Format results
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Talk
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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 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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Lecture - Mathematical Physics, PHYS 777
Mykola Semenyakin Perimeter Institute for Theoretical Physics
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Ideas in Multiplicative Non-abelian Hodge theory
Marielle Ong University of Toronto
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The sewing-factorization theorem for $C_2$-cofinite VOAs
Hao Zhang Tsinghua University
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Matroids and the Moduli Space of Abelian Varieties
Juliette Bruce Dartmouth College
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Graphs, curves, and their moduli spaces (Part 2 of 2)
Michael Borinsky 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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Entanglement Hamiltonian and Heun operator
The ground state of a bipartite quantum system resembles a thermal state from the perspective of an observer with access to only one of the two regions. This observation has led to the introduction of the entanglement Hamiltonian, which has numerous applications in quantum information and the study of quantum many-body systems. This talk will explore two approaches to computing the entanglement Hamiltonian: one in the context of quantum field theories (QFTs), focusing on the Bisognano-Wichmann Hamiltonian, and the other for free fermion models on a lattice, where connections with algebraic Heun operators will be highlighted. Additionally, the relationship between the discrete and continuum cases will be examined. -
Lecture - Mathematical Physics, PHYS 777
Mykola Semenyakin Perimeter Institute for Theoretical Physics
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Ideas in Multiplicative Non-abelian Hodge theory
Marielle Ong University of Toronto
Non-abelian Hodge theory is a profound three-way equivalence between topological, smooth and holomorphic objects, i.e. representations of the fundamental group, flat connections and Higgs bundles. It is natural to explore a group-theoretic or multiplicative version — an enterprise that has been untaken by Soibelman, Kontsevich, Mochizuki and others. In this talk, we will review the current landscape of multiplicative non-abelian Hodge theory and discuss some outstanding questions. -
The sewing-factorization theorem for $C_2$-cofinite VOAs
Hao Zhang Tsinghua University
In this talk, I will present a sewing-factorization theorem for conformal blocks in arbitrary genus associated to a (possibly nonrational) $C_2$-cofinite VOA $V$. This result gives a higher genus analog of Huang-Lepowsky-Zhang's tensor product theory. Moreover, I will explain the relation between our result and pseudotraces, and confirm some of the conjectures by Gainuditnov-Runkel. The relationship between our result and coends will also be discussed. The talk is based on an ongoing project (arXiv: 2305.10180, 2411.07707) joint with Bin Gui.
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Matroids and the Moduli Space of Abelian Varieties
Juliette Bruce Dartmouth College
Inspired by recent work calculating the top weight cohomology of the moduli space $\mathcal{A}_g$ of principally polarized abelian varieties of dimension $g$ for small values of $g$, I will discuss a connection between matroids and compactifications of $\mathcal{A}_g$ that is anlogous to the connection between graphs and compactifications of the moduli space of curves. Given time I will also discuss recent work computing the homology of various matroid complexes. -
Graphs, curves, and their moduli spaces (Part 2 of 2)
Michael Borinsky Perimeter Institute for Theoretical Physics
I will give a gentle introduction to the moduli space of graphs and its fine moduli space cousin known as Outer Space. This moduli space of graphs has many applications to various branches of mathematical physics, algebraic geometry, and geometric group theory. It is a natural object to consider while studying Feynman amplitudes in parametric space, and it can be seen as the configuration space of one-dimensional quantum gravity. I will explain how this moduli space of graphs recently became the largest provider of information on the homology of the moduli space of curves of genus g and how associated graph complexes can be used to shed light on the 'dark-matter problems' of these moduli space's cohomology. -
Heun operator and Bethe ansatz
After an introduction to the notion of Leonard pairs, I explain their different uses. Then, I provide the definition of the associated Heun operator and how it allows us to simplify the computation of the quantum entanglement entropy. Finally, I show, in the simplest example, how the Bethe ansatz can be used to diagonalize the Heun operator.