Venue Practical Info Participants Topics Program Notes Organizers

Singular algebraic curves and quantitative symplectic embeddings

September 22nd - 26th, 2025 · Villa Boninchi · Geneva, Switzerland

Overview

This workshop aims to bridge connections between two specific areas of mathematics: (i) singular algebraic curve theory, and (ii) the study of quantitative symplectic embeddings. Although relations between these areas have been observed going back to Gromov’s foundational pseudoholomorphic curves paper, the relevant groups of researchers are still largely isolated from one another, partly due to a lack of widespread familiarity with each other’s terminology, literature, and motivating questions. Thanks to many important developments in the last two decades, and especially in the last few years, this is an opportune time to bring researchers from these areas together, in order to discuss how recent techniques might shed light on major questions in both fields. We expect that a small amount of overhead in conveying background results and terminology could open up significant new opportunities for interdisciplinary collaborations, with the potential for fruitful flow of information in multiple directions.

Venue

G·(IST) - Institut de Sciences Théoriques de Genève

Villa du Nant d’Aisy (“Villa Boninchi”)
Chemin du Nant-d’Aisy 11
1246 Corsier (Genève), Switzerland

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Practical Information

Participants

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  • Thomas Blomme (Université de Genève)
  • Joé Brendel (ETH Zürich)
  • Aloïs Demory (Université de Genève)
  • Ilia Itenberg (IMJ-PRG, Sorbonne Université)
  • Gurvan Mével (Université de Genève)
  • Stepan Orevkov (Université Toulouse III – Paul Sabatier)
  • Felix Schlenk (Université de Neuchâtel)
  • Antoine Toussaint (Université de Genève)
  • Georgios Rizell (Uppsala University)
  • Rick Miranda (Colorado State University)
  • Leonid Polterovich (Tel Aviv University)
  • Halszka Tutaj-Gasińska (Jagiellonian University)
  • Ciro Ciliberto (University of Rome "Tor Vergata")
  • Dusa McDuff (Barnard College, Columbia University)
  • Dan Cristofaro-Gardiner (University of Maryland)
  • Jonny Evans (Lancaster University)
  • Richard Hind (University of Notre Dame)
  • Viatcheslav Kharlamov (Université de Strasbourg / IRMA)
  • Grigory Mikhalkin (Université de Genève)
  • Joaquim Roé (Universitat Autònoma de Barcelona)
  • Kyler Siegel (University of Southern California)

Topics

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Note: this list is highly tentative and by no means exhaustive!

  • Nagata's conjecture and its many generalizations and variations
  • existence and classification problems for singular (algebraic, symplectic, topological) curves with prescribed singularities
  • the role of tropical geometry in constructing and obstructing singular algebraic curves
  • positivity phenomena in enumerative geometry
  • the bounded negativity conjecture
  • obstructions for singular algebraic and symplectic curves beyond adjunction
  • infinite staircase functions in symplectic and algebraic geometry
  • symplectic and Kähler ball packings and packing stability
  • almost toric fibrations, $\mathbb{Q}$-Gorenstein deformations, and Newton–Okounkov bodies in dimensions four and higher
  • the classification of unicuspidal and sesquicuspidal curves in smooth projective surfaces
  • generalized ellipsoid embeddings, Markov triples, and singular algebraic curves
  • connections between ellipsoid embeddings, singular algebraic curves, symplectic field theory in higher dimensions
  • singular algebraic curves from the perspectives of mirror symmetry and cluster algebras
  • construction of real algebraic plane curves with prescribed cusp singularities and the minimal degree problem

Program

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Note: this program is still tentative and will be partly decided by the participants during the week.

  • Monday (September 22nd, 2025)
    • Informal congregation at Villa Boninchi: 10:00–11:15
    • Talk by Joaquim Roé: 11:15–12:15
    • Lunch: 12:15–14:00
    • Talk by Felix Schlenk: 14:00–15:00
    • Talk by Rick Miranda: 15:30–16:30
    • Discussion and planning: 16:30–17:30
  • Tuesday (September 23rd, 2025)
    • Talk by Jonny Evans: 10:00–11:00
    • Talk by Halszka Tutaj-Gasińska: 11:15–12:15
    • Lunch: 12:15–14:00
    • Talk by Dan Cristofaro-Gardiner: 14:00–15:00
    • Group discussion: 15:30–17:00
  • Wednesday (September 24th, 2025)
    • Talk by Stepan Orevkov: 10:00–11:00
    • Talk by Leonid Polterovich: 11:15–12:15
    • Lunch: 12:15–14:00
    • Group discussion: 14:00-15:30
    • Talk by Georgios Dimitroglou Rizell: 16:00-17:00
    • Dinner at 19:30 at Maison L'Orelic, Avenue Industrielle 11, Carouge
  • Thursday (September 25th, 2025)
    • Talk by Ciro Ciliberto: 10:00-11:00
    • Group discussion: 11:15-12:00
    • Talk by Richard Hind: 12:00-13:00
    • Lunch: 13:00-14:00
    • Maxim Kontsevich talk at UNIGE: 16:15–17:15
  • Friday (September 26th, 2025)
    • Talk by Ilia Itenberg: 10:00-11:00
    • Group discussion: 11:15-12:45
    • Lunch: 12:45-14:00
    • Talk by Joé Brendel: 14:00-15:00
    • Free discussion: 15:00-17:30

Notes

Organizers

Grigory Mikhalkin (Université de Genève): grigory.mikhalkin@unige.ch
Joaquim Roé (Universitat Autònoma de Barcelona): joaquim.roe@uab.cat
Kyler Siegel (University of Southern California): kyler.siegel@usc.edu