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Autumn Semester 2012

Date / Time Speaker Title Location
20 September 2012
14:00-18:00 		Benjamin Cooper
University of Zurich
Samuel Monnier
University of Zurich
Marcello Porta
ETH Zurich
Thomas Willwacher
ETH Zurich
Details

Talks in Mathematical Physics

Title End of Summer meeting in mathematical physics
Speaker, Affiliation Benjamin Cooper, University of Zurich
Samuel Monnier, University of Zurich
Marcello Porta, ETH Zurich
Thomas Willwacher, ETH Zurich
Date, Time 20 September 2012, 14:00-18:00
Location HIT E 41.1
Documents Monnier's beamerfile_download
Porta's beamerfile_download
End of Summer meeting in mathematical physicsread_more
HIT E 41.1
27 September 2012
15:15-16:15 		Chiara Esposito
Oberwolfach
Details

Talks in Mathematical Physics

Title Momentum map and reduction in Poisson geometry and deformation quantization
Speaker, Affiliation Chiara Esposito, Oberwolfach
Date, Time 27 September 2012, 15:15-16:15
Location HG G 43
Documents beamerfile_download
Momentum map and reduction in Poisson geometry and deformation quantizationread_more
HG G 43
4 October 2012
15:15-16:15 		Prof. Dr. Caldararu Andrei
Univ. Wisconsin Madison & Max Planck Institut
Details

Talks in Mathematical Physics

Title Formality of ordinary and twisted de Rham complex from derived algebraic geometry
Speaker, Affiliation Prof. Dr. Caldararu Andrei, Univ. Wisconsin Madison & Max Planck Institut
Date, Time 4 October 2012, 15:15-16:15
Location HG G 43
Abstract Beautiful results of Deligne-Illusie, Sabbah, and Ogus-Vologodsky show that certain modifications of the de Rham complex (either the usual one, or twisted versions of it that appear in the study of the cyclic homology of categories of matrix factorizations) are formal in positive characteristic. These are the crucial steps in proving algebraic analogues of the Hodge theorem (again, either in the ordinary setting or in the presence of a twisting). I will present these results along with a new approach to understanding them using derived intersection theory. This is joint work with Dima Arinkin and Marton Hablicsek.
Formality of ordinary and twisted de Rham complex from derived algebraic geometryread_more
HG G 43
11 October 2012
15:15-16:15 		Yuri Berest
Cornell University, USA
Details

Talks in Mathematical Physics

Title Topics in noncommutative geometry (FIM Minicourse) 1/5
Speaker, Affiliation Yuri Berest, Cornell University, USA
Date, Time 11 October 2012, 15:15-16:15
Location HG G 43
Abstract In these lectures, we will discuss a variety of topics from algebraic geometry, noncommutative algebra and representation theory that usually go under the name of noncommutative geometry. Our aim is to give an overview of several popular approaches to noncommutative geometry and look at some interesting applications (mostly, in mathematical physics). Although the level of the lectures will be uneven (some topics will be covered in more detail while others will be touched upon only briefly), an effort will be made to make the discussion accessible for graduate students. A tentative syllabus: Rings of Differential Operators on Algebraic Varieties (Morita theory of differential operators. Differential operators on smooth and singular varieties. Differential equivalence and isomorphism. Ideals and commutative rings of differential operators on curves . Relation to integrable systems: Wilson's adelic Grassmannian and the KP hierarchy) Noncommutative Projective Geometry, I. Introduction (Coherent sheaves on projective varieties, Serre's Theorem. Artin-Zhang's noncommutative Proj. Twisted homogeneous coordinate rings. AS regular algebras associated to elliptic curves. Example: Sklyanin algebras. Classification of noncommutative projective planes and quadrics) Noncommutative Projective Geometry, II. Applications (Moduli spaces of framed torsion-free sheaves on NC projective planes and quiver varieties. The ADHM construction and the twistor transform in noncommutative geometry. Noncommutative instantons) Smooth Algebras and the Representation Functor (NC symplectic geometry. The formalism of double derivations: bisymplectic geometry and double Poisson brackets. Examples. Application: Calogero-Moser spaces over algebraic curves) Homotopical Algebra and Noncommutative Geometry (Quillen's model categories. Nonabelian derived functors. Pointed model categories: the loop and suspension functors. Examples: model categories of DG algebras and DG categories. Quillen cohomology. Applications: Ginzburg DG algebras, deformed Calabi-Yau completions (after Keller and Van den Bergh). Derived representation schemes)
Topics in noncommutative geometry (FIM Minicourse) 1/5read_more
HG G 43
18 October 2012
15:15-16:15 		Dr. Matthieu Anel
ETH Zurich, Switzerland
Details

