Mathematical physics

Holomorphic-topological field theories and representation theory

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Conference Speakers

Mina Aganagic (University of California, Berkeley) Christopher Beem (University of Oxford) Tudor Dimofte (University of Edinburgh) Sergei Gukov (California institute of Technology) Hans Jockers (Johannes Gutenberg University Mainz) Ahsan Khan (Harvard University) Satoshi Nawata (Fudan University) Andrew Neitzke (Yale University) Tony Pantev (University of Pennsylvania) Harold Williams (University of Southern California) Brian Williams (Boston University)

 

Workshop Organizers
Davide Gaiotto
Wenjun Niu
Ben Webster

This series is a crash course introduction to a handful of advanced topics designed to tackle the general problem of how to engineer Positive Operator-Valued Measures (POVMs) using observable building blocks, the so-called Instrument Manifold Program.  This program emerged from a recent fundamental breakthrough: how to realize the measurement of a spin’s direction, a.k.a. the spin-coherent-state POVM, a spherical set of outcomes analogous to the well known coherent-state POVM of the standard phase plane.

Outline: Oct 27: Introduction: The Planimeter and the "Spherimeter'' Oct 30: Supplement Nov 03: CANCELLED Nov 06: Supplement Nov 10: POVMs and Decoherence Nov 13: Supplement Nov 17: Generalized Observables: Phase-Point and Spin-Direction Nov 20: Supplement Nov 24: Transformation Groups and Enveloping Algebras Nov 27: Supplement Dec 01: Frame Operators and Quasi-Probability Distributions Dec 04: Supplement Dec 08: The Arthurs-Kelly (1965) and D’Ariano (2002) Measurements Dec 11: Supplement

Location & Building Access: Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo (Exception - November 27 in Space Room, 4th Floor)

Registration: Please sign-up here: https://forms.office.com/r/dEA4EUq0CU

Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact [email protected].

Scroll down to Registration and Enrollment to participate.

Structure:

We will discuss 8 papers which had huge impact in physics. One week Instructor Pedro Vieira will discuss a paper; students should read it beforehand. One week later students discuss recent papers referring to that paper (20 min each student, ~ 3 presentations; at the end of the class Pedro will grade the presentations based on “Physics”, “Presentation”, “Question handling”; and give comments).

By the end of the course, students will have explored a vast set of topics in theoretical physics — spotting potential gaps to be fixed — sharpened their presentation skills through steady practice, and sparked cross-disciplinary conversations through our shared physics language.

Familiarity with Quantum Field Theory and General Relativity is assumed.

The papers:

Sept 12 & 19: On the Quantum Correction for Thermodynamic Equilibrium, Wigner, 1932 Topic: Quantum Mechanics

Sept 22 & 29: Existence theorem for certain systems of nonlinear PDEs, Foures-Bruhat, 1952 Topic: General relativity

Oct 3 & 10: The Renormalization Group and the Epsilon Expansion, Wilson and Kogut, 1973 Topic: Quantum Field Theory

Oct 10 (EXTRA) & 17: More about the Massive Schwinger Model, Coleman, 1976 Topic: 2D Quantum Field Theory

Oct 20 & 27: A sequence of approximated solutions to the S-K model for spin glasses, Parisi, 1980 Topic: Statistical Mechanics

Oct 29 (New Date) & Nov 7: Quantum Field Theory and the Jones Polynomial, Witten, 1988 Topic: Topological Quantum Field Theory

Nov 10 & 17: Exactly Solvable Field Theories of Closed Strings, Brezin, Kazakov, 1989 Topic: 2D Quantum Gravity

Nov 21 & Nov 28: Unpaired Majorana fermions in quantum wires, Kitaev, 2000 Topic: Quantum Matter/Quantum Information

Schedule: This is a Friday / Monday alternating week schedule from 915am-1045am.

Exceptions: There will be an afternoon session at 130pm on Friday October 10 to avoid the Thanksgiving holiday.

Location & Building Access: Alice Room, 3rd Floor, Perimeter Institute, 31 Caroline St N, Waterloo Participants who do not have an access card for Perimeter Institute must sign in at the security desk before each session. For information on parking or accessibility please contact [email protected].

Registration and Enrollment: Please sign-up here: https://forms.office.com/r/nDQ6SDxSR4

Zoom Link https://pitp.zoom.us/j/95238695187?pwd=G6EjbywTpOagSxpbMZtgznxmuwFFBp.1

Quantum field theory intertwines continuous and discrete structures. On the discrete side, combinatorics plays a central role in describing and understanding its expansions and models. This lecture series focuses on the combinatorial aspects of quantum field theory. In the first part, we explore analytic combinatorics techniques, inspired by QFT, for the enumeration of graphs. These methods turn out to be surprisingly powerful in addressing deep questions in algebraic geometry, topology, and statistical models on graphs. In the second part, we turn to discrete structures arising in perturbative expansions of QFT. We study these from a modern combinatorics viewpoint, using tools such as Lorentzian polynomials and generalized permutahedra to better understand the mathematical objects at the heart of quantum field theory.

