Holomorphic-topological field theories and representation theory
Holomorphic-topological (HT) field theories form a fascinating class of quantum field theories. These theories combine features of topological quantum field theories (TQFT) and conformal field theories (CFT).
Due to the mixed holomorphic-topological nature of such theories, they create interactions between TQFT data (e.g., algbras, monoidal categories, etc) and CFT data (e.g., chiral algebras and chiral categories). This leads to exciting new mathematical structures, and connections to integrable systems, quantum topology and many other areas of mathematics. Recently. much progress has been made on the representation-theoretic aspects of HT theories. Examples include:
1. (Shifted) Poisson vertex algebras and their quantizations are constructed from local operators in HT theories.
2. Dimensional reduction of 4d HT theories lead to integrable systems and solutions of quantum Yang-Baxter equations.
3. 4d N=2 theories are linked to representation theory of K-theoretic Coulomb branches, cluster algebra categorifications, wall crossings and elliptic stable envelops.
4. New examples of chiral algebras and their dualities are derived from boundary conditions and dualities of 3d HT theories.
Moreover, many interesting TQFTs are given by deformations of holomorphic-topological theories. Examples include topological twists of 3d N=4 and 4d N=2 theories. These theories have attracted considerable attention in recent years for their connections to 3d mirror symmetry and the Langlands program. Some of these TQFTs only admit Lagrangian descriptions as HT QFTs, and therefore studying HT theories offers a possible approach for understanding these non-Lagrangian TQFTs.
This conference will focus on the representation-theoretic aspects of HT theories, particularly:
1. Chiral algebras arising from observables of HT QFT.
2. Quantum algebras, including Yangians and quantum affine algebras, and their relation to HT theories.
3. Chiral categories and OPE of line operators in HT theories.
4. Deformation of HT theories and their relation to chiral algebra deformations.
5. Relation between various HT theories under dimensional-reduction.
We aim to bring together leading mathematicians and physicists, to inform each other about the recent progress made in this area.
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Conference Speakers
Mina Aganagic (University of California, Berkeley)Christopher Beem (University of Oxford)Tudor Dimofte (University of Edinburgh)Angela Gibney (University of Pennsylvania)Sergei Gukov (California institute of Technology)Hans Jockers (Johannes Gutenberg University Mainz)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: Indirect Measurement and System-Meter Interaction
Nov 03: POVMs and Decoherence
Nov 06: Generalized Observables: Phase-Point and Spin-Direction
Nov 10: Transformation Groups and Enveloping Algebras
Nov 13: Frame Operators and Quasi-Probability Distributions
Nov 17: The Arthurs-Kelly (1965) and D’Ariano (2002) Measurements
Nov 20: Optical Homodyne and Heterodyne
Nov 24: Continuous Measurement and the Kraus-Operator Density
Nov 27: Simultaneous Measurements of Non-Commuting Observables
Dec 01: Instrumental Groups and Universal Markov Processes
Dec 04: Universal Instrument Navigation
Dec 08: Non-Euclidean Geometry
Dec 11: Non-Euclidean POVMs
**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 academic@perimeterinstitute.ca.
In July 1925, Heisenberg published his paper on matrix mechanics, followed shortly thereafter (in early 1926) by Schrodinger’s paper on wave mechanics. As such, 2025 is the centenary of the modern quantum theory. This conference aims to bring together experts in the history and philosophy of quantum theory and researchers working on various foundational issues to shed new light on the past, present and future of the theory.
The meeting aims to benefit from the useful synergy that exists between historical studies and efforts to push forward the frontier of our knowledge. On one side, the details of the path to discovery of various quantum concepts or applications of quantum ideas can inform contemporary research. For instance, whenever there is a paradigm of thinking that is sufficiently pervasive today that it is difficult to even recognize the possibility of alternatives, familiarity with the debates at the historical origin of this paradigm can help to make explicit what is usually left implicit. On the other side, modern developments can often shed new light on various historical and philosophical issues.
The fact that there is still no broad consensus on many of the conceptual issues that have been controversial since the birth of modern quantum theory suggests that a proper understanding of these remains to be achieved. The occasion of the quantum centenary provides a good opportunity for the community to develop a broader perspective on these issues, draw connections between research programs that aim to address them, and set objectives for future research.
