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Higher Structures in Geometry and Mathematical Physics
from
Monday, April 17, 2023 (7:30 AM)
to
Friday, July 14, 2023 (7:30 PM)
Monday, April 17, 2023
8:00 AM
Ecole introductive à Marseille
Ecole introductive à Marseille
8:00 AM - 4:00 PM
Tuesday, April 18, 2023
8:00 AM
Ecole introductive à Marseille
Ecole introductive à Marseille
8:00 AM - 4:00 PM
Wednesday, April 19, 2023
8:00 AM
Ecole introductive à Marseille
Ecole introductive à Marseille
8:00 AM - 4:00 PM
Thursday, April 20, 2023
8:00 AM
Ecole introductive à Marseille
Ecole introductive à Marseille
8:00 AM - 4:00 PM
Friday, April 21, 2023
8:00 AM
Ecole introductive à Marseille
Ecole introductive à Marseille
8:00 AM - 12:00 PM
Saturday, April 22, 2023
Sunday, April 23, 2023
Monday, April 24, 2023
10:00 AM
Introduction to dg-manifolds, and homological vector fields (I) by Camille Laurent-Gengoux
Introduction to dg-manifolds, and homological vector fields (I) by Camille Laurent-Gengoux
10:00 AM - 12:00 PM
Room: Amphitheater Darboux
Tuesday, April 25, 2023
Wednesday, April 26, 2023
10:00 AM
Introduction to dg-manifolds and homological vector fields (II) by Camille Laurent-Gengoux
Introduction to dg-manifolds and homological vector fields (II) by Camille Laurent-Gengoux
10:00 AM - 12:00 PM
Room: Amphitheater Darboux
Thursday, April 27, 2023
Friday, April 28, 2023
9:25 AM
Dg-manifolds and self-commuting vector fields (III) by Camille Laurnet-Gengoux.
Dg-manifolds and self-commuting vector fields (III) by Camille Laurnet-Gengoux.
9:25 AM - 10:50 AM
Room: Amphitheater Darboux
11:00 AM
Serguei Merkulov (Luxembourg) : Gravity properad, moduli spaces M_g,n, and string topology
Serguei Merkulov (Luxembourg) : Gravity properad, moduli spaces M_g,n, and string topology
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
Saturday, April 29, 2023
Sunday, April 30, 2023
Monday, May 1, 2023
Tuesday, May 2, 2023
10:00 AM
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications.
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications.
10:00 AM - 12:00 PM
Room: Amphitheater Darboux
3:00 PM
Higher structures and dg-manifolds (I) by Ping Xu
Higher structures and dg-manifolds (I) by Ping Xu
3:00 PM - 4:00 PM
Room: Amphitheater Darboux
4:15 PM
Higher structures and dg-manifolds (II) by Ping Xu
Higher structures and dg-manifolds (II) by Ping Xu
4:15 PM - 5:15 PM
Room: Amphitheater Darboux
Wednesday, May 3, 2023
11:00 AM
Higher structures and dg-manifolds (II) by Ping Xu
Higher structures and dg-manifolds (II) by Ping Xu
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
2:00 PM
Benoît Fresse : Operads, Graph complexes, and Grothendieck-Teichmuller groups (I)
Benoît Fresse : Operads, Graph complexes, and Grothendieck-Teichmuller groups (I)
2:00 PM - 4:30 PM
Room: Amphitheater Darboux
Benoit Fresse : Operads, Graph complexes, and Grothendieck-Teichmuller groups (May 3rd, May 10th, May 17th, frm 2pm to 4:30pm). ((May 3d : General introduction, Introduction to Operads, May 10th : Rational homotopy. Sullivan models, May 17th : Applications : relation with GT. Embedding Calculus.))
Thursday, May 4, 2023
10:00 AM
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications.
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications.