Talks in Mathematical Physics

Title A new approach to the bar and cobar constructions through Sweedler's theory of coalgebras
Speaker, Affiliation Dr. Matthieu Anel, ETH Zurich, Switzerland
Date, Time 18 October 2012, 15:15-16:15
Location HG G 43
Abstract We will explain how the category dgCoalg of dg-coalgebras is monoidal closed and how the category dgAlg of dg-algebras is naturally enriched, tensor and cotensored over dgCoalg. This leads to six operations on algebras and coalgebras that we call Sweedler's theory. In particular, these operations can be used to produce various adjunctions between dgCoalg and dgAlg. We will explain how this gives back the bar-cobar adjunction. This a joint work with André Joyal.
A new approach to the bar and cobar constructions through Sweedler's theory of coalgebrasread_more
HG G 43
25 October 2012
15:15-16:15 		Yuri Berest
Cornell University, USA
Details

Talks in Mathematical Physics

Title Topics in noncommutative geometry (FIM Minicourse) 2/5
Speaker, Affiliation Yuri Berest, Cornell University, USA
Date, Time 25 October 2012, 15:15-16:15
Location HG G 43
Abstract In these lectures, we will discuss a variety of topics from algebraic geometry, noncommutative algebra and representation theory that usually go under the name of noncommutative geometry. Our aim is to give an overview of several popular approaches to noncommutative geometry and look at some interesting applications (mostly, in mathematical physics). Although the level of the lectures will be uneven (some topics will be covered in more detail while others will be touched upon only briefly), an effort will be made to make the discussion accessible for graduate students. A tentative syllabus: Rings of Differential Operators on Algebraic Varieties (Morita theory of differential operators. Differential operators on smooth and singular varieties. Differential equivalence and isomorphism. Ideals and commutative rings of differential operators on curves . Relation to integrable systems: Wilson's adelic Grassmannian and the KP hierarchy) Noncommutative Projective Geometry, I. Introduction (Coherent sheaves on projective varieties, Serre's Theorem. Artin-Zhang's noncommutative Proj. Twisted homogeneous coordinate rings. AS regular algebras associated to elliptic curves. Example: Sklyanin algebras. Classification of noncommutative projective planes and quadrics) Noncommutative Projective Geometry, II. Applications (Moduli spaces of framed torsion-free sheaves on NC projective planes and quiver varieties. The ADHM construction and the twistor transform in noncommutative geometry. Noncommutative instantons) Smooth Algebras and the Representation Functor (NC symplectic geometry. The formalism of double derivations: bisymplectic geometry and double Poisson brackets. Examples. Application: Calogero-Moser spaces over algebraic curves) Homotopical Algebra and Noncommutative Geometry (Quillen's model categories. Nonabelian derived functors. Pointed model categories: the loop and suspension functors. Examples: model categories of DG algebras and DG categories. Quillen cohomology. Applications: Ginzburg DG algebras, deformed Calabi-Yau completions (after Keller and Van den Bergh). Derived representation schemes)
Topics in noncommutative geometry (FIM Minicourse) 2/5read_more
HG G 43
1 November 2012
15:15-16:15 		Yuri Berest
Cornell University, USA
Details

