Geometric moduli spaces - rigidity, genericity, stability | ICMS - International Centre for Mathematical Sciences

Scientific organiers

Izar Alonso Lorenzo, Rutgers University
Bernhard Hanke , University of Augsburg
Christos Mantoulidis , Rice University
Markus Upmeier, University of Aberdeen

About:

The workshop’s goal is to explore connections across mathematical communities that study different geometric moduli spaces. Our workshop will bring together researchers from positive scalar curvature geometry, minimal surface theory, harmonic mapping theory, and special geometries. The study of moduli spaces naturally draws on a confluence of ideas from neighbouring fields, and in each of these areas there is a tradition of exploiting rigidity, genericity, and stability phenomena.

Despite many parallel developments, there has been surprisingly limited interaction and cross-collaboration across these communities. This workshop aims to foster new connections and to elucidate future research directions.

Resources

Programme:

	MONDAY 19 MAY 2025
09.00 - 09.50	Registration and refreshments
09.50 - 10.00	Welcome and housekeeping
10.00 - 11.30	John Pardon, Stony Brook University	Derived moduli spaces of pseudo-holomorphic curves	Abstract
11.30 - 12.00	Refreshments
12.00 - 13.00	Kai Cieliebak, University of Augsburg	Moduli spaces of holomorphic curves	Abstract
13.00 - 14.30	Lunch
14.30 - 15.30	Dominic Joyce, University of Oxford	Bordism categories and orientations of moduli spaces	Abstract
15.30 - 16.00	Refreshments
16.00 - 17.00	Martinus Kool, University of Utrecht	Virtual structure on Hilbert schemes of affine 4-space	Abstract
17.00 – 17.15	Refreshments
17.15 – 18.15	Sebastian Goette, University of Freiburg	A Cobordism approach to calibrated submanifolds	Abstract
18.15 – 19.00	Welcome reception, hosted at ICMS
	TUESDAY 20 MAY 2025
09.15 - 10.45	Simon Brendle, Columbia University	Systolic inequalities and the Horowitz-Myers conjecture	Abstract
10.45 - 11.15	Refreshments
11.15 - 12.15	Christian Bär, Universität Potsdam	Dirac eigenvalues, the hyperspherical radius and applications	Abstract
12.15 - 13.45	Lunch
13.45 - 14.45	Thomas Schick, Universität Göttingen	Rigidity of positive scalar curvature under low regularity	Abstract
14.45 - 15.15	Refreshments
15.15 - 16.15	Rudolf Zeidler, University of Potsdam	Positive scalar curvature with point singularities	Abstract
16.15 - 16.30	Refreshments
16.30 - 17.30	Sven Hirsch, Columbia University	Rigidity in General Relativity	Abstract
	WEDNESDAY 21 MAY 2025
09.15 - 10.45	Chikako Mese, Johns Hopkins University	Harmonic map and rigidity	Abstract
10.45 - 11.15	Refreshments
11.15 - 12.15	Felix Schulze, University of Warwick	Generic regularity of area minimising hypersurfaces up to dimension 11	Abstract
12.15	Group photograph then lunch and free afternoon
	THURSDAY 22 MAY 2025
09.15 - 10.15	Jonathan Bowden, University of Regensburg	The geometry of surface automorphism groups	Abstract
10.15 - 11.15	Refreshments and poster session
11.15 - 12.15	Ruxandra Moraru, University of Waterloo	New examples of compact holomorphic symplectic manifolds	Abstract
12.15 - 13.45	Lunch
13.45 - 14.45	Uwe Semmelmann, University of Stuttgart	Quaternionic Kähler manifolds of non-negative curvature	Abstract
14.45 - 15.15	Refreshments
15.15 - 16.15	Marie-Amelie Lawn, Imperial College	Generalized spin structures on homogeneous and cohomogeneity one spaces
16.15 - 16.30	Refreshments
16.30 - 17.30	Aleksander Doan, University College London	On the fixed domain Gromov–Witten invariants of positive symplectic manifolds	Abstract
19.00	Workshop dinner, hosted at Apex Grassmarket Hotel
	FRIDAY 23 MAY 2025
09.15 - 10.15	Marina Logares, Universidad Complutense de Madrid	Poisson geometry of wild parabolic Higgs bundles	Abstract
10.15 - 11.15	Refreshments and poster session
11.15 - 12.15	Jason Lotay, University of Oxford	The heterotic SU(3) moduli space	Abstract
12.15	Lunch and end of workshop

Sponsors and Funders:

Organised in partnership with the Clay Mathematics Institute