10:00 AM - 12:05 PM
Room: Amphitheater Darboux
3:00 PM
Duflo-Kontsevich Theorem for dg-manifolds by Mathieu Stiénon (I)
Duflo-Kontsevich Theorem for dg-manifolds by Mathieu Stiénon (I)
3:00 PM - 4:00 PM
Room: Amphitheater Darboux
4:15 PM
Duflo-Kontsevich Theorem for dg-manifolds by Mathieu Stiénon (II)
Duflo-Kontsevich Theorem for dg-manifolds by Mathieu Stiénon (II)
4:15 PM - 5:15 PM
Room: Amphitheater Darboux
Friday, May 5, 2023
11:00 AM
Duflo-Kontsevich Theorem for dg-manifolds by Mathieu Stiénon (III)
Duflo-Kontsevich Theorem for dg-manifolds by Mathieu Stiénon (III)
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
Saturday, May 6, 2023
Sunday, May 7, 2023
Monday, May 8, 2023
Tuesday, May 9, 2023
10:00 AM
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications.(III)
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications.(III)
10:00 AM - 12:00 PM
Room: Amphitheater Darboux
Wednesday, May 10, 2023
2:00 PM
Operads, Graph complexes, and Grothendieck-Teichmuller groups, by Benoît Fresse
Operads, Graph complexes, and Grothendieck-Teichmuller groups, by Benoît Fresse
2:00 PM - 4:30 PM
Room: Amphitheater Darboux
Benoit Fresse : Operads, Graph complexes, and Grothendieck-Teichmuller groups (May 3rd, May 10th, May 17th, frm 2pm to 4:30pm). ((May 3d : General introduction, Introduction to Operads, May 10th : Rational homotopy. Sullivan models, May 17th : Applications : relation with GT. Embedding Calculus.))
Thursday, May 11, 2023
10:00 AM
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications.(IV)
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications.(IV)
10:00 AM - 12:00 PM
Room: Amphitheater Darboux
Friday, May 12, 2023
11:00 AM
Seminar
Seminar
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
Saturday, May 13, 2023
Sunday, May 14, 2023
Monday, May 15, 2023
9:00 AM
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications. (V)
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications. (V)
9:00 AM - 11:00 AM
Room: Amphitheater Darboux
11:00 AM
Vladimir Salnikov : Z-graded manifolds I, properties of functional spaces and some applications
Vladimir Salnikov : Z-graded manifolds I, properties of functional spaces and some applications
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
3:30 PM
Bernhard Keller : Derived categories and Hochschild cohomology (I)
Bernhard Keller : Derived categories and Hochschild cohomology (I)
3:30 PM - 5:30 PM
Room: Amphitheater Darboux
Tuesday, May 16, 2023
Wednesday, May 17, 2023
10:00 AM
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications.(VI)
Olivier Schiffmann : Cohomological Hall algebras in dimensions one and two and applications.(VI)
10:00 AM - 12:00 PM
Room: Amphitheater Darboux
2:00 PM
Operads, Graph complexes, and Grothendieck-Teichmuller groups (I), by Benoît Fresse
Operads, Graph complexes, and Grothendieck-Teichmuller groups (I), by Benoît Fresse
2:00 PM - 4:30 PM
Room: Amphitheater Darboux
Benoit Fresse : Operads, Graph complexes, and Grothendieck-Teichmuller groups (May 3rd, May 10th, May 17th, frm 2pm to 4:30pm). ((May 3d : General introduction, Introduction to Operads, May 10th : Rational homotopy. Sullivan models, May 17th : Applications : relation with GT. Embedding Calculus.))
Thursday, May 18, 2023
Friday, May 19, 2023
Saturday, May 20, 2023
Sunday, May 21, 2023
Monday, May 22, 2023
9:30 AM
Registration and welcome coffee
Registration and welcome coffee
9:30 AM - 10:30 AM
Room: Amphitheater Darboux
10:30 AM
Bernhard Keller (Université Paris Cité) : Singularity categories, Leavitt path algebras and Hochschild homology
Bernhard Keller (Université Paris Cité) : Singularity categories, Leavitt path algebras and Hochschild homology
10:30 AM - 11:30 AM
Room: Amphitheater Darboux
11:30 AM
Domenico Fiorenza, Sapienza (Università di Roma) : String bordism invariants in dimension 3 from U(1)-valued TQFTs
Domenico Fiorenza, Sapienza (Università di Roma) : String bordism invariants in dimension 3 from U(1)-valued TQFTs
11:30 AM - 12:30 PM
Room: Amphitheater Darboux
2:15 PM
Leonid Positselski,( Czech Academy of Sciences, Prague) : The homomorphism removal and repackaging construction
