 – 1st Floor |
11:00 – 12:00pm |
Pavel Safronov, Oxford University |
Alice Room |
12:00 – 2:00pm |
Lunch |
Bistro – 2nd 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.
Symplectic and Lagrangian structures on mapping stacks
An important result in shifted symplectic geometry is the existence of shifted symplectic forms on mapping spaces with symplectic target and oriented source. I provide several examples of more complicated situations where stacks of maps shifted symplectic structures, or maps between them have Lagrangian structures. These include spaces of framed maps, pushforwards of perfect complexes, and perfect complexes on open varieties.
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.
What is the Todd class of an orbifold?
The Todd class enters algebraic geometry in two places, in the Hirzebruch-Riemann-Roch formula and in the correction of the HKR isomorphism needed to make the Hochschild cohomology isomorphic to polyvector field cohomology (Kontsevich’s claim, proved by Calaque and van den Bergh). In the case of orbifolds the Riemann-Roch formula is known, but not the analogue of Kontsevich’s result. However, we can try to use the former as a guide towards a conjectural formulation for the latter.
Shifted structures and quantization
I will discuss the comparison of shifted Poisson and symplectic geometry and applications to the shifted quantization of moduli spaces.
Categorification of shifted symplectic geometry using perverse sheaves
Let (X,w) be a -1-shifted symplectic derived scheme or stack over C in the sense of Pantev-Toen-Vaquie-Vezzosi with an "orientation" (square root of det L_X). We explain how to construct a perverse sheaf P on the classical truncation X=t_0(X), over a base ring A. The hypercohomology H*(P) is regarded as a categorification of X.
Now suppose i : L --> X is a Lagrangian in (X,w) in the sense of PTVV, with a "relative orientation". We outline a programme (work in progress) to construct a natural morphism
\mu : A_L[vdim L] --> i^!(P)
An overview of derived analytic geometry
After the pioneering work of J. Lurie in [DAG-IX], the possibility of a derived version of analytic geometry drew the attention of several mathematicians. The goal of this talk is to provide an overview of the state of art of derived analytic geometry, addressing both the complex and the non-archimedean setting.
Formal derived stack and Formal localization
A crucial ingredient in the theory of shifted Poisson structures on general derived Artin stacks is the method of formal localization.
Formal localization is interesting in its own right as a new, very power ful tool that will prove useful in order to globalize tricky constructions and results, whose extension from the local case presents obstructions that only vanish formally locally.
Pages
Scientific Organizers:
- Damien Calaque, IMAG, University of Montpellier 2
- Kevin Costello, Perimeter Institute
- Ryan Grady, Perimeter Institute
- Tony Pantev, University of Pennsylvania