2024 Simons Collaboration on Global Categorical Symmetries Annual Meeting
Invitation Only
Organizer:
Constantin Teleman, University of California, Berkeley
Meeting Goals:
The Simons Collaboration on Global Categorical Symmetries centers on the systematic study of the role of generalized symmetries in quantum field theory, with focus on topological symmetries implemented by extended operators. Their study involves the new mathematical calculus of higher categories, including fusion and braided categories, homotopy theory, dualities, such as electromagnetic duality for homotopy types and Langlands duality for Lie groups, and their role in controlling lattice models and phase transitions.
This year’s Annual Meeting of the Collaboration will offer a broad review of the results obtained to date, both by our collaboration and by related groups of researchers, as well as snapshots of ongoing work and future challenges and projects. We will discuss developments in the arithmetic of fusion categories, skein theory, symmetries of lattice models, symmetries arising form string theory and holography, continuous symmetries, the study of anomalies and their role in controlling low-energy limit of QFTs.
Previous Meeting:
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Agenda
Thursday, November 14
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Constantin Teleman | Categorical Symmetries in QFT: Progress and Outlook I 10:30 AM BREAK 11:00 AM Kenneth Intriligator |Categorical Symmetries in QFT: Progress and Outlook II 12:00 PM LUNCH 1:00 PM Michael Hopkins | The mutual influence of homotopy theory and quantum field theory 2:00 PM BREAK 2:30 PM Tomer Schlank | Ambidexterity and Quantum Field Theories 3:30 PM BREAK 4:00 PM Michele Del Zotto | Exploring the higher structure of symmetries 5:00 PM DAY ONE CONCLUDES Friday, November 15
8:30 AM CHECK-IN & BREAKFAST 9:30 AM Julia Plavnik | The Homotopy Coherent Classification of Fusion 2-Categories 10:30 AM BREAK 11:00 AM David Jordan | The quantum A-polynomial from parabolic defects 12:00 PM LUNCH 1:00 PM Clay Còrdova | Representation Theory of Solitons 2:00 PM MEETING CONCLUDES -
Abstracts
Clay Còrdova
University of ChicagoRepresentation Theory of Solitons
Solitons in two-dimensional quantum field theory exhibit patterns of degeneracies and associated selection rules on scattering amplitudes. We develop a representation theory that captures these intriguing features of solitons. This representation theory is based on an algebra we refer to as the “strip algebra,” which is defined in terms of the non-invertible symmetry, i.e., a fusion category, and its action on boundary conditions encoded by a module category. The strip algebra is a weak Hopf algebra, a fact which can be elegantly deduced by quantizing the three-dimensional Drinfeld center TQFT, on a spatial manifold with corners. These structures imply that the representation category of the strip algebra is also a unitary fusion category which we identify with a dual category. We present a straightforward method for analyzing these representations in terms of quiver diagrams where nodes are vacua and arrows are solitons and provide examples demonstrating how the representation theory reproduces known degeneracies and selection rules of soliton scattering. Our analysis provides the general framework for analyzing non-invertible symmetry on manifolds with boundary and applies both to the case of boundaries at infinity, relevant to particle physics, and boundaries at finite distance, relevant in conformal field theory or condensed matter systems.
Michele Del Zotto
Uppsala UniversityExploring the higher structure of symmetries
I will review recent progress in understanding the higher structure of topological defects in higher dimensional field theories (as well as some of its applications). In particular, I will discuss and contrast aspects of the worldvolume approach towards the calculus of defects and the topological symmetry theory, as well as some consequences of higher structures on RG flows, allowing to establish dictionaries between UV and IR physics. Along the way, I will also briefly touch upon some aspects of recent proposals to generalize the topological symmetry theory framework to include continuous global symmetries.
Michael Hopkins
Harvard UniversityThe mutual influence of homotopy theory and quantum field theory
I will describe some projects in the collaboration that involve the application of homotopy theoretic methods to questions arising from quantum field theory. My focus will be on the ways in which this relationship has generated new research directions in both fields.
Kenneth Intriligator
University of California at San DiegoCategorical Symmetries in QFT: Progress and Outlook II
We will continue to review some of the major motivations and themes of our collaboration’s work, highlighting applications of generalized symmetries towards a deeper understanding of quantum field theory, renormalization group flows, and IR phases.
