Format results
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Talk
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String Theory for Mathematicians - Lecture 7
Kevin Costello Perimeter Institute for Theoretical Physics
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String Theory for Mathematicians - Lecture 3
Kevin Costello Perimeter Institute for Theoretical Physics
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String Theory for Mathematicians - Lecture 2
Kevin Costello Perimeter Institute for Theoretical Physics
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String Theory for Mathematicians - Lecture 1
Kevin Costello Perimeter Institute for Theoretical Physics
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Talk
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Critical points and spectral curves
Nigel Hitchin University of Oxford
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Generalizing Quivers: Bows, Slings, Monowalls
Sergey Cherkis University of Arizona
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Nahm transformation for parabolic harmonic bundles on the projective line with regular residues
Szilard Szabo Budapest University of Technology and Economics
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A mathematical definition of 3d indices
Tudor Dimofte University of Edinburgh
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Perverse Hirzebruch y-genus of Higgs moduli spaces
Tamas Hausel Institute of Science and Technology Austria
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Motivic Classes for Moduli of Connections
Alexander Soibelman University of Southern California
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BPS algebras and twisted character varieties
Ben Davison University of Edinburgh
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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 University of Vienna
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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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Mathematica School Lecture - 2015
Jason Harris Wolfram Research (United States)
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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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2-dimensional topological field theories via the genus filtration
Jan Steinebrunner -
Edge-colored graphs and exponential integrals
Maximilian Wiesmann Max Planck Institute for Mathematics in the Sciences
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Perverse coherent sheaves and cluster categorifications
Ilya Dumanskiy Massachusetts Institute of Technology (MIT) - Department of Mathematics
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Lecture - Mathematical Physics, PHYS 777
Kevin Costello Perimeter Institute for Theoretical Physics
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Topological Feynman integrals and the odd graph complex
Paul-Hermann Balduf -
Lecture - Mathematical Physics, PHYS 777
Kevin Costello Perimeter Institute for Theoretical Physics
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Lecture - Mathematical Physics, PHYS 777
Kevin Costello Perimeter Institute for Theoretical Physics
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Lecture - Mathematical Physics, PHYS 777
Kevin Costello Perimeter Institute for Theoretical Physics
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String Theory for Mathematicians - Kevin Costello
String Theory for Mathematicians - Kevin Costello -
Hitchin Systems in Mathematics and Physics
Hitchin Systems in Mathematics and Physics
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Deformation Quantization of Shifted Poisson Structures
Deformation Quantization of Shifted Poisson Structures
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2-dimensional topological field theories via the genus filtration
Jan SteinebrunnerBy a folk theorem (non-extended) 2-dimensional TFTs valued in the category of vector spaces are equivalent to commutative Frobenius algebras. Upgrading the bordism category to an (infinity, 1)-category whose 2-morphism are diffeomorphisms, one can study 2D TFTs valued in higher categories, leading for example to (derived) modular functors and cohomological field theories. I will explain how to describe such more general (non-extended) 2D TFTs as algebras over the modular infinity-operad of surfaces. In genus 0 this yields an E_2^{SO}-Frobenius algebra and I will outline an obstruction theory for inductively extending such algebras to higher genus. Specialising to invertible TFTs, this amounts to a genus filtration of the classifying space of the bordism category and hence the Madsen--Tillmann spectrum MTSO_2. The aforementioned obstruction theory identifies the associated graded in terms of curve complexes and thereby yields a spectral sequence starting with the unstable and converging to the stable cohomology of mapping class groups. -
Edge-colored graphs and exponential integrals
Maximilian Wiesmann Max Planck Institute for Mathematics in the Sciences
We show that specific exponential integrals serve as generating functions of labeled edge-colored graphs. Based on this, we derive asymptotics for the number of edge-colored graphs with arbitrary weights assigned to different vertex structures. The asymptotic behavior is governed by the critical points of a polynomial. As an application, we discuss the Ising model on a random graph and show how its phase transitions arise from our formula.
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Perverse coherent sheaves and cluster categorifications
Ilya Dumanskiy Massachusetts Institute of Technology (MIT) - Department of Mathematics
K-theoretical Coulomb branches are expected to have cluster structure. Cautis and Williams categorified this expectation. In particular, they conjecture (and prove in type A) that the category of perverse coherent sheaves on the affine Grassmannian is a cluster monoidal categorification. We discuss recent progress on this conjecture. In particular, we construct cluster short exact sequences of certain perverse coherent sheaves. We do that by constructing a bridge, relating this (geometric) category to the (algebraic) category of finite dimensional modules over the quantum affine group. This is done by relating both categories to the notion of Feigin--Loktev fusion product.
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Topological Feynman integrals and the odd graph complex
Paul-Hermann BaldufRecent work by Davide Gaiotto and collaborators introduced a new type of parametric Feynman integrals to compute BRST anomalies in topological and holomorphic quantum field theories. The integrand of these integrals is a certain differential form in Schwinger parameters. In a new article together with Simone Hu, we showed that this "topological" differential form coincides with a "Pfaffian" differential form that had been used by Brown, Panzer, and Hu, to compute cohomology of the odd graph complex and of the linear group. In my talk, I will review some aspects of the graph complex and the role played by the Pfaffian form there, sketch the proof of equivalence, and comment on various observations on either side of the equivalence and their natural counterparts on the other side.
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Lecture - Mathematical Physics, PHYS 777
Kevin Costello Perimeter Institute for Theoretical Physics
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Lecture - Mathematical Physics, PHYS 777
Kevin Costello Perimeter Institute for Theoretical Physics
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Lecture - Mathematical Physics, PHYS 777
Kevin Costello Perimeter Institute for Theoretical Physics