Talks in Mathematical Physics

Title Topics in noncommutative geometry (FIM Minicourse) 3/5
Speaker, Affiliation Yuri Berest, Cornell University, USA
Date, Time 1 November 2012, 15:15-16:15
Location HG G 43
Abstract In these lectures, we will discuss a variety of topics from algebraic geometry, noncommutative algebra and representation theory that usually go under the name of noncommutative geometry. Our aim is to give an overview of several popular approaches to noncommutative geometry and look at some interesting applications (mostly, in mathematical physics). Although the level of the lectures will be uneven (some topics will be covered in more detail while others will be touched upon only briefly), an effort will be made to make the discussion accessible for graduate students. A tentative syllabus: Rings of Differential Operators on Algebraic Varieties (Morita theory of differential operators. Differential operators on smooth and singular varieties. Differential equivalence and isomorphism. Ideals and commutative rings of differential operators on curves . Relation to integrable systems: Wilson's adelic Grassmannian and the KP hierarchy) Noncommutative Projective Geometry, I. Introduction (Coherent sheaves on projective varieties, Serre's Theorem. Artin-Zhang's noncommutative Proj. Twisted homogeneous coordinate rings. AS regular algebras associated to elliptic curves. Example: Sklyanin algebras. Classification of noncommutative projective planes and quadrics) Noncommutative Projective Geometry, II. Applications (Moduli spaces of framed torsion-free sheaves on NC projective planes and quiver varieties. The ADHM construction and the twistor transform in noncommutative geometry. Noncommutative instantons) Smooth Algebras and the Representation Functor (NC symplectic geometry. The formalism of double derivations: bisymplectic geometry and double Poisson brackets. Examples. Application: Calogero-Moser spaces over algebraic curves) Homotopical Algebra and Noncommutative Geometry (Quillen's model categories. Nonabelian derived functors. Pointed model categories: the loop and suspension functors. Examples: model categories of DG algebras and DG categories. Quillen cohomology. Applications: Ginzburg DG algebras, deformed Calabi-Yau completions (after Keller and Van den Bergh). Derived representation schemes)
Topics in noncommutative geometry (FIM Minicourse) 3/5read_more
HG G 43
* 2 November 2012
10:15-11:15 		Marco Zambon
Universidad Autonoma de Madrid, ICMAT
Details

Talks in Mathematical Physics

Title Homotopy moment maps
Speaker, Affiliation Marco Zambon, Universidad Autonoma de Madrid, ICMAT
Date, Time 2 November 2012, 10:15-11:15
Location Y27 H 28
Abstract The notion of moment map is central in symplectic geometry, where the functions on the symplectic manifold (the "observables") form a Lie algebra. We extend this notion to higher differential forms, defining a homotopy moment map to be an $L_{\infty}$-algebra morphism into the observables. We give a cohomological interpretation (which provides a natural notion of equivalence), show that certain equivariant cocycles induce homotopy moment maps, and discuss obstructions. This is joint work in progress with Chris L. Rogers (Göttingen) and Yael Fregier (MIT).
Homotopy moment mapsread_more
Y27 H 28
8 November 2012
15:15-16:15 		Yuri Berest
Cornell University, USA
Details