David Jordan
University of EdinburghThe quantum A-polynomial from parabolic defects
I will describe a joint project with Jennifer Brown to construct the so-called quantum A-polynomial invariants of knots functorially using the theory of parabolic induction and restriction for quantum groups, encoded via certain non-invertible defects. We obtain an algorithm computing our invariant from an ideal triangulation of the knot complement; the algorithm is sufficiently explicit that it can be executed in Sage.
Julia Plavnik
Indian UniversityThe Homotopy Coherent Classification of Fusion 2-Categories
Fusion 2-categories are a higher categorical analog of fusion categories that have gained a lot of attention in the last years because of their importance in many fields of math and physics, such as TQFTs, condensed matter and high energy physics. The classification of fusion (1-) categories is a very active research area and has provided new examples and led to the development of new invariants and tools to understand these categories.
In this talk, we will present a parametrization of multifusion 2-categories in terms of lower categorical data, involving braided fusion categories, group theory and cohomological data. If time allows, we will also show some applications of this result. This is a joint work in progress with Décoppet, Johnson-Freyd, Huston, Nikshych, Penneys, Reutter and Yu.
Tomer Schlank
University of ChicagoAmbidexterity and Quantum Field Theories
Ambidexterity is an ∞-categorical phenomenon that leads to a highly structured form of integration. For certain types of quantum field theories, such as Dijkgraaf-Witten theories, this form of integration enables a mathematically rigorous definition of path integrals. In this talk, we will examine how results from the abstract theory of ambidexterity can be used to compute universal target (∞,n)-categories for quantum field theories with various structures and properties motivated by physics. These include universal targets with well-behaved partition functions or those exhibiting electro-magnetic duality. Additionally, we will discuss ongoing efforts to extend this approach to more general forms of quantum field theories. This talk is based on collaborative projects with Scheimbauer, Del Zotto, Ohmori, and Yanovski.
Constantin Teleman
University of California BerkeleyCategorical Symmetries in QFT: Progress and Outlook I
We will review some major themes of our collaboration work, listing some of the significant results and methods: the Quiche/SymTFT calculus of symmetries and defects, the role of homotopy theory, boundary theories, dualities and anomalies; classification of structured categories; and gauge theory dualities and applications to geometry. Many of the ideas introduced will be developed comprehensively in our program lectures. This talk will emphasize the mathematical side story and conclude with open questions building on recent developments.
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Participation & Funding
Participation in the meeting falls into the following four categories. An individual’s participation category is communicated via their letter of invitation.
Group A – Organizers and Speakers
- Economy Class: For flights that are three hours or less to your destination, the maximum allowable class of service is Economy class.
- Premium Economy Class: For flights where the total air travel time (excluding connection time) is more than three hours and less than seven hours per segment to your destination, the maximum allowable class of service is premium economy.
- Business Class: When traveling internationally (or to Hawaii/Alaska) travelers are permitted to travel in Business Class on those segments that are seven hours or more. If the routing is over budget, a premium economy or mixed-class ticket will be booked.
Group B – Funded Participants
The foundation will arrange and pay for round-trip air or train travel to the conference as well as hotel accommodations and reimbursement of local expenses. Economy-class airfare will be booked for all flights.Group C – Unfunded Participants
Individuals in Group C will not receive financial support, but are encouraged to enjoy all conference-hosted meals.Group D – Remote Participants
Individuals in Group D will participate in the meeting remotely. -
Travel & Hotel
Air & Rail
For funded individuals, the foundation will arrange and pay for round-trip travel from their home city to the conference.All travel and hotel arrangements must be booked through the Simons Foundation’s preferred travel agency.
Travel specifications, including preferred airline, will be accommodated provided that these specifications are reasonable and within budget.
Travel arrangements not booked through the preferred agency, including triangle trips and routing/preferred airlines outside budget, must be pre-approved by the Simons Foundation and a reimbursement quote must be obtained through the foundation’s travel agency.
All costs related to changes made to ticketed travel are to be paid for by the participant and are not reimbursable. Please contact the foundation’s travel agency for further assistance.
