Format results
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Talk
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Formal derived stack and Formal localization
Michel Vaquie Laboratoire de Physique Théorique, IRSAMC, Université Paul Sabatier
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An overview of derived analytic geometry
Mauro Porta Institut de Mathématiques de Jussieu
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Categorification of shifted symplectic geometry using perverse sheaves
Dominic Joyce University of Oxford
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Shifted structures and quantization
Tony Pantev University of Pennsylvania
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What is the Todd class of an orbifold?
Andrei Caldararu University of Wisconsin–Madison
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Singular support of categories
Dima Arinkin University of Wisconsin-Milwaukee
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Symplectic and Lagrangian structures on mapping stacks
Theodore Spaide Universität Wien
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The Maslov cycle and the J-homomorphism
David Treumann Boston College
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Talk
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Welcome to “Mathematica Summer School”
Pedro Vieira Perimeter Institute for Theoretical Physics
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Mathematica School Lecture - 2015
Horacio Casini Bariloche Atomic Centre
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Quantum mechanics in the early universe
Juan Maldacena Institute for Advanced Study (IAS) - School of Natural Sciences (SNS)
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Ground state entanglement and tensor networks
Guifre Vidal Alphabet (United States)
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Quantum mechanics in the early universe
Juan Maldacena Institute for Advanced Study (IAS) - School of Natural Sciences (SNS)
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Mathematica School Lecture - 2015
Pedro Vieira Perimeter Institute for Theoretical Physics
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Holographic entanglement entropy
Robert Myers Perimeter Institute for Theoretical Physics
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Principal 2-group bundles and the Freed--Quinn line bundle
Emily Cliff University of Sherbrooke
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Quantization of the Ngô morphism (VIRTUAL)
Tom Gannon University of California, Los Angeles
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Integrable Deformations on Twistor Space
Joaquin Liniado National University of La Plata
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Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics
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Exact Operator Algebras in Superconformal Field Theories
Exact Operator Algebras in Superconformal Field Theories
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Deformation Quantization of Shifted Poisson Structures
Deformation Quantization of Shifted Poisson Structures
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Symplectic Duality and Gauge Theory
Symplectic Duality and Gauge Theory
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Symplectic Duality and Gauge Theory
Symplectic Duality and Gauge Theory
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Condensed Matter Physics and Topological Field Theory
Condensed Matter Physics and Topological Field Theory -
Noncommutative Geometry and Physics
Noncommutative Geometry and Physics -
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Principal 2-group bundles and the Freed--Quinn line bundle
Emily Cliff University of Sherbrooke
A 2-group is a categorical generalization of a group: it's a category with a multiplication operation which satisfies the usual group axioms only up to coherent isomorphisms. The isomorphism classes of its objects form an ordinary group, G. Given a 2-group G with underlying group G, we can similarly define a categorical generalization of the notion of principal bundles over a manifold (or stack) X, and obtain a bicategory Bun_G(X), living over the category Bun_G(X) of ordinary G-bundles on X. For G finite and X a Riemann surface, we prove that this gives a categorification of the Freed--Quinn line bundle, a mapping-class group equivariant line bundle on Bun_G(X) which plays an important role in Dijkgraaf--Witten theory (i.e. Chern--Simons theory for the finite group G). This talk is based on joint work with Daniel Berwick-Evans, Laura Murray, Apurva Nakade, and Emma Phillips.
I will not assume previous knowledge of 2-groups: I will provide a quick overview in the main talk, as well as a more detailed discussion during a pre-talk on Tuesday.
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Quantization of the Ngô morphism (VIRTUAL)
Tom Gannon University of California, Los Angeles
We will discuss work, joint with Victor Ginzburg, on the quantization (non-commutative deformation) of the Ngô morphism, a morphism of group schemes which plays a key role in Ngô’s proof of the fundamental lemma in the Langlands program. We will also discuss how the tools used to construct this morphism can be used to prove conjectures of Ben-Zvi—Gunningham, which predict that this morphism gives “spectral decomposition” of DG categories with an action of a reductive group over the coarse quotient of a maximal Cartan subalgebra by the affine Weyl group.
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Quantum difference equations from shuffle algebra: affine type A quiver varieties
Tianqing Zhu Tsinghua University
The quantum difference equation (qde) is the $q$-difference equation which is proposed by Okounkov and Smirnov to encode the $K$-theoretic twisted quasimap counting for the Nakajima quiver varieties. In this talk, we will give a direct quantum toroidal algebra $U_{q,t}(\hat{\hat{\mf{sl}}}_{n})$ construction for the qde of the affine type $A$ quiver varieties. We will show that there is a really explicit and concise formula for the quantum difference operators. Moreover we will show that the degeneration limit of the quantum difference equation is equivalent to the Dubrovin connection for the quantum cohomology of the affine type A quiver varieties, which will give the description of the monodromy representation of the Dubrovin connection via the monodromy operators in the quantum difference equation.
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Integrable Deformations on Twistor Space
Joaquin Liniado National University of La Plata
Integrable field theories in two dimensions are known to originate as defect theories of 4d Chern-Simons theory and as symmetry reductions of the 4d anti-self-dual Yang-Mills equations. Based on ideas of Costello, it has been proposed in work of Bittleston and Skinner that these two approaches can be unified starting from holomorphic Chern-Simons theory in 6 dimensions. In this talk I will introduce the first complete description of this diamond of integrable theories for a family of deformed sigma models, going beyond the Dirichlet boundary conditions that have been considered thus far. The talk is based on the recent work https://arxiv.org/abs/2311.17551.
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Mathematical Physics Lecture
Kevin Costello Perimeter Institute for Theoretical Physics