The aim is to have two types of talks concerning the history: those that present novel takes on well-studied historical topics and those that address more unconventional historical questions. The second category aims to include talks on the history of a variety of subfields of quantum theory, such quantum information, quantum field theory, quantum optics, quantum logic, quantum chemistry, quantum gravity, quantum matter and quantum foundations..
Conference topics include:
The prehistory of modern quantum theory
The historical development of modern quantum theory
The discovery of Important concepts in quantum theory (the uncertainty principle, wave-particle duality, particle statistics, the no-cloning theorem, teleportation, etc.)
The discovery of important no-go results (von Neumann’s no-go theorem, the 1935 Einstein-Podolsky-Rosen argument, Bell’s theorem, the Kochen-Specker theorem)
The history of quantum information, quantum field theory, quantum optics, quantum logic, quantum chemistry, quantum gravity, and quantum matter
The sociology of quantum physics
The conference will include invited as well as contributed talks.
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Scientific Organizers:
Robert Spekkens (Perimeter Institute)
Wayne Myrvold (Western University)
Doreen Fraser (University of Waterloo)
Katherine Mack (Perimeter Institute)
David Schmid (Perimeter Institute)
Nick Ormrod (Perimeter Institute)
Marina Maciel Ansanelli (Perimeter Institute)
Yile Ying (Perimeter Institute)
Confirmed Speakers:
A. Douglas Stone (Yale University)
Benjamin Schumacher (Kenyon College)
Daniela Monaldi (York University)
Diana Taschetto (Utrecht University)
Don Howard (University of Notre Dame)
Elise Crull (City University of New York)
Guido Bacciagaluppi (Utrecht University)
Howard Wiseman (Griffith University)
James Fraser (Paris 1 Panthéon-Sorbonne University)
Jos Uffink (University of Minnesota)
Matthew Leifer (Chapman University)
Michel Janssen (University of Minnesota)
William Wootters (Williams College)
William Unruh (University of British Columbia)
Additional invited speakers will be added as they are confirmed.
Year of Quantum Across Canada: From Fundamental Science to Applications
The Institute for Quantum Computing and the Perimeter Institute for Theoretical Physics will jointly host a meeting celebrating the 100 year anniversary of the discovery of quantum mechanics.
The conference will celebrate and aim to strengthen the quantum information science community in Canada and beyond, by bringing together leading Canadian researchers as well as members of the broader quantum community. The program will highlight the fundamental advances being made in quantum information theory and how these advances lead to applications.
Topics included in the program will include:
Quantum metrology
Quantum simulation and quantum advantage
Quantum error-correction and fault tolerance
Quantum complexity and algorithms
Quantum communication and networks
Quantum cryptography
Quantum information in quantum matter and quantum gravity
Participation is open to all scientists who are interested in the conference topics.
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Speakers
Christian Bauer (Lawrence Berkeley National Laboratory) Alexandre Blais (Université de Sherbrooke) Sergey Bravyi (IBM Research - Thomas J. Watson Research Center) Nikolas Breuckmann (University of Bristol) Soonwon Choi (MIT) Zohreh Davoudi (University of Maryland) Matthew Fisher (University of California, Santa Barbara) Dakshita Khurana (University of Illinois Urbana-Champaign) Aleksander Kubica (Yale University) Hank Lamm (Fermilab) Laura Mancinska (University of Copenhagen) Antonio Mezzacapo (IBM) John Preskill (Caltech) Martin Savage (University of Washington) Brian Swingle (Brandeis University) Nathan Wiebe (University of Toronto) Yu-Xiang Yang (The University of Hong Kong)
Co-Chairpersons
Marcela Carena (Perimeter Institute & University of Chicago & Fermilab) Norbert Lütkenhaus (University of Waterloo, Institute for Quantum Computing)
Scientific Organizers and Convenors
Alexandre Blais (Université de Sherbrook) Anne Broadbent (University of Ottawa) Shohini Ghose (Wilfrid Laurier University & Quantum Algorithms Institute) David Gosset (University of Waterloo, IQC, Perimeter Institute) Tim Hsieh (Perimeter Institute) Ray Laflamme (University of Waterloo, IQC) Alex May (Perimeter Institute) Christine Muschik (University of Waterloo, IQC, Perimeter Institute) John Preskill (CalTech) Barry Sanders (University of Calgary & Quantum City) Aephraim Steinberg (University of Toronto, CQIQC) Beni Yoshida (Perimeter Institute) Peter Zoller (University of Innsbruck & IQOQI) Sisi Zhou (Perimeter Institute)
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