2025, Semester 2

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David T. GAY (Chair) and Delphine MOUSSARD (Local Project Leader)

TRISECTIONS AND THEIR GENERALIZATIONS

LES TRISECTIONS ET LEURS GÉNÉRALISATIONS

July to December, 2025

Chair > Prof. David T. GAY
University of Georgia

David T. GAY has been a professor at the University of Georgia since 2011. He has thought about topology and taught mathematics at many levels around the world, with postdoctoral positions at the University of Arizona, the Nankai Institute of Mathematics, and the University of Quebec, a Senior Lectureship at the University of Cape Town, and, most recently, a visiting position as Hirzebruch Research Chair at the Max Planck Institute of Mathematics in Bonn in 2019–20.

Local Project Leader > Delphine MOUSSARD
Institut de Mathématiques de Marseille
Aix-Marseille Université

Delphine MOUSSARD is a maîtresse de conférences (assistant professor) at the I2M, Aix-Marseille University.
Her research domain is low-dimensional topology, more specifically:
– finite type invariants and quantum invariants of rational homology 3-spheres and their knots,
– ribbon and slice knots in all dimensions,
– trisections of 4-dimensional manifolds and higher-dimensional generalizations.

 
SCIENTIFIC PROGRAM
The notion of trisection for a smooth 4-manifold, introduced by David Gay and Robion Kirby, is an analogue of a Heegaard splitting in dimension 3, a key notion in the study of 3-manifolds. The theory of trisections provides a new tool to study smooth 4-manifolds, where we are very much in need of new approaches that could eventually lead to progress on some of the most important open problems in topology, such as the smooth 4-dimensional Poincaré conjecture and the smooth 4-dimensional Schoenflies problem.
Since the 2016 publication of Gay and Kirby’s original paper on trisections, fundamental questions have been answered and extensive generalizations have been developed, broadening the reach of the field to include contact and symplectic topology, higher dimensional manifolds, piecewise linear topology, and other geometric structures on manifolds.

This Jean Morlet chair will focus on four specific areas in which there is exciting work to be done on trisections and their generalizations: (1) the relationship between trisections and contact and symplectic topology, (2) using trisections to produce new 4-dimensional invariants, appropriating tools from Floer theory and algebraic geometry, (3) generalizations of trisections to higher dimensions, building on recent work on higher dimensional multisections and (4) understanding trisections and their generalizations from the non-smooth piecewise linear perspective.
In addition to these topics, other areas of significant interest are the potential to use trisections to study diffeomorphisms of 4-manifolds, studying Goeritz groups of trisected 4-manifolds, and setting up a careful theory of parameterized families of trisections, parameterized by arbitrarily many dimensions, to address naturality issues in invariant constructions.
WORKSHOP 1

Multisectors
Multisecteurs
7-11 July, 2025

RESEARCH IN RESIDENCE 1

Multisections of symplectic manifolds
Multisections des variétés symplectiques
22-26 September, 2025

RESEARCH SCHooL

Trisections and related topics
Trisections et interactions
6-10 October, 2025

CONFERENCE

Trisections and related topics
Trisections et interactions
13-17  October, 2025

WORKSHOP 2

Symplectic structures and trisections
Structures symplectiques et trisections
17-21 November, 2025

RESEARCH IN RESIDENCE 2

Multisections of non smooth PL–manifolds
Multisections des variétés PL non lissables
15-19 December, 2025

PROGRAM OF INVITATIONS

Guests in residence during the semester
Invités du semestre

SPONSORS
Bandeau Chaire JM