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AKSZ quantization of shifted Poisson structures

Nick Rozenblyum University of Chicago
April 22, 2016

PIRSA:16040085
Mathematical Physics
PSI 2015/2016 - Explorations in Particle Theory - Lecture 10

Cliff Burgess McMaster University

April 22, 2016

PIRSA:16040029
Spin and evolution in geometric models of matter

Bernd Schroers Heriot-Watt University
April 21, 2016

PIRSA:16040063
General Relativity & Quantum Cosmology
Formal loop spaces

Benjamin Hennion Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
April 21, 2016

PIRSA:16040084
Mathematical Physics
Free linear BV-quantization as an infinity-functor

Rune Haugseng Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
April 21, 2016

PIRSA:16040083
Mathematical Physics
PSI 2015/2016 - Explorations in Cosmology - Lecture 9

Kendrick Smith Perimeter Institute for Theoretical Physics

April 21, 2016

PIRSA:16040043
On the stable homotopy theory of stacks and elliptic cohomology

David Gepner Purdue University
April 21, 2016

PIRSA:16040082
Mathematical Physics
PSI 2015/2016 - Explorations in Particle Theory - Lecture 9

Cliff Burgess McMaster University

April 21, 2016

PIRSA:16040028
Derived symplectic geometry and classical Chern-Simons theory

Damien Calaque University of Montpellier
April 20, 2016

PIRSA:16040081
Mathematical Physics
Towards a general description of derived self-intersections

Julien Grivaux Aix-Marseille University
April 20, 2016

PIRSA:16040080
Mathematical Physics
PSI 2015/2016 - Explorations in Cosmology - Lecture 8

Kendrick Smith Perimeter Institute for Theoretical Physics

April 20, 2016

PIRSA:16040042
Relative non-commutative Calabi-Yau structures and shifted Lagrangians

Christopher Brav National Research University Higher School of Economics
April 20, 2016

PIRSA:16040079
Mathematical Physics

AKSZ quantization of shifted Poisson structures

Nick Rozenblyum University of Chicago
April 22, 2016

PIRSA:16040085
Mathematical Physics
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. One pleasant consequence is that every deformation quantization problem reduces to a version of BV-quantization. Time permitting, I will describe several geometric applications of the theory.
PSI 2015/2016 - Explorations in Particle Theory - Lecture 10

Cliff Burgess McMaster University

April 22, 2016

PIRSA:16040029
Spin and evolution in geometric models of matter

Bernd Schroers Heriot-Watt University
April 21, 2016

PIRSA:16040063
General Relativity & Quantum Cosmology
In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.

In the geometric models of matter, proposed in a joint paper with Michael Atiyah and Nick Manton, static particles like the electron or proton are modelled by Riemannian 4-manifolds. In this talk I will explain how the spin degrees of freedom appear in the geometric framework. I will also discuss a proposal for time evolution in one particular model, namely the Taub-NUT model of the electron.
Formal loop spaces

Benjamin Hennion Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
April 21, 2016

PIRSA:16040084
Mathematical Physics
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

Rune Haugseng Max Planck Institute for Gravitational Physics - Albert Einstein Institute (AEI)
April 21, 2016

PIRSA:16040083
Mathematical Physics
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.
PSI 2015/2016 - Explorations in Cosmology - Lecture 9

Kendrick Smith Perimeter Institute for Theoretical Physics

April 21, 2016

PIRSA:16040043
On the stable homotopy theory of stacks and elliptic cohomology

David Gepner Purdue University
April 21, 2016

PIRSA:16040082
Mathematical Physics
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.
PSI 2015/2016 - Explorations in Particle Theory - Lecture 9

Cliff Burgess McMaster University

April 21, 2016

PIRSA:16040028
Derived symplectic geometry and classical Chern-Simons theory

Damien Calaque University of Montpellier
April 20, 2016

PIRSA:16040081
Mathematical Physics
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

Julien Grivaux Aix-Marseille University
April 20, 2016

PIRSA:16040080
Mathematical Physics
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.
PSI 2015/2016 - Explorations in Cosmology - Lecture 8