Talks in Mathematical Physics

Title Topics in noncommutative geometry (FIM Minicourse) 4/5
Speaker, Affiliation Yuri Berest, Cornell University, USA
Date, Time 8 November 2012, 15:15-16:15
Location HG G 43
Abstract In these lectures, we will discuss a variety of topics from algebraic geometry, noncommutative algebra and representation theory that usually go under the name of noncommutative geometry. Our aim is to give an overview of several popular approaches to noncommutative geometry and look at some interesting applications (mostly, in mathematical physics). Although the level of the lectures will be uneven (some topics will be covered in more detail while others will be touched upon only briefly), an effort will be made to make the discussion accessible for graduate students. A tentative syllabus: Rings of Differential Operators on Algebraic Varieties (Morita theory of differential operators. Differential operators on smooth and singular varieties. Differential equivalence and isomorphism. Ideals and commutative rings of differential operators on curves . Relation to integrable systems: Wilson's adelic Grassmannian and the KP hierarchy) Noncommutative Projective Geometry, I. Introduction (Coherent sheaves on projective varieties, Serre's Theorem. Artin-Zhang's noncommutative Proj. Twisted homogeneous coordinate rings. AS regular algebras associated to elliptic curves. Example: Sklyanin algebras. Classification of noncommutative projective planes and quadrics) Noncommutative Projective Geometry, II. Applications (Moduli spaces of framed torsion-free sheaves on NC projective planes and quiver varieties. The ADHM construction and the twistor transform in noncommutative geometry. Noncommutative instantons) Smooth Algebras and the Representation Functor (NC symplectic geometry. The formalism of double derivations: bisymplectic geometry and double Poisson brackets. Examples. Application: Calogero-Moser spaces over algebraic curves) Homotopical Algebra and Noncommutative Geometry (Quillen's model categories. Nonabelian derived functors. Pointed model categories: the loop and suspension functors. Examples: model categories of DG algebras and DG categories. Quillen cohomology. Applications: Ginzburg DG algebras, deformed Calabi-Yau completions (after Keller and Van den Bergh). Derived representation schemes)
Topics in noncommutative geometry (FIM Minicourse) 4/5read_more
HG G 43
15 November 2012
15:15-16:15 		Yuri Berest
Cornell University, USA
Details

Talks in Mathematical Physics

Title Topics in noncommutative geometry (FIM Minicourse) 5/5
Speaker, Affiliation Yuri Berest, Cornell University, USA
Date, Time 15 November 2012, 15:15-16:15
Location HG G 43
Abstract In these lectures, we will discuss a variety of topics from algebraic geometry, noncommutative algebra and representation theory that usually go under the name of noncommutative geometry. Our aim is to give an overview of several popular approaches to noncommutative geometry and look at some interesting applications (mostly, in mathematical physics). Although the level of the lectures will be uneven (some topics will be covered in more detail while others will be touched upon only briefly), an effort will be made to make the discussion accessible for graduate students. A tentative syllabus: Rings of Differential Operators on Algebraic Varieties (Morita theory of differential operators. Differential operators on smooth and singular varieties. Differential equivalence and isomorphism. Ideals and commutative rings of differential operators on curves . Relation to integrable systems: Wilson's adelic Grassmannian and the KP hierarchy) Noncommutative Projective Geometry, I. Introduction (Coherent sheaves on projective varieties, Serre's Theorem. Artin-Zhang's noncommutative Proj. Twisted homogeneous coordinate rings. AS regular algebras associated to elliptic curves. Example: Sklyanin algebras. Classification of noncommutative projective planes and quadrics) Noncommutative Projective Geometry, II. Applications (Moduli spaces of framed torsion-free sheaves on NC projective planes and quiver varieties. The ADHM construction and the twistor transform in noncommutative geometry. Noncommutative instantons) Smooth Algebras and the Representation Functor (NC symplectic geometry. The formalism of double derivations: bisymplectic geometry and double Poisson brackets. Examples. Application: Calogero-Moser spaces over algebraic curves) Homotopical Algebra and Noncommutative Geometry (Quillen's model categories. Nonabelian derived functors. Pointed model categories: the loop and suspension functors. Examples: model categories of DG algebras and DG categories. Quillen cohomology. Applications: Ginzburg DG algebras, deformed Calabi-Yau completions (after Keller and Van den Bergh). Derived representation schemes)
Topics in noncommutative geometry (FIM Minicourse) 5/5read_more
HG G 43
22 November 2012
15:15-16:15 		Dmitry Roytenberg
University of Utrecht
Details

Talks in Mathematical Physics

Title Superalgebras of differentiable functions and derived geometry
Speaker, Affiliation Dmitry Roytenberg, University of Utrecht
Date, Time 22 November 2012, 15:15-16:15
Location HG G 43
Superalgebras of differentiable functions and derived geometry
HG G 43
* 23 November 2012
10:15-11:15 		Dr. Benoit Dherin
Berkeley
Details