Leonid Positselski,( Czech Academy of Sciences, Prague) : The homomorphism removal and repackaging construction
2:15 PM - 3:15 PM
Room: Amphitheater Darboux
3:15 PM
Dominique Mouhanna, Deputy Director of IHP : Welcome Address
Dominique Mouhanna, Deputy Director of IHP : Welcome Address
3:15 PM - 3:30 PM
Room: Amphitheater Darboux
4:00 PM
Wendy Lowen, (Universiteit Antwerpen) : Higher structures and deformations of non-commutative spaces
Wendy Lowen, (Universiteit Antwerpen) : Higher structures and deformations of non-commutative spaces
4:00 PM - 5:00 PM
Room: Amphitheater Darboux
5:00 PM
Poster Session
Poster Session
5:00 PM - 6:00 PM
Room: Amphitheater Darboux
Tuesday, May 23, 2023
9:00 AM
Martin Markl, (Czech Academy of Sciences, Prague) : Operads and the blob complex
Martin Markl, (Czech Academy of Sciences, Prague) : Operads and the blob complex
9:00 AM - 10:00 AM
Room: Amphitheater Darboux
10:30 AM
Julien Grivaux, (Sorbonne Univ) : Algebraic structures attached to a closed embedding
Julien Grivaux, (Sorbonne Univ) : Algebraic structures attached to a closed embedding
10:30 AM - 11:30 AM
Room: Amphitheater Darboux
11:30 AM
Shahn Majid, (Queen Mary Univ.) : Braided bimodules, quantum jet bundles and quantum geodesics
Shahn Majid, (Queen Mary Univ.) : Braided bimodules, quantum jet bundles and quantum geodesics
11:30 AM - 12:30 PM
Room: Amphitheater Darboux
2:00 PM
Kirsten Wickelgren (Duke University) : A quadratically enriched zeta function
Kirsten Wickelgren (Duke University) : A quadratically enriched zeta function
2:00 PM - 3:00 PM
Room: Amphitheater Darboux
3:30 PM
Adrian Ocneanu, (Pennsylvania State University), We describe a stronger analog of the Weyl character formula, which has a similar form, but generates all the representation vectors, rather than only their weghts.
Adrian Ocneanu, (Pennsylvania State University), We describe a stronger analog of the Weyl character formula, which has a similar form, but generates all the representation vectors, rather than only their weghts.
3:30 PM - 4:30 PM
Room: Amphitheater Darboux
Wednesday, May 24, 2023
9:00 AM
Benoît Dhérin, (Google) : Symplectic microgeometry and quantization
Benoît Dhérin, (Google) : Symplectic microgeometry and quantization
9:00 AM - 10:00 AM
Room: Amphitheater Darboux
10:30 AM
Olivier Schiffmann, (Université Paris-Saclay) : Cohomological Hall algebras associated to curves in surfaces
Olivier Schiffmann, (Université Paris-Saclay) : Cohomological Hall algebras associated to curves in surfaces
10:30 AM - 11:30 AM
Room: Amphitheater Darboux
11:30 AM
Thomas Willwacher, (ETH Zürich) : Graph complexes and moduli spaces of curves
Thomas Willwacher, (ETH Zürich) : Graph complexes and moduli spaces of curves
11:30 AM - 12:30 PM
Room: Amphitheater Darboux
Thursday, May 25, 2023
9:00 AM
Muriel Livernet, (Univ. Paris Cité) : Homotopy theory of spectral sequences
Muriel Livernet, (Univ. Paris Cité) : Homotopy theory of spectral sequences
9:00 AM - 10:00 AM
Room: Amphitheater Darboux
10:30 AM
Alexander Berglund, (Stockholm University) : Higher structures in automorphisms of manifolds
Alexander Berglund, (Stockholm University) : Higher structures in automorphisms of manifolds
10:30 AM - 11:30 AM
Room: Amphitheater Darboux
11:30 AM
Christoph Schweigert, (Universität Hamburg) : String-net methods for CFT correlators
Christoph Schweigert, (Universität Hamburg) : String-net methods for CFT correlators
11:30 AM - 12:30 PM
Room: Amphitheater Darboux
2:00 PM
Mikhail Kapranov, (Kavli IPMU) : Categorification of Euler’s continuants, N-spherical functors and periodic semiorthogonal decompositions
Mikhail Kapranov, (Kavli IPMU) : Categorification of Euler’s continuants, N-spherical functors and periodic semiorthogonal decompositions
2:00 PM - 3:00 PM
Room: Amphitheater Darboux
3:30 PM
Pavel Mnev, (University of Notre Dame) : On the Fukaya-Morse A-infinity category
Pavel Mnev, (University of Notre Dame) : On the Fukaya-Morse A-infinity category
3:30 PM - 4:30 PM
Room: Amphitheater Darboux
Friday, May 26, 2023
9:00 AM
Ralph Kaufmann, (Purdue University) : Higher operations from algebra and geometry.
Ralph Kaufmann, (Purdue University) : Higher operations from algebra and geometry.
