Symplectic Geometry Workshop

Workshop Overview

This three-day workshop in St Andrews brings together researchers working in symplectic topology, Floer theory, mirror symmetry, and related areas to discuss recent progress and open problems.

Invited Speakers

Hülya Argüz — Oxford University
Giulia Gugiatti — University of Edinburgh
Matt Habermann — Imperial College London
Jeff Hicks — University of St Andrews
Kai Hugtenburg — University of St Andrews
Yankı Lekili — Imperial College London
Yoav Len — University of St Andrews
Cheuk Yu Mak — University of Sheffield
Ana Rita Pires — University of Edinburgh
Nick Sheridan — University of Edinburgh

(* to be confirmed)

Schedule

Tuesday, 28 July 2026

12:00	Lunch

13:00	Giulia Gugiatti University of Edinburgh	Kuznetsov components in mirror symmetry
In this talk I will discuss how the structural features of Kuznetsov components of Fano varieties are reflected in the geometry of their mirror Landau-Ginzburg models. I will focus on Fano varieties arising as cyclic covers of weighted projective spaces branched along Calabi-Yau or Fano hypersurfaces. I will discuss the case of the quartic double solid in detail. The talk is based on work in progress with Ilaria Di Dedda, Danil Kozevnikov, and Nick Sheridan.
14:00	Coffee

14:30	Jeff Hicks University of St Andrews	Rigidity and Realizability in dimension 3
Let $V$ be a tropical curve in a tropical abelian threefold $Q$ admitting a pair-of-pants decomposition. In this talk we will talk about what pseudoholomorphic curves can appear with boundary on $L_V$, its tropical Lagrangian lift. We will show that the boundary classes of these curves are null-homologous in $L_V$ whenever $V$ is a rigid tropical curve.
15:30	Yanki Lekili Imperial College London	Curves on surfaces and moduli of associative algebras
A signed Gauss word determines an immersion of a circle in a surface. We can view such an immersion as an object in a Fukaya category of any partial compactification of the surface. We will explain how to efficiently calculate the corresponding A_infty structures, and use this to construct explicit flat families of finite-dimensional associative algebras. It turns out this construction realizes essentially all associative algebras of rank less than or equal to 4, and all radical square zero algebras (of any rank).
16:30	Reception

Wednesday, 29 July 2026

09:30	Hülya Argüz University of Oxford	b-Complex Manifolds with Generalized Corners and Kato–Nakayama Spaces
Manifolds with generalized corners (g-corners), introduced by Joyce, are spaces that locally look like rational polyhedral cones. We describe the notion of b-complex manifolds with g-corners, and establish an analogue of the (formal) Newlander–Nirenberg theorem ensuring the existence of local complex coordinates on such manifolds. We also show that Kato–Nakayama spaces associated to log smooth complex analytic spaces naturally carry the structure of a $b$-complex manifold with $g$-corners. Conversely, we provide necessary and sufficient conditions characterizing which $b$-complex manifolds with $g$-corners arise as Kato–Nakayama spaces. This establishes a bridge between differential-geometric and algebro-geometric perspectives on spaces with singular boundary behavior. This is joint work with Dominic Joyce.
10:30	Coffee

11:00	Ana Rita Pires University of Edinburgh	Ellipsoid embeddings and infinite staircases

12:00	Lunch

13:00	Matt Habermann Imperial College London	Dubrovin’s conjectures in the Landau—Ginzburg setting
Landau–Ginzburg (LG) models are the natural mirror candidates to Fano manifolds and have an enumerative theory analogous to quantum cohomology, known as FJRW theory. In this talk, I will begin by giving an overview of these ideas, keeping a running comparison to quantum cohomology in order to explain some of the similarities and subtleties. I will then briefly explain the notion of Frobenius manifolds, how they arise in FJRW theory and how Dubrovin’s conjectures for Fano varieties lead to natural analogues in this LG setting. Finally, I would like to discuss work-in-progress in collaboration with Yefeng Shen and Weiqiang He.
14:00	Yoav Len University of St Andrews	The universal Prym variety
The talk will revolve around a distinguished class of abelian varieties known as Prym varieties, which arise from double covers of algebraic curves. Pryms have deep connections with rationality questions of threefolds, Lagrangian fibrations, and spin structures on Riemann surfaces. Despite their importance, constructing a compact moduli space that parametrises Pryms is a notoriously difficult problem. Recent tools from tropical geometry offer a combinatorial approach for handling degenerations of Pryms. I will begin by explaining what Prym varieties are, both in the algebraic and tropical settings. I will then discuss ongoing work with Poiret towards a compact universal moduli space of Prym varieties and joint work with Nabijou and Molcho towards computing the tautological class of Prym varieties.
15:00	Coffee

15:30	Cheuk Yu Mak University of Sheffield	Lagrangian torus fibration on Calabi-Yau hypersurfaces
In joint work with Matessi-Ruddat-Zharkov, we prove the existence of Lagrangian torus fibrations on Calabi-Yau hypersurfaces in toric Fano manifolds given by a reflexive polytope. The result is motivated by the Strominger-Yau-Zaslow conjecture, which predicts the existence of these fibrations on Calabi-Yau manifolds near large complex structure limits. In this talk, I will outline the main setup of the construction. The idea is to replace the ordinary algebraic equation with a new one involving "ironing coefficients" and a convex (but not strictly convex!) potential which has the effect of breaking the manifold into local models. Over these models, we apply the Liouville flow technique in the style of Evans-Mauri.
16:30	Open Discussion

Thursday, 30 July 2026

09:30	Kai Hugtenburg University of St Andrews	Open-closed Deligne-Mumford Field Theories
This talk reports on joint work with Amanda Hirschi, in which we construct an open-closed Deligne-Mumford Field Theory (DMFT) associated to a Lagrangian submanifold of a symplectic manifold. An open-closed DMFT is a field theory associated to Riemann surfaces both with and without boundary. The construction of such a DMFT is the first step in proving that homological mirror symmetry implies enumerative mirror symmetry in all genus.
10:30	Coffee

11:00	Nick Sheridan University of Edinburgh	On fractional Calabi-Yau structures in mirror symmetry

12:00	Lunch

Registration

Please register for the workshop using the official registration form. There is a small registration fee of 40GBP to cover the cost of lunch and coffee during the workshop. Registration fees should be paid through the University of St Andrews online shop.

We have a limited amount of financial support for doctoral students and early career researchers. Please indicate in the registration page if you are requesting support.

Open Registration Form Pay Registration Fee

Practical Information

Venue: Mathematical Institute, University of St Andrews.

Accommodation

We have secured a block of accommodation at David Russell Apartments which is available at a very economical rate. If you are interested in reserving one of these rooms during the conference, please indicate when you register or email the organizers.

Getting to St Andrews

We suggest arriving in St Andrews by taking the train to Leuchars Station, followed by a bus or taxi to the St Andrews Bus Station.

We recommend international participants fly into Edinburgh International Airport. From there, you can take the tram or bus to Edinburgh Gateway station for frequent train connections to Leuchars, or take a direct bus service (via Stagecoach JET 747).

Contacts

Organiser: Kai Hugtenburg (kh315@st-andrews.ac.uk)
Organiser: Jeff Hicks (jeff.hicks@st-andrews.ac.uk)

Sponsorship

This event is supported by LMS Awards 92505 and 92508, EPSRC Project EP/Z53528X/1, and the School of Mathematics and Statistics at University of St Andrews.