Talks in Mathematical Physics

Title Quantization of actions and momentum maps
Speaker, Affiliation Dr. Benoit Dherin, Berkeley
Date, Time 23 November 2012, 10:15-11:15
Location Y27 H 26
Abstract We will introduce a space of (unitary) representations quantizing a (volume-preserving) action of a group on R^d. These representations are obtained by deforming the pullback representation on the functions on R^d using certain Fourier integral operators. We will give cohomological conditions on the existence and rigidity of such deformations and introduce corresponding "quantum momentum maps" quantizing the classical momentum map of the cotangent lift action. The main tool is a differential graded algebra (of amplitudes) whose Maurer-Cartan elements correspond to the representations. This is joint work with Igor Mencattini (ICMC-USP).
Quantization of actions and momentum mapsread_more
Y27 H 26
* 26 November 2012
14:00-15:00 		Francesco Bonechi
INFN Firenze
Details

Talks in Mathematical Physics

Title Quantization of the symplectic groupoid
Speaker, Affiliation Francesco Bonechi, INFN Firenze
Date, Time 26 November 2012, 14:00-15:00
Location Y27 H 28
Abstract The symplectic groupoid is a symplectic manifold that is associated to integrable Poisson manifolds. A quantization compatible with the groupoid structure provides a quantization of the underlying Poisson manifold. After a brief introduction, I will discuss in particular the role of the integrability of the modular function in the definition of a (singular) polarization. This procedure is in principle applicable to Poisson Lie groups and their homogeneous spaces; I will discuss the Poisson complex projective spaces.
Quantization of the symplectic groupoidread_more
Y27 H 28
29 November 2012
13:15-14:15 		Amnon Yekutieli
Ben Gurion University
Details

Talks in Mathematical Physics

Title Higher descent
Speaker, Affiliation Amnon Yekutieli, Ben Gurion University
Date, Time 29 November 2012, 13:15-14:15
Location HG G 43
Abstract Classical descent is about gluing a global geometric object out of local information. Or conversely, it is about classifying global geometric objects using open coverings and cocycles. I will begin the lecture with a rather thorough discussion of how descent theory let's us classify twisted forms of a sheaf on a topological space (this is 1st nonabelian cohomology). Next I will recast this geometric construction in terms of cosimplicial groups, in this way getting something that is of purely combinatorial nature. Higher descent refers to the classification of twisted forms of a stack on a topological space (a sort of 2nd nonabelian cohomology). But in this talk I will adhere to the combinatorial point of view, so stacks will only appear as motivations, and in one or two examples. Thus, in the talk, ``higher descent'' will be mostly a study of cosimplicial crossed groupoids and their descent data. (These concepts will be defined.) I will present a recent result, the ``Equivalence Theorem'', and mention its role in my work on twisted deformation quantization. Finally I will briefly discuss how model structures enter the picture, and a very new proof of this theorem by Prezma. - Lecture notes are at http://www.math.bgu.ac.il/~amyekut/lectures/higher-descent/notes.pdf - The paper is at http://arxiv.org/abs/1109.1919
Higher descentread_more
HG G 43
29 November 2012
15:15-16:15 		Francesco Bonechi
INFN Firenze
Details

Talks in Mathematical Physics

Title Reduction of AKSZ theories
Speaker, Affiliation Francesco Bonechi, INFN Firenze
Date, Time 29 November 2012, 15:15-16:15
Location HG G 43
Abstract I will discuss a general procedure to encode the symplectic reduction of the target manifold into AKSZ sigma models. This is done by considering the AKSZ construction with target the BFV model associated to the constrained system. The relation with the model with reduced target will be illustrated in some finite dimensional examples.
Reduction of AKSZ theoriesread_more
HG G 43
* 3 December 2012
10:30-12:30 		Damiano Anselmi
Università di Pisa
Details