9:00 AM - 10:00 AM
Room: Amphitheater Darboux
10:30 AM
Yuri Berest, (Cornell University) : Spaces of quasi-invariants and homotopy Lie groups
Yuri Berest, (Cornell University) : Spaces of quasi-invariants and homotopy Lie groups
10:30 AM - 11:30 AM
Room: Amphitheater Darboux
Saturday, May 27, 2023
10:00 AM
Maosong Xiang : The standard cohomology of regular Courant algebroids
Maosong Xiang : The standard cohomology of regular Courant algebroids
10:00 AM - 10:30 AM
Room: Amphitheater Darboux
10:30 AM
Zheng Hua : Standard poisson structure on Grassmannian revisited
Zheng Hua : Standard poisson structure on Grassmannian revisited
10:30 AM - 11:00 AM
Room: Amphitheater Darboux
11:30 AM
Ruggero Bandiera : Higher derived brackets and splitting principle
Ruggero Bandiera : Higher derived brackets and splitting principle
11:30 AM - 12:00 PM
Room: Amphitheater Darboux
12:00 PM
Alberto Cattaneo : BV pushforward and Yang-Mills theory
Alberto Cattaneo : BV pushforward and Yang-Mills theory
12:00 PM - 12:30 PM
Room: Amphitheater Darboux
12:30 PM
Francesco Bonechi : Equivariant Yang-Mills
Francesco Bonechi : Equivariant Yang-Mills
12:30 PM - 1:00 PM
Room: Amphitheater Darboux
1:00 PM
Discussion
Discussion
1:00 PM - 1:30 PM
Room: Amphitheater Darboux
Sunday, May 28, 2023
Monday, May 29, 2023
Tuesday, May 30, 2023
3:00 PM
Exposé grand Public, Adrian Ocneanu, Lois mathématiques, structure mathématique, et théorie quantique des champs
Exposé grand Public, Adrian Ocneanu, Lois mathématiques, structure mathématique, et théorie quantique des champs
3:00 PM - 4:00 PM
Room: Amphitheater Darboux
Wednesday, May 31, 2023
Thursday, June 1, 2023
Friday, June 2, 2023
Saturday, June 3, 2023
Sunday, June 4, 2023
Monday, June 5, 2023
11:00 AM
Seminar :Lander Hermans : Deforming prestacks, a calculus of rectangles
Seminar :Lander Hermans : Deforming prestacks, a calculus of rectangles
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
In his foundational work Gerstenhaber furnishes the guiding example for algebraic deformation theory: for an associative algebra A he defined a dgLie bracket on its Hochschild complex and showed that it controls the deformations of A through the Maurer-Cartan equation. Algebraic geometry motivates the natural question whether a similar story exists for diagrams of associative algebras, e.g. when applied to the structure sheaf of a scheme. In this talk I will explain how the Gerstenhaber-Schack complex fulfils this role, yet also motivates to generalize from diagrams to prestacks (i.e. pseudofunctors) as the most suitable objects to start with. Inspired by the fact that the Lie-structure of the Hochschild complex arises from an underlying operadic calculus, we introduce a new L-infinity structure arising from a rectangular operadic calculus. We show it completes the story: the higher Lie brackets on the GS complex control the deformations of prestacks through the generalized MC equation. Along the way, we introduce a new type of operad, called “box operads”, which can be seen as an enriched version of Leinster’s fc-multicategories (also called virtual double categories). This is joint work with Hoang Dinh Van and Wendy Lowen.
3:30 PM
Bernhard Keller : Derived categories and Hochschild cohomology (II)
Bernhard Keller : Derived categories and Hochschild cohomology (II)
3:30 PM - 5:30 PM
Room: Amphitheater Darboux
Tuesday, June 6, 2023
11:00 AM
Seminar : Lothar Göttsche (Trieste) :: (Refined) Verlinde and Segre formulas for Hilbert schemes of points.
Seminar : Lothar Göttsche (Trieste) :: (Refined) Verlinde and Segre formulas for Hilbert schemes of points.
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
This is joint work with Anton Mellit. Segre and Verlinde numbers of Hilbert schemes of points have been studied for a long time. The Segre numbers are evaluations of top Chern and Segre classes of so-called tautological bundles on Hilbert schemes of points. The Verlinde numbers are the holomorphic Euler characteristics of line bundles on these Hilbert schemes. We give the generating functions for the Segre and Verlinde numbers of Hilbert schemes of points. The formula is proven for surfaces with K_S^2=0, and conjectured in general. Without restriction on K_S^2 we prove the conjectured Verlinde-Segre correspondence relating Segre and Verlinde numbers of Hilbert schemes. Finally we find a generating function for finer invariants, which specialize to both the Segre and Verlinde numbers, giving some kind of explanation of the Verlinde-Segre correspondence.