Kendrick Smith Perimeter Institute for Theoretical Physics

April 20, 2016

PIRSA:16040042
Relative non-commutative Calabi-Yau structures and shifted Lagrangians

Christopher Brav National Research University Higher School of Economics
April 20, 2016

PIRSA:16040079
Mathematical Physics
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. When A itself is endowed with a Calabi-Yau structure and relative Calabi-Yau structure on f is compatible with the absolute structure on A, then we sketch the construction of a shifted symplectic structure on the derived moduli space M_A of pseudo-perfect A-modules, as well as the construction of a Lagrangian structure on the induced map f* : M_B --> M_A of derived moduli. This is joint work with Tobias Dyckerhoff.

Title	Date	Collection	Type	Info
AKSZ quantization of shifted Poisson structures	2016‑04‑22	Deformation Quantization of Shifted Poisson Structures	Conference	View details
PSI 2015/2016 - Explorations in Particle Theory - Lecture 10	2016‑04‑22	PSI 2015/2016 - Explorations in Particle Theory (Burgess)	Course	View details
Spin and evolution in geometric models of matter	2016‑04‑21	Quantum Gravity	Scientific Series	View details
Formal loop spaces	2016‑04‑21	Deformation Quantization of Shifted Poisson Structures	Conference	View details
Free linear BV-quantization as an infinity-functor	2016‑04‑21	Deformation Quantization of Shifted Poisson Structures	Conference	View details
PSI 2015/2016 - Explorations in Cosmology - Lecture 9	2016‑04‑21	PSI 2015/2016 - Explorations in Cosmology (Smith)	Course	View details
On the stable homotopy theory of stacks and elliptic cohomology	2016‑04‑21	Deformation Quantization of Shifted Poisson Structures	Conference	View details
PSI 2015/2016 - Explorations in Particle Theory - Lecture 9	2016‑04‑21	PSI 2015/2016 - Explorations in Particle Theory (Burgess)	Course	View details
Derived symplectic geometry and classical Chern-Simons theory	2016‑04‑20	Deformation Quantization of Shifted Poisson Structures	Conference	View details
Towards a general description of derived self-intersections	2016‑04‑20	Deformation Quantization of Shifted Poisson Structures	Conference	View details
PSI 2015/2016 - Explorations in Cosmology - Lecture 8	2016‑04‑20	PSI 2015/2016 - Explorations in Cosmology (Smith)	Course	View details
Relative non-commutative Calabi-Yau structures and shifted Lagrangians	2016‑04‑20	Deformation Quantization of Shifted Poisson Structures	Conference	View details

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Format results

AKSZ quantization of shifted Poisson structures

PSI 2015/2016 - Explorations in Particle Theory - Lecture 10

Spin and evolution in geometric models of matter

Formal loop spaces

Free linear BV-quantization as an infinity-functor

PSI 2015/2016 - Explorations in Cosmology - Lecture 9

On the stable homotopy theory of stacks and elliptic cohomology

PSI 2015/2016 - Explorations in Particle Theory - Lecture 9

Derived symplectic geometry and classical Chern-Simons theory

Towards a general description of derived self-intersections

PSI 2015/2016 - Explorations in Cosmology - Lecture 8

Relative non-commutative Calabi-Yau structures and shifted Lagrangians

AKSZ quantization of shifted Poisson structures

PSI 2015/2016 - Explorations in Particle Theory - Lecture 10

Spin and evolution in geometric models of matter

Formal loop spaces

Free linear BV-quantization as an infinity-functor

PSI 2015/2016 - Explorations in Cosmology - Lecture 9

On the stable homotopy theory of stacks and elliptic cohomology

PSI 2015/2016 - Explorations in Particle Theory - Lecture 9

Derived symplectic geometry and classical Chern-Simons theory

Towards a general description of derived self-intersections

PSI 2015/2016 - Explorations in Cosmology - Lecture 8

Relative non-commutative Calabi-Yau structures and shifted Lagrangians