Personal & Rental Cars
Personal car and rental trips over 250 miles each way require prior approval from the Simons Foundation via email.Rental cars must be pre-approved by the Simons Foundation.
The James NoMad Hotel offers valet parking. Please note there are no in-and-out privileges when using the hotel’s garage, therefore it is encouraged that participants walk or take public transportation to the Simons Foundation.
Hotel
Funded individuals who require hotel accommodations are hosted by the foundation for a maximum of three nights at The James NoMad, arriving one day before the meeting and departing one day after the meeting.Any additional nights are at the attendee’s own expense. To arrange accommodations, please register at the link included in your invitation.
The James NoMad
22 East 29th Street
New York, NY 10016
https://www.jameshotels.com/ -
Reimbursement
Overview:
Funded individuals will be reimbursed for meals and local expenses including ground transportation. Expenses should be submitted through the foundation’s online expense reimbursement platform after the meeting’s conclusion.Expenses accrued as a result of meetings not directly related to the Simons Foundation-hosted meeting (a satellite collaboration meeting held at another institution, for example) will not be reimbursed by the Simons Foundation and should be paid by other sources.
Below are key reimbursement takeaways; a full policy will be provided with the final logistics email circulated approximately 2 weeks prior to the meeting’s start.
Meals:
The daily meal limit is $125; itemized receipts are required for expenses over $24 USD. The foundation DOES NOT provide a meal per diem and only reimburses actual meal expenses up the following amounts.- Breakfast $20
- Lunch $30
- Dinner $75
Allowable Meal Expenses
- Meals taken on travel days (when you traveled by air or train).
- Meals not provided on a meeting day, dinner for example.
- Group dinners consisting of fellow meeting participants paid by a single person will be reimbursed up to $75 per person and the amount will count towards each individual’s $125 daily meal limit.
Unallowable Meal Expenses
- Meals taken outside those provided by the foundation (breakfast, lunch, breaks and/or dinner).
- Meals taken on days not associated with Simons Foundation-coordinated events.
Minibar expenses. - Meal expenses for a non-foundation guest.
Ubers, Lyfts, taxis, etc., taken to and from restaurants in Manhattan. - Accommodations will be made for those with mobility restrictions.
Ground Transportation:
Expenses for ground transportation will be reimbursed for travel days (i.e. traveling to/from the airport or train station) as well as subway and bus fares while in Manhattan are reimbursable.
Transportation to/from satellite meetings are not reimbursable. -
Attendance & Building Protocols
Attendance
In-person participants and speakers are expected to attend all meeting days. Participants receiving hotel and travel support wishing to arrive on meeting days which conclude at 2:00 PM will be asked to attend remotely.COVID-19 Vaccination
Individuals accessing Simons Foundation and Flatiron Institute buildings must be fully vaccinated against COVID-19.Entry & Building Access
Upon arrival, guests will be required to show their photo ID to enter the Simons Foundation and Flatiron Institute buildings. After checking-in at the meeting reception desk, guests will be able to show their meeting name badge to re-enter the building. If you forget your name badge, you will need to provide your photo ID.The Simons Foundation and Flatiron Institute buildings are not considered “open campuses” and meeting participants will only have access to the spaces in which the meeting will take place. All other areas are off limits without prior approval.
If you require a private space to conduct a phone call or remote meeting, please contact your meeting manager at least 48-hours ahead of time so that they may book a space for you within the foundation’s room reservation system.
Guests & Children
Meeting participants are required to give 24 hour advance notice of any guests meeting them at the Simons Foundation either before or after the meeting. Outside guests are discouraged from joining meeting activities, including meals.With the exception of Simons Foundation and Flatiron Institute staff, ad hoc meeting participants who did not receive a meeting invitation directly from the Simons Foundation are not permitted.
Children under the age of 18 are not permitted to attend meetings at the Simons Foundation. Furthermore, the Simons Foundation does not provide childcare facilities or support of any kind. Special accommodations will be made for nursing parents.
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Contacts
Meeting & Policy Questions
Christina Darras
Event Manager
[email protected]Travel & Hotel Support
FCM Travel Meetings & Events
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