3:30 PM
Boris Tsygan : Gauss-Manin connection in noncommutative geometry (I)
Boris Tsygan : Gauss-Manin connection in noncommutative geometry (I)
3:30 PM - 5:00 PM
Room: Amphitheater Darboux
Wednesday, June 7, 2023
Thursday, June 8, 2023
Friday, June 9, 2023
3:30 PM
Boris Tsygan : Gauss-Manin connection in noncommutative geometry.(II)
Boris Tsygan : Gauss-Manin connection in noncommutative geometry.(II)
3:30 PM - 5:00 PM
Room: Amphitheater Darboux
Saturday, June 10, 2023
Sunday, June 11, 2023
Monday, June 12, 2023
Tuesday, June 13, 2023
Wednesday, June 14, 2023
3:30 PM
Finski Siarhei
Finski Siarhei
3:30 PM - 4:30 PM
Room: Amphitheater Darboux
Thursday, June 15, 2023
Friday, June 16, 2023
3:30 PM
Andrey Lazarev
Andrey Lazarev
3:30 PM - 4:30 PM
Room: Amphitheater Darboux
Saturday, June 17, 2023
Sunday, June 18, 2023
Monday, June 19, 2023
3:30 PM
Bernhard Keller : Derived categories and Hochschild cohomology (III)
Bernhard Keller : Derived categories and Hochschild cohomology (III)
3:30 PM - 5:40 PM
Room: Amphitheater Darboux
Tuesday, June 20, 2023
Wednesday, June 21, 2023
3:00 PM
Elements of oo-category theory (I), Emily Riehl
Elements of oo-category theory (I), Emily Riehl
3:00 PM - 5:00 PM
Room: Amphitheater Darboux
Two lectures on infinity category theory Speaker: Emily Riehl, Johns Hopkins University Time: June 21, and June 23, 15:00-17:00 Place: IHP Abstract: I will explain some core basics of infinity category theory: equivalences, adjunctions, limits and colimits, with the goal of introducing stable infinity categories. The only essential prerequisite is the notion of a strict 2-category. If folks want to look at something in advance, I'd suggest section B.1 of the "Elements" book, and in fact B.1.1 - B.1.7 is enough, with the notion of pasting diagram in B.1.4-B.1.5 being the most important.
Thursday, June 22, 2023
Friday, June 23, 2023
3:00 PM
Elelments of oo-category theory, Emily Riehl
Elelments of oo-category theory, Emily Riehl
3:00 PM - 5:00 PM
Room: Amphitheater Darboux
Two lectures on infinity category theory Speaker: Emily Riehl, Johns Hopkins University Time: June 21, and June 23, 15:00-17:00 Place: IHP Abstract: I will explain some core basics of infinity category theory: equivalences, adjunctions, limits and colimits, with the goal of introducing stable infinity categories. The only essential prerequisite is the notion of a strict 2-category. For participants willing to look at something in advance, section B.1 of my "Elements in Infinite Category Theory" book, is adviced (in fact B.1.1 - B.1.7 is enough), with the notion of pasting diagram in B.1.4-B.1.5 being the most important.
Saturday, June 24, 2023
Sunday, June 25, 2023
Monday, June 26, 2023
9:00 AM
Hadi Nahari
Hadi Nahari
9:00 AM - 9:30 AM
Room: Amphitheater Darboux
10:00 AM
Aliaksandr Hancharuk
Aliaksandr Hancharuk
10:00 AM - 10:30 AM
Room: Amphitheater Darboux
11:00 AM
Seminar : Dimitry Roytenberg
Seminar : Dimitry Roytenberg
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
2:00 PM
Rosa Marchesini : On the notion of homotopy for Lie algebroids.
Rosa Marchesini : On the notion of homotopy for Lie algebroids.
2:00 PM - 2:30 PM
Room: Amphitheater Darboux
The definition of homotopy as a smooth curve of Lie algebroid morphisms does not guarantee the homotopy invariance of Lie algebroid cohomology. In order to obtain the desired property, we need to focus on a more restrictive notion that has appeared sporadically in the literature but has not yet been explored to its full potential. We motivate the choice of definition with new examples and relevant applications. The results are a joint work with my supervisor Madeleine Jotz.
