# Yamabe Memorial Symposium

## 2024 Yamabe Memorial Symposium: October 4 - 6, 2024

The School of Mathematics will host the eleventh Yamabe Memorial Symposium from October 4th to Sunday, October 6th, 2024, on the University of Minnesota–Twin Cities campus. This year's program will focus on the topic of *Symplectic and Contact Geometry*. Speaker abstracts and the event schedule will be posted when details become available.

### Speakers

- Mohammed Abouzaid (Stanford University)
- Daniel Cristofaro-Gardiner (University of Maryland, College Park)
- John Etnyre (Georgia Institute of Technology)
- Ko Honda (University of California, Los Angeles)
- Yael Karshon (Tel-Aviv University and University of Toronto)
- John Pardon (Simons Center for Geometry and Physics)
- Margaret Symington (Mercer University)
- Chris Woodward (Rutgers University, New Brunswick)

### Organizers

- Scot Adams
- Anar Akhmedov
- Erkao Bao
- Michelle Chu
- Ionut Ciocan-Fontanine
- David Favero
- Tian-Jun Li
- Alexander Voronov

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Schedule

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Friday, October 4th

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Friday, October 4th

2:00 pm - 3:15 pm – Registration

3:20 pm - 3:30 pm – Welcome

3:30 pm - 4:30 pm – Ko Honda (University of California, Los Angeles)

4:30 pm - 4:45 pm – Break

4:45 pm - 5:45 pm – Chris Woodward (Rutgers University, New Brunswick)

6:30 pm – Speaker & Organizer dinner

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Saturday, October 5th

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Saturday, October 5th

8:00 am - 9:00 am – Breakfast

9:00 am - 10:00 am – Mohammed Abouzaid (Stanford University)

10:00 am - 10:30 am – Group photo and break

10:30 am - 11:30 am – John Etnyre (Georgia Institute of Technology)

11:30 am - 1:30 pm – Lunch break

1:30 pm - 2:30 pm – Margaret Symington (Mercer University)

2:30 pm - 3:00 pm – Break

3:00 pm - 4:00 pm – Daniel Cristofaro-Gardiner (University of Maryland, College Park)

4:00 pm - 6:00 pm – Soccer

6:00 pm - 9:00 pm – Banquet at the Campus Club, Coffman Memorial Union

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Sunday, October 6th

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Sunday, October 6th

8:00 am - 9:00 am – Breakfast

9:00 am - 10:00 am – Yael Karshon (Tel-Aviv University and University of Toronto)

10:00 am - 10:30 am – Break

10:30 am - 11:30 am – John Pardon (Simons Center for Geometry and Physics)

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Talk details

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Ko Honda

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Ko Honda

**Title**: A Morse *A*_{∞}-model for the higher-dimensional Heegaard Floer homology of cotangent fibers**Abstract**: Given a smooth closed *n*-manifold *M* and a *κ*-tuple of basepoints q ⊂ *M*, we define a Morse-type *A*_{∞}-algebra called the based multiloop *A*_{∞}-algebra and show the equivalence with the higher-dimensional Heegaard Floer *A*_{∞}-algebra of *κ* disjoint cotangent fibers of *T∗M.*

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Christopher Woodward

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Christopher Woodward

**Title**: Disk counting for tropical Lagrangians**Abstract**: This is a continuation of work with Sushmita Venugopalan (Chennai). I will describe how to compute the potentials of the Lagrangian tori in del Pezzo surfaces (first computed by Pascaleff-Tonkonog), the potentials of tropical Lagrangians such as Manin collections of Lagrangian spheres, and the corresponding open-closed maps. The results work best for almost toric four-manifolds, but also work in some higher dimensional situations such as representation varieties

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Mohammed Abouzaid

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Mohammed Abouzaid

**Title**: Floer homotopy as a bordism theory**Abstract**: Floer envisioned that Morse theory should have an extension, beyond ordinary homology, to generalised homology theories such as stable homotopy or K-theory. Cohen, Jones, and Segal constructed a framework for defining such an extension, using as their main building block a formulation of the Pontryagin-Thom construction for manifolds with corners. I will describe an alternative approach which does not rely on such a construction, and which has the advantage both of giving a direct definition of generalised Floer homology groups, as well as providing a model for the category of spectra, in terms of objects that are completely natural in Floer theory.

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John Etnyre

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John Etnyre

**Title**: Symplectic rational homology ball fillings of Seifert fibered spaces**Abstract**: Determining when a rational homology ball bounds a rational homology ball has a long history in topology and symplectic geometry. Answering such questions allows one to prove that the important 4-manifold construction of rational blowdown can be done in the symplectic category. In this talk, I will discuss what is known about symplectic rational homology ball fillings of small Seifert fibered spaces and give a complete classification of which contact structures on a small Seifert fibered space admit a symplectic rational homology ball filling when the e0e0 invariant is less than -3. We will also show that the only spherical manifolds that bound rational homology balls are a small class of lens spaces and give evidence towards the Gompf conjecture that no Brieskorn homology sphere bounds a symplectic homology ball. This is joint work with Ozbagi and Tosun.

