2026 Yamabe Memorial Symposium

Low-Dimensional Topology and Gauge Theory

Friday, October 2nd to Sunday, October 4th, 2026, Vincent Hall, University of Minnesota, Minneapolis, MN.

The 12th Yamabe Memorial Symposium features eight speakers over 2.5 days. See the official symposium page for registration, travel information, and applications for financial support (graduate students and postdoctoral scholars; applications are reviewed on a rolling basis, and early applications are encouraged).

Organizers: Anar Akhmedov, Erkao Bao, Michelle Chu, David Favero, Tian-Jun Li, and Alexander Voronov.

View the symposium poster

Speakers

Schedule

All talks are in Vincent Hall.

Friday, October 2

Saturday, October 3

Sunday, October 4

Titles and Abstracts

Paul Feehan

Title: Towards a Bogomolov-Miyaoka-Yau inequality for symplectic 4-manifolds

Abstract: The Bogomolov-Miyaoka-Yau inequality for minimal compact complex surfaces of general type was proved in 1977 independently by Miyaoka, using methods of algebraic geometry, and by Yau, as an outgrowth of his proof of the Calabi conjectures. In this talk, we describe progress in our ongoing program to prove the conjecture that symplectic 4-manifolds obey the Bogomolov-Miyaoka-Yau inequality. Our program uses Morse theory on the gauge theoretic moduli space of non-Abelian monopoles, where the Morse function is a Hamiltonian for a natural circle action and natural two-form. We shall describe generalizations of Donaldson’s symplectic subspace criterion (1996) from finite to infinite dimensions and generalizations of Taubes’ perturbation analysis from the Seiberg-Witten to non-Abelian monopole equations. These methods have application to the problem of showing that the fundamental two-form is non-degenerate and thus an almost symplectic form on the moduli space of non-Abelian monopoles. This talk is based on joint work with Tom Leness and the monographs arXiv:2010.15789 (to appear in AMS Mathematical Surveys and Monographs), arXiv:2206.14710 and arXiv:2410.13809.

Jennifer Hom

Title: Distinguishing exotic $\mathbb{R}^4$’s with Heegaard Floer homology

Abstract: Attaching a Casson handle to a slice disk complement yields a smooth 4-manifold that is homeomorphic to $\mathbb{R}^4$. We show that if two slice knots have sufficiently different knot Floer homology, then the resulting exotic $\mathbb{R}^4$’s made using the simplest positive Casson handle are not diffeomorphic, giving us a countably infinite family of pairwise nondiffeomorphic exotic $\mathbb{R}^4$’s. Our main tool is Gadgil’s end Floer homology. This is joint work with Sean Eli and Tye Lidman.

Michael Hutchings

Title: From gauge theory to three-dimensional Reeb dynamics

Abstract: We describe some recent results about the existence and properties of periodic orbits of Reeb vector fields on three-manifolds. A key ingredient in the proofs is a “Weyl law” for spectral invariants in embedded contact homology (ECH). The Weyl law arises from Taubes’s isomorphism between ECH and monopole Floer homology.

Hokuto Konno

Title: Constraints on 6-dimensional Lefschetz fibrations from families Bauer-Furuta invariants

Abstract: We give a constraint on smooth 6-dimensional Lefschetz fibrations (i.e., Lefschetz fibrations with 4-dimensional fibers) using families Bauer-Furuta invariants. This constraint can be used to rule out certain relations in the mapping class groups of smooth 4-manifolds that arise as regular fibers. As an application, we give a negative answer to a question of Donaldson concerning the symplectic Torelli group. This is joint work with Jianfeng Lin, Anubhav Mukherjee, and Juan Muñoz-Echániz.

Francesco Lin

Title: Dirac spectral flow and Floer theory of hyperbolic three-manifolds

Abstract: An outstanding problem in three-dimensional topology is to understand the interplay between hyperbolic geometry and Floer theory, if any. In this talk I will discuss how one can completely describe the monopole Floer theory of certain torsion $\mathrm{spin}^c$ three-manifolds with $b_1=1$ in terms of data arising in hyperbolic geometry; even though these manifolds do not admit irreducible solutions to the Seiberg-Witten equations, they have non-trivial Floer homology arising from Dirac spectral flow. This is joint work with M. Lipnowski.

András Stipsicz

Title: Smooth involutions on four-manifolds

Abstract: By constructing free smooth involutions on exotic four-manifolds we show the existence of exotica on a wide variety of topological four-manifolds with nontrivial fundamental groups, including smooth ‘fake projective planes’. Involutions with non-empty fixed point sets will be also discussed. This is joint work with İnanç Baykur and Zoltán Szabó.

Zoltán Szabó

Title: TBD

Clifford Taubes

Title: Gauge theory from the old days and the Vafa-Witten equations

Abstract: The limits of non-convergent sequences of solutions to the Vafa-Witten equations are characterized (in part) by $\mathbb{Z}/2$ harmonic, self-dual 2-forms that vanish on closed sets with Hausdorff dimension at most 2. What does this look like when there are no dimension 2 parts of the vanishing locus? There is an interesting story here with some old-time topology, geometry and analysis.