3:00 PM
Florian Dorsch
Florian Dorsch
3:00 PM - 3:30 PM
Room: Amphitheater Darboux
Tuesday, June 27, 2023
9:00 AM
Sylvain Lavau. Deformations of singular foliations
Sylvain Lavau. Deformations of singular foliations
9:00 AM - 10:00 AM
Room: Amphitheater Darboux
The study of deformations of singular foliations cannot be streamlined as for regular foliations, due to the presence of singularities. However, upon replacing the singular foliation by its corresponding Lie infinity-algebroid, we can construct a DGLA whose Maurer-Cartan elements control the deformations of the given singular foliation. It appears that deforming the singular foliation amounts to deforming the corresponding Lie infinity-structure. We use this approach to study the deformations of several kinds of singular foliations. Work in collaboration with Camille Laurent-Gengoux.
11:00 AM
Alfonso Garmendia. E-manifolds and Poisson manifolds.
Alfonso Garmendia. E-manifolds and Poisson manifolds.
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
Abstract: In this talk we will discuss the concept of E-maifolds (by Miranda and Scott) which are manifolds with a projective foliation. We will give some examples used in the literature, such as the case of b-, c-manifolds and 0-manifolds. We will also give some constructions on Poisson manifolds and these objects.
1:30 PM
Higher Structures and Foliations : discussion
Higher Structures and Foliations : discussion
1:30 PM - 4:20 PM
Room: Amphitheater Darboux
4:30 PM
Higher Structures and Foliations : Omar Moshen
Higher Structures and Foliations : Omar Moshen
4:30 PM - 5:30 PM
Room: Amphitheater Darboux
Wednesday, June 28, 2023
10:00 AM
Mini-course : Alexei Kotov
Mini-course : Alexei Kotov
10:00 AM - 12:00 PM
Room: Amphitheater Darboux
3:30 PM
David Carchedi
David Carchedi
3:30 PM - 4:30 PM
Room: Amphitheater Darboux
Thursday, June 29, 2023
11:00 AM
Séminaire : Ricardo Campos
Séminaire : Ricardo Campos
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
2:00 PM
Alex Takeda
Alex Takeda
2:00 PM - 3:00 PM
Room: Amphitheater Darboux
3:30 PM
Giovanni Felder
Giovanni Felder
3:30 PM - 4:30 PM
Room: Amphitheater Darboux
Friday, June 30, 2023
9:00 AM
Geometry and Analysis at the foundations of QFT
Geometry and Analysis at the foundations of QFT
9:00 AM - 5:20 PM
Room: Amphitheater Darboux
Saturday, July 1, 2023
Sunday, July 2, 2023
Monday, July 3, 2023
10:00 AM
Ezra Getzler
Ezra Getzler
10:00 AM - 11:00 AM
Room: Amphitheater Darboux
11:00 AM
Leonid Ryvkin : Differentiation of simplicial manifolds
Leonid Ryvkin : Differentiation of simplicial manifolds
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
Kan simplicial manifolds provide with a very explicit model for $L_\infty$-groupoids. Pavol Severa proposed a procedure of differentiation for these objects, yielding an $L_\infty$-algebroid, (an NQ-manifold). In the talk I will report on joint work with Rui Fernandes, Du Li, Arne Wessel and Chenchang Zhu, where we have proven that this procedure always works.
2:00 PM
Pavel Mnev : “Examples of bulk-boundary correspondences of field theories as BV pushforwards”
Pavel Mnev : “Examples of bulk-boundary correspondences of field theories as BV pushforwards”
2:00 PM - 3:00 PM
Room: Amphitheater Darboux
I will explain how one can obtain 2d Wess-Zumino-Witten model on a surface as a Batalin-Vilkovisky pushforward (perturbative fiber BV integral, or “quantized” pushforward of dg manifolds) from 3d Chern-Simons theory on the cylinder (surface)x(interval). Here Chern-Simons is treated in BV formalism with functorial cutting-gluing. A similar construction applied to abelian Chern-Simons on a 7d cylinder yields the 6d Kodaira-Spencer gravity (a.k.a. BCOV theory). The talk is based on a joint work with Alberto S. Cattaneo and Konstantin Wernli, arXiv:2012.13983 .
