2024 Simons Collaboration on Global Categorical Symmetries Annual Meeting

Clay Còrdova
University of Chicago

Representation 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 University

Exploring 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 University

The 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 Diego

Categorical 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 Edinburgh

The 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 University

The 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 Chicago

Ambidexterity 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 Berkeley

Categorical 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.

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.

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/

Overview

In-person participants 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 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 on Friday 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
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.

Meeting & Policy Questions
Christina Darras
Event Manager
[email protected]

Travel & Hotel Support
FCM Travel Meetings & Events
[email protected]
Hours: M-F, 8:30 AM-5:00 PM ET
+1-877-300-7108