Topology workshops

Explore recent results in symplectic, Hamiltonian and contact dynamics, emphasizing the use of holomorphic curves and spectral invariants. The workshop connects these techniques with symplectic geometry and considers how they may extend to more general dynamical systems. 2–6 November 2026, Eastern Standard Time (America/New_York). The scientific programme starts Monday at 09:00, with registration from 08:30, and ends Friday at 12:30. Monday–Thursday sessions extend to 17:00. In-person tickets cost USD 25 and seating is limited; registration is required except for IAS faculty, members and speakers.

Topological data analysis captures connectivity, loops and multiscale organization that can be obscured by assuming data occupy ordinary Euclidean space. The workshop connects this mathematical viewpoint with the need for interpretable, robust learning systems. Mathematicians, computer scientists and researchers in chemistry, biology and materials science will examine theory, computational methods and scientific applications. Discussions link mathematical frameworks, efficient algorithms and practical datasets, with the goal of developing reliable, scalable methods and connecting early-career researchers across these communities.

Mathematicians and physicists will investigate how topological structures constrain quantum fields and quantum gravity. Properties unchanged by local deformation can impose strong restrictions on microscopic physical theories. The programme brings together expertise in topology and quantum theory to study broader classes of these structures and their implications for physics at very short distance scales.

Researchers investigate three- and four-dimensional manifolds and their connections to algebraic topology, differential geometry, group theory and theoretical physics. The programme considers major recent results alongside unresolved questions, including smooth four-dimensional topology, surgery, L-spaces and the effectiveness of geometrisation. It brings international experts together with Indian researchers and doctoral students. Participants should already know basic algebraic topology, differential geometry and low-dimensional topology. The programme is organized in partnership with the Clay Mathematics Institute, and ICTS provides accommodation for outstation participants.

This research workshop examines topological descriptors for complex data, including multiparameter and generalized persistence, algorithms, connections with non-Euclidean geometry and knot-theoretic applications. Introductory lectures lead into focused group research, problem sessions and discussion to exchange methods across topology, geometry and computer science. Six group leaders coordinate collaborative projects. The event is organized in partnership with the Clay Mathematics Institute.