Talks in Mathematical Physics

Title Field-covariant quantum field theory: formulation, renormalization and Batalin-Vilkovisky formalism I
Speaker, Affiliation Damiano Anselmi, Università di Pisa
Date, Time 3 December 2012, 10:30-12:30
Location 27 H 28
Abstract The transformation properties of generating functionals under arbitrary perturbative changes of field variables are studied, emphasizing the role of composite fields. While the functionals Z and W = ln Z behave as scalars, the generating functional Gamma of one-particle irreducible correlation functions has unexpected transformation properties. A new functional, called master functional, is introduced to supersede it, obtained extending the Legendre transform and the set of integrated fields to the sector of composite fields. The Batalin-Vilkovisky formalism is generalized to work with the new functional. The main cohomological theorems are extended to the new approach and used to work out the renormalization algorithm for gauge theories in a field-covariant setting.
Field-covariant quantum field theory: formulation, renormalization and Batalin-Vilkovisky formalism Iread_more
27 H 28
3 December 2012
16:00-18:00 		Damiano Anselmi
Università di Pisa
Details

Talks in Mathematical Physics

Title Field-covariant quantum field theory: formulation, renormalization and Batalin-Vilkovisky formalism II
Speaker, Affiliation Damiano Anselmi, Università di Pisa
Date, Time 3 December 2012, 16:00-18:00
Location 27 H 28
Abstract The transformation properties of generating functionals under arbitrary perturbative changes of field variables are studied, emphasizing the role of composite fields. While the functionals Z and W = ln Z behave as scalars, the generating functional Gamma of one-particle irreducible correlation functions has unexpected transformation properties. A new functional, called master functional, is introduced to supersede it, obtained extending the Legendre transform and the set of integrated fields to the sector of composite fields. The Batalin-Vilkovisky formalism is generalized to work with the new functional. The main cohomological theorems are extended to the new approach and used to work out the renormalization algorithm for gauge theories in a field-covariant setting.
Field-covariant quantum field theory: formulation, renormalization and Batalin-Vilkovisky formalism IIread_more
27 H 28
6 December 2012
15:15-16:15 		Damiano Anselmi
Università di Pisa
Details

Talks in Mathematical Physics

Title Renormalization of quantum field theories that violate Lorentz symmetry at high energies
Speaker, Affiliation Damiano Anselmi, Università di Pisa
Date, Time 6 December 2012, 15:15-16:15
Location HG G 43
Renormalization of quantum field theories that violate Lorentz symmetry at high energies
HG G 43
* 13 December 2012
13:15-14:15 		Oleg Chalykh
University of Leeds
Details

Talks in Mathematical Physics

Title Calogero-Moser spaces over curves
Speaker, Affiliation Oleg Chalykh, University of Leeds
Date, Time 13 December 2012, 13:15-14:15
Location HG G 43
Abstract I will compare two existing definitions of Calogero-Moser spaces over algebraic curves and explain how to compute their motivic class.
Calogero-Moser spaces over curves read_more
HG G 43
13 December 2012
15:15-16:15 		Iakovos Androulidakis
University of Athens
Details

Talks in Mathematical Physics

Title Singular foliations and their holonomy
Speaker, Affiliation Iakovos Androulidakis, University of Athens
Date, Time 13 December 2012, 15:15-16:15
Location HG G 43
Abstract Foliations with singularities arise in an abundance of phenomena, for instance in Poisson geometry (a Poisson structure is completely determined by its symplectic foliation, which presents singularities more than often). In this talk we discuss the construction of the holonomy groupoid in the singular case, which in general is a very ill-behaved object. We explain how its longitudinal smoothness is controlled by a certain "essential isotropy" group attached to each leaf. Finally, we discuss how this groupoid provides some first partial results on the problem of stability about a (compact) leaf for the singular case. This is joint work with Georges Skandalis and Marco Zambon.
Documents beamerfile_download
Singular foliations and their holonomyread_more
HG G 43

Notes: events marked with an asterisk (*) indicate that the time and/or location are different from the usual time and/or location.

Organisers: Anna Beliakova, Damien Calaque, Alberto Cattaneo, Giovanni Felder, Matthias Gaberdiel, Gian Michele Graf, Horst Knörrer

Archive: AS 24 SS 24 AS 23 SS 23 AS 22 SS 22 AS 21 SS 21 AS 20 SS 20 AS 19 SS 19 AS 18 SS 18 AS 17 SS 17 AS 16 SS 16 AS 15 SS 15 AS 14 SS 14 AS 13 SS 13 AS 12 SS 12 AS 11

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