3:00 PM
Jae-Suk Park : Grothendieck-Galois theories over symmetric monoidal categories
Jae-Suk Park : Grothendieck-Galois theories over symmetric monoidal categories
3:00 PM - 4:00 PM
Room: Amphitheater Darboux
4:00 PM
Ruben Louis
Ruben Louis
4:00 PM - 4:30 PM
Room: Amphitheater Darboux
4:30 PM
Poster Session, discussions (and coffee)
Poster Session, discussions (and coffee)
4:30 PM - 6:00 PM
Room: Amphitheater Darboux
Tuesday, July 4, 2023
8:30 AM
Thomas Strobl : Arborescent Koszul-Tate resolutions and BFV for singular coisotropic reductions (joint work with Hancharuk)
Thomas Strobl : Arborescent Koszul-Tate resolutions and BFV for singular coisotropic reductions (joint work with Hancharuk)
8:30 AM - 9:30 AM
Room: Amphitheater Darboux
Let I be an ideal in a commutative (associative) algebra O. Starting from a resolution of O/I as an O-module, we construct a Koszul-Tate resolution for this quotient, i.e.\ a graded symmetric algebra over O with a differential which provides simultaneously a resolution as an O-module. This algebra resolution has the beautiful structure of a forest of decorated trees and is related to an A-infinity algebra on the original module resolution. Considering O to be a Poisson algebra and I a finitely generated Poisson subalgebra, we use the above construction to obtain the corresponding BFV formulation. Its cohomology at degree zero is proven to coincide with the reduced Poisson algebra N(I)/I, where N(I) is the normaliser of I inside O, thus generalising ordinary coisotropic reduction to the singular setting. As an illustration we use the example where O consists of functions on T^*(\R^3) and I is the ideal generated by angular momenta. This is joint work with Aliaksandr Hancharuk and, in part, with Camille Laurent-Gengoux.
10:00 AM
Oleksii Kotov
Oleksii Kotov
10:00 AM - 11:00 AM
Room: Amphitheater Darboux
11:00 AM
Hsuan-Yi Liao : Homotopy fiber product and dg manifolds of finite positive amplitudes
Hsuan-Yi Liao : Homotopy fiber product and dg manifolds of finite positive amplitudes
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
A main motivation for developing derived differential geometry is to deal with singularities arising from zero loci or intersections of submanifolds. Both zero loci and intersections can be considered as fiber products of manifolds which may not be manifolds. To deal with this issue, we extend the category of differentiable manifolds to the category of dg manifolds of finite positive amplitudes in which "homotopy fiber products" exist. In this talk, I would like to explain properties of this larger category (it is a category of fibrant objects) and our construction of homotopy fiber products of manifolds. The talk is mainly based on a joint work with Kai Behrend and Ping Xu.
2:00 PM
Madeleine Jotz
Madeleine Jotz
2:00 PM - 3:00 PM
Room: Amphitheater Darboux
3:00 PM
Marco Zambon : Reduction of Courant algebroids via graded manifolds.
Marco Zambon : Reduction of Courant algebroids via graded manifolds.
3:00 PM - 4:00 PM
Room: Amphitheater Darboux
Courant algebroids are certain objects in Lie theory that are used to define, for instance, Dirac structures and generalized complex structures. We will use the correspondence between degree 2 symplectic manifolds and Courant algebroids, due to Roytenberg, to approach the reduction of Courant algebroids using graded geometry. For this purpose we will consider both graded coisotropic submanifolds and a graded version of moment maps. The resulting reduction procedure, in a particular case, recovers the work of Bursztyn-Cavalcanti-Gualtieri around 2007. This talk is based on joint work with Bursztyn, Cattaneo and Metha.
Wednesday, July 5, 2023
8:30 AM
Joost Nuiten
Joost Nuiten
8:30 AM - 9:30 AM
Room: Amphitheater Darboux
9:30 AM
Jon Pridham : Shifted Poisson structures
Jon Pridham : Shifted Poisson structures
9:30 AM - 10:30 AM
Room: Amphitheater Darboux
11:00 AM
Francesca Pratali : Dendroidal ∞-operads
Francesca Pratali : Dendroidal ∞-operads
11:00 AM - 11:30 AM
Room: Amphitheater Darboux
The dendroidal formalism offers a powerful approach to defining operads as specific presheaves on a tree-based category. This combinatorial framework enables the definition of ∞-operads, wherein composition is determined up to homotopy via presheaves that satisfy a weak dendroidal inner Kan condition. Notably, the homotopy theory of ∞-operads has been shown to be equivalent, in both Quillen's sense and Lurie's ∞-categorical sense, to the theories of topological and simplicial operads. In this talk we will review these concepts and present some open questions in enriched settings.
