2026 Simons Collaboration on New Structures in Low-Dimensional Topology Annual Meeting

Aaron Lauda
University of Southern California

Quantum Algorithms and the Spectral Geometry of Khovanov Homology

One of the central challenges in quantum algorithm design is to identify problems of genuine computational interest that admit exponential speedups over classical approaches. Shor’s algorithm for factoring is a landmark example, and quantum algorithms for approximating the Jones polynomial have similarly demonstrated exponential advantage. In this talk, we present a quantum algorithm that estimates the ranks of Khovanov homology groups using Hodge theory. This approach can be applied to a broad class of homology problems given certain assumptions.

In this talk, we present a quantum algorithm developed in collaboration with Alexander Schmidhuber, Michele Reilly, Paolo Zanardi, and Seth Lloyd for estimating the ranks of Khovanov homology groups utilizing a combinatorial Hodge theory. We introduce the notion of “harmonic Khovanov homology,” where we identify unique representatives of homology classes as the kernel of a Khovanov-Hodge Laplacian. While classical computation of these groups scales exponentially with the number of crossings, our quantum algorithm provides an efficient alternative, provided the Laplacian satisfies certain spectral conditions. We will discuss joint work with Jernej Grlj exploring the “higher spectrum” of this Laplacian and the question of what information the non-zero eigenvalues encode about the underlying link diagram. We conclude with numerical evidence for the algorithm’s efficiency and open questions regarding analytic bounds on the spectral gap for general knots.

Lisa Piccirillo
The University of Texas at Austin

and

Tye Lidman
North Carolina State University

More Exotic Constructions and More Alpha-Type Invariants II

We give some new exotica constructions in dimension 4 by further developing the invariants we studied previously with Levine. This is part two of a joint talk with Lisa Piccirillo.

Francesco Lin
Columbia University

Floer Theory and the Geometry of Hyperbolic Three-Manifolds

Floer theory and hyperbolic geometry have revolutionized our understanding of three-dimensional topology in the past few decades. Despite this, uncovering mutual interactions between them (if any) remains an outstanding open problem in the field. In this talk, based on joint work with M. Lipnowski, Francesco Lin will discuss how techniques from spectral theory allow to make some first steps towards this goal.

Peter Ozsvath
Princeton University

Bordered Floer Homology for Three-Manifolds with Torus Boundary

Peter Ozsvath will describe on-going work with Robert Lipshitz and Dylan Thurston, in which we define Heegaard Floer invariants for three-manifolds with torus boundary. Ozsvath will also describe a pairing theorem, which describes the Heegaard Floer homology of the torus sum of two such three-manifolds in terms of the bordered invariants of the summands.

Lisa Piccirillo
UT Austin

More Exotic Constructions and More Alpha-Type Invariants

We give some new exotica constructions in dimension 4 by further developing the invariants we studied previously with Levine. This is part one of a joint talk with Tye Lidman.

Raphaël Rouquier
University of California, Los Angeles

Categorified R-Matrices and Knot Invariants

2-representations are categorical versions of representations of Lie algebras. Tensoring 2-representations is a homotopical operation of a new type. On the other hand, the braiding is given by a surprisingly simple homological construction. Raphaël Rouquier will explain how the usual braiding or the R-matrix describes some homotopical information, and he will discuss the possibility for these to provide Gukov–Manolescu and Gukov–Pei–Putrov–Vafa invariants.

Zoltán Szabó
Princeton University

Exotic Structures on Smooth Four-Manifolds

The purpose of this talk is to study smooth four-manifolds with small Euler characteristics. Topics will include the construction of fake projective spaces with finite fundamental group, the study of Xiao’s genus-2 Lefschetz fibrations, and some fibration problems for complex ball quotients. Part of the work presented is a joint work with Andras Stipsicz and Inanc Baykur.

Melissa Zhang
University of California, Davis

Skein Lasagna Modules with 1-Dimensional Inputs

In this talk, Melissa Zhang will describe joint work with Qiuyu Ren, Ian Sullivan, Paul Wedrich, and Michael Willis, where we define a new version of Morrison–Walker–Wedrich’s skein lasagna modules by replacing the input balls with neighborhoods of 1-complexes.

This version is more amenable to computations for 4-manifolds with 1-handles. The strategy is to use an isomorphism discovered in previous joint work with Ian Sullivan, where we related the skein lasagna module of S2 x D2 to Rozansky–Willis homology, a version of Khovanov homology for links in connected sums of S2 x S1.

Participation in the meeting falls into the following four categories. An individual’s participation category is communicated via their letter of invitation.

The Simons Foundation will never ask for credit card information or require payment for registration to our events.

Group A – Speakers & Organizers

Individuals in Group A receive travel and hotel coordination within the following parameters:

Travel
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.

Hotel
Up to three nights at the conference hotel, arriving on Wednesday, March 25 and departing on Saturday, March 28.

Group B – Funded Participants

Individuals in Group B receive travel and hotel coordination within the following parameters:

Travel
Economy class travel will be booked regardless of flight length.

Hotel
Up to three nights at the conference hotel, arriving on Wednesday, March 25 and departing on Saturday, March 28.

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 and Rail

For funded individuals, the foundation will arrange and pay for round-trip travel from their home city to the conference city. All travel and hotel arrangements must be booked through the Simons Foundation’s preferred travel agency.

Travel Deviations

The following travel specifications are considered deviations and will only be accommodated if the cost is less than or equal to the amount the Simons Foundation would pay for a standard round-trip ticket from your home city to the conference city:

• Preferred airline
• Preferred travel class
• Specific flights/flight times
• Travel dates outside those associated with the conference
• Arriving or departing from an airport other than your home city or conference city airports, i.e. multi-segment or triangle trips.

All deviations must be reviewed and approved by the Simons Foundation and, if the cost is more than what would normally be paid, a reimbursement quote must be obtained through the foundation’s travel agency before proceeding to booking and paying for travel out of pocket. All reimbursements for travel booked directly will be paid after the conclusion of the meeting.

Changes After Ticketing

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 Hotel AKA NoMad 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, arriving on Wednesday, January 21 and departing on Saturday, January 24.

Any additional nights are at the attendee’s own expense. To arrange accommodations, please register at the link included in your invitation.

Hotel AKA NoMad
131 Madison Ave
New York, NY 10016
(between 30th and 31st Streets)
https://www.stayaka.com/

For driving directions to the Hotel AKA NoMad please click here.

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 because of meetings not directly related to the Simons Foundation-hosted meeting (a satellite meeting or 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 the $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.

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

Meghan Fazzi
Senior Manager, Events & Administration, MPS
[email protected]

Travel & Hotel Support

FCM Travel Meetings & Events
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