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Margaret Symington

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Margaret Symington

**Title**: Beyond reflexivity, symplectically**Abstract**: Reflexive polytopes play an important role in mirror symmetry, as they define toric varieties within which mirror families of Calabi-Yau manifolds limit onto a union of toric varieties. A challenging problem in mirror symmetry is to construct dual Lagrangian fibrations on mirror Calabi-Yau manifolds. In this setting, three-dimensional polytopes yield Lagrangian-fibered K3 surfaces. Forgetting complex structures, one can construct Lagrangian-fibered symplectic K3 surfaces directly from the boundary of a reflexive polytope by recognizing the integral affine structures with nodes that are supported by the polytope. In this talk, I will explain a natural condition on a three-dimensional polytope for its boundary to support an integral affine structure with nodes and examine the implications of that condition if the polytope is Delzant. (Joint work with Liat Kessler.)

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Daniel Cristofaro-Gardiner

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Daniel Cristofaro-Gardiner

**Title**: Two or infinity**Abstract**: We explain some of the main ideas behind a recent joint work, proving that every Reeb flow on a closed connected three-manifold has either two or infinitely many simple periodic orbits, as long as the associated contact structure has torsion Chern class. This resolves longstanding conjectures of Hofer-Wysocki-Zehnder (about Reeb flows on the three-sphere, giving the standard contact structure) and Alvarez-Paiva, Burns, Matveev and Long (about geodesic flows on Finsler surfaces).

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Yael Karshon

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Yael Karshon

**Title**: Symplectic excision**Abstract**: Removing a properly embedded ray from a (noncompact) manifold does not affect the topology nor the diffeotype. What about the symplectic analogue of this fact? And can we go beyond rays? We use incomplete Hamiltonian flows to excise interesting subsets of positive codimension: the product of a ray with a Cantor set, a “box with a tail”, and - more generally - epigraphs of lower semicontinuous functions. This is joint work with Xiudi Tang, motivated by a question of Alan Weinstein.

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John Pardon

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John Pardon

**Title**: Universally counting curves in Calabi–Yau threefolds**Abstract**: Enumerating curves in algebraic varieties traditionally involves choosing a compactification of the space of smooth embedded curves in the variety. There are many such compactifications, hence many different enumerative invariants. I will propose a “universal” (very tautological) enumerative invariant which takes values in a certain “Grothendieck group of 1-cycles”. It is often the case with such “universal” constructions that the resulting Grothendieck group is essentially uncomputable. But in this case, the cluster formalism of Ionel and Parker shows that, in the case of threefolds with nef anticanonical bundle, this Grothendieck group is freely generated by local curves. This reduces the MNOP conjecture (in the case of nef anticanonical bundle and primary insertions) to the case of local curves, where it is already known due to work of Bryan–Pandharipande and Okounkov–Pandharipande.

### Location

The 11th Yamabe Memorial Symposium: *Symplectic and Contact Geometry* will take place in Vincent Hall at the University of Minnesota in Minneapolis, MN.

*The Yamambe Memorial Symposium is funded by the Yamabe Memorial Symposium Fund and the National Science Foundation DMS-2415356.*

### Child care

Care.com connects visiting families with experienced local caregivers.

## History

Professor Hidehiko Yamabe (1924-1960) came to Minnesota from IAS as an assistant professor in 1956. During his four years here he worked on a number of diverse topics in geometry and analysis: he initiated the problem of whether, given a Riemannian metric on a smooth compact manifold of dimension > 2, there exists a conformally equivalent metric of constant scalar curvature; he made contributions to Hilbert's 5th problem and various diffusion problems. Yamabe died in 1960, at age 37, of a massive stroke, said to have been brought on by war injuries as a civilian. This tragedy happened soon after he was appointed a full professor at Northwestern University. Yamabe's widow and two young daughters were left virtually penniless as Yamabe no longer had a pension from Minnesota and hadn't yet gained one from Northwestern. Faculty of both Northwestern and Minnesota raised a small amount of money to help the family, who then moved back to Japan.

The Yamabe Memorial Lecture was initiated jointly with Northwestern around 1962. It featured a lecture by a prominent mathematician each year, alternating between Northwestern (odd-numbered years) and Minnesota (even-numbered years). Initially supported by a small subsidy from Yamabe’s widow, this donation was later augmented by significant faculty contributions in Minnesota, resulting in the present endowment known as the Yamabe Fund. The distinguished speakers brought in year after year established the Lectures as a significant event in the mathematical calendar, particularly in the Midwest.

Notable speakers before 2002 include Neil Trudinger, Eugenio Calabi, Rick Schoen, Shizuo Kakutani, Craig Evans, Walter Rudin, Robert Hardt, Katsumi Nomizu, Fred Gehring, Richard Hamilton, Peter Sarnak, Jeff Cheeger, Shing-Tung Yau, Terence Tao, Igor Rodnianski, Luis Caffarelli, Tai-Ping Liu, Sergiu Klainerman, and Simon Brendle. In 2002, the Yamabe Memorial Lecture evolved into the Yamabe Memorial Symposium, a biannual conference featuring eight speakers over 2.5 days, supported by the Yamabe Fund and the NSF, enhancing participation and expanding its impact. Detailed information about past Yamabe Memorial Symposia can be found as follows:

## Hidehiko & Etsuko Yamabe

## Hidehiko, Etsuko & Kimiko Yamabe