For updates visit: https://michaelborinsky.com/combqft.html

This course is offered by the University of Waterloo's Department of Combinatorics & Optimization; UW students can enroll through Quest.

Lectures will be held at Perimeter Institute, 31 Caroline St N, Waterloo. Students will need to sign in and out of Perimeter each day. Note: session is cancelled for Sept 25; there is a room change for Oct 2 & Nov 11, and no classes week of October 13.

This is a theoretical physics course that aims to review the basics of theoretical mechanics, special relativity, and classical field theory, with the emphasis on geometrical notions and relativistic formalism, thus setting the stage for the forthcoming courses in Quantum Mechanics, and Quantum Field Theory in particular, as well as in General Relativity and Quantum Gravity. Instructor: Aldo Riello Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

We will discuss mathematical aspects of classical and quantum field theory, including topics such as: symplectic manifolds and the phase space, symplectic reduction, geometric quantization, Chern-Simons theory, and others. Instructor: Kevin Costello/Mykola Semenyakin Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

This course will introduce you to some of the geometrical structures underlying theoretical physics. Previous knowledge of differential geometry is not required. Topics covered in the course include: Introduction to manifolds, differential forms, symplectic manifolds, symplectic version of Noether’s theorem, integration on manifolds, fiber bundles, principal bundles and applications to gauge theory. Instructor: Mykola Semenyakin/Maite Dupuis Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

This is a theoretical physics course that aims to review the basics of theoretical mechanics, special relativity, and classical field theory, with the emphasis on geometrical notions and relativistic formalism, thus setting the stage for the forthcoming courses in Quantum Mechanics, and Quantum Field Theory in particular, as well as in General Relativity and Quantum Gravity. Instructor: Aldo Riello Students who are not part of the PSI MSc program should review enrollment and course format information here: https://perimeterinstitute.ca/graduate-courses

We will discuss mathematical aspects of classical and quantum field theory, including topics such as: symplectic manifolds and the phase space, symplectic reduction, geometric quantization, Chern-Simons theory, and others.

Quantum phases have become a staple of modern physics, thanks to their appearance in fields as diverse as condensed matter physics, quantum field theory, quantum information processing, and topology. The description of quantum phases of matter requires novel mathematical tools that lie beyond the old symmetry breaking perspective on phases. Techniques from topological field theory, homotopy theory, and (higher) category theory show great potential for advancing our understanding of the characterization and classification of quantum phases. The goal of this workshop is to bring together experts from across mathematics and physics to discuss recent breakthroughs in these mathematical tools and their application to physical problems. 

 

Scientific Organizers

Lukas Mueller
Alex Turzillo
Davide Gaiotto
 

Sponsored in part by the Simons Collaboration on Global Categorical Symmetries 

 

 

This course introduces quantum field theory from scratch and then develops the theory of the quantum fluctuations of fields and particles. We will focus, in particular, on how quantum fields are affected by curvature and by spacetime horizons. This will lead us to the Unruh effect, Hawking radiation and to inflationary cosmology. Inflationary cosmology, which we will study in detail, is part of the current standard model of cosmology which holds that all structure in the universe - such as the distribution of galaxies - originated in tiny quantum fluctuations of a scalar field and of space-time itself. For intuition, consider that quantum field fluctuations of significant amplitude normally occur only at very small length scales. Close to the big bang, during a brief initial period of nearly exponentially fast expansion (inflation), such small-wavelength but large-amplitude quantum fluctuations were stretched out to cosmological wavelengths. In this way, quantum fluctuations are thought to have seeded the observed inhomogeneities in the cosmic microwave background - which in turn seeded the condensation of hydrogen into galaxies and stars, all closely matching the increasingly accurate astronomical observations over recent years. The prerequisites for this course are a solid understanding of quantum theory and some basic knowledge of general relativity, such as FRW spacetimes.

https://uwaterloo.ca/physics-of-information-lab/teaching/quantum-field-theory-cosmology-amath872phys785-w2024

https://pitp.zoom.us/j/96567241418?pwd=U3I1V1g4YXdaZ3psT1FrZUdlYm1zdz09

 

This course will introduce you to some of the geometrical structures underlying theoretical physics. Previous knowledge of differential geometry is not required. Topics covered in the course include: Introduction to manifolds, differential forms, symplectic manifolds, symplectic version of Noether’s theorem, integration on manifolds, fiber bundles, principal bundles and applications to gauge theory.