11:30 AM
Sarah Scherotzke
Sarah Scherotzke
11:30 AM - 12:30 PM
Room: Amphitheater Darboux
Thursday, July 6, 2023
8:30 AM
Tilmann Wurzbacher
Tilmann Wurzbacher
8:30 AM - 9:30 AM
Room: Amphitheater Darboux
10:00 AM
Christian Blohmann
Christian Blohmann
10:00 AM - 11:00 AM
Room: Amphitheater Darboux
11:00 AM
Owen Gwilliams : 4-dimensional gauge theories and their holomorphic twists
Owen Gwilliams : 4-dimensional gauge theories and their holomorphic twists
11:00 AM - 12:00 PM
Room: Amphitheater Darboux
Yang-Mills theories have had an enormous impact in mathematics, perhaps most famously the Donaldson and Seiberg-Witten invariants, which arise via the topological twists of supersymmetric Yang-Mills theories. In this talk I will describe derived moduli spaces that arise from holomorphic and topological-holomorphic twists of these theories and then explore what it means to quantize such spaces. Given time, we will examine how various notions of duality might carry over to this setting, such as the S-duality that Kapustin and Witten used to offer a physical view on the geometric Langlands program or the Seiberg duality that plays a key role for N=1 theories. This work is joint, in various combinations, with Chris Elliott, Eugene Rabinovich, and Brian Williams.
2:00 PM
Kasia Rejzner : BV formalism in the infinite dimensional setting
Kasia Rejzner : BV formalism in the infinite dimensional setting
2:00 PM - 3:00 PM
Room: Amphitheater Darboux
Batalin-Vilkovisky (BV) formalism has been originally developed in quantum field theory (QFT) and its finite-dimensional analog can be elegantly formulated in the language of dg-manifolds. The latter is relatively well understood in mathematics, but in QFT it is more natural to use an infinite-dimensional setting. This poses several technical problems, since infinite dimensional calculus comes into play. In this talk, I will review some results obtained in this direction by myself and collaborators over the last 10 years
3:00 PM
Chenchang Zhu
Chenchang Zhu
3:00 PM - 4:00 PM
Room: Amphitheater Darboux
Friday, July 7, 2023
8:30 AM
Adrien Brochier : Quantum exponentiation of Hamiltonian Poisson varieties
Adrien Brochier : Quantum exponentiation of Hamiltonian Poisson varieties
8:30 AM - 9:30 AM
Room: Amphitheater Darboux
Let G be a complex reductive algebraic group. Various authors have developed notions of (quas G-Poisson varieties equipped with a multiplicative version of a moment map, valued in the group G. One of the main motivations for that formalism is that it provides a nice combinatorial description of the canonical Atiyah--Bott Poisson structure on character varieties of surfaces. A crucial feature of these structures is that they come equipped with certain operations (fusion and Hamiltonian reduction) which in particular expresses the compatibility of the Poisson structure on character varieties with cutting and gluing of surfaces. Exponentiation is a procedure taking an ordinary Hamiltonian variety (i.e. a Poisson variety equipped with a moment map into the dual of the Lie algebra g of G) and turning it (formally) into a "multiplicative" one. Crucially, this operation is compatible with fusion and Hamiltonian reduction on both sides, showing that the character variety of a surface is formally Poisson isomorphic to a much simpler Poisson variety. All of these structures/operations have natural interpretations in the framework of shifted Poisson structures. Exponentation, in particular, comes from a certain formal isomorphism of 1-shifted Poisson stacks g^*/G --> G/G. In this talk, I'll describe a quantization of this construction which is essentially given by pulling back along a certain monoidal functor from quantum to classical Harish-Chandra bimodules, which quantizes the above 1-shifted Poisson map. I'll then explain how this construction is compatible with categorical/quantum analogs of fusion and Hamiltonian reduction, and I'll present some applications.
9:30 AM
Michele Schiavina
Michele Schiavina
9:30 AM - 10:30 AM
Room: Amphitheater Darboux
11:00 AM
Jérémy Pierard de Maujouy
Jérémy Pierard de Maujouy
11:00 AM - 11:30 AM
Room: Amphitheater Darboux
11:30 AM
Pavol Severa
Pavol Severa
11:30 AM - 12:30 PM
Room: Amphitheater Darboux
Saturday, July 8, 2023
Sunday, July 9, 2023
Monday, July 10, 2023
3:30 PM
Markus J. Pfaum : Homological reduction as a tool in deformation quantization and an application to the quantization of a lattice gauge model.
Markus J. Pfaum : Homological reduction as a tool in deformation quantization and an application to the quantization of a lattice gauge model.
3:30 PM - 4:30 PM
Room: Amphitheater Darboux
Tuesday, July 11, 2023
Wednesday, July 12, 2023
Thursday, July 13, 2023
Friday, July 14, 2023
