Geometry 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.

Solve shape-analysis problems in R using measurements, landmarks and outlines. The programme develops data organisation and image processing before geometric transformations, alternative superimposition methods and Procrustes analysis. Participants visualise shape differences, test allometry and multivariate hypotheses, and compare principal-component, discriminant and regression approaches. Outline analysis introduces several Fourier representations and their statistical interpretation; participants can bring their own morphological datasets. Live sessions: 10, 11, 14, 15, 16, 17 and 18 December, 12:00–17:00, Europe/Madrid (CET, UTC+01:00). Total 40 hours: 35 live plus five independent. English-language live online course; Fee €495 until 31 October, then €565; Ambassador rates €396/€452. VAT included. Capacity: 16. Basic R, multivariate statistics and geometric morphometrics are recommended; this is not an introductory morphometrics course. Registration requires acceptance; payment follows confirmation. Recordings are provided, but live attendance is required for a certificate.

NeurReps, Symmetry and Geometry in Neural Representations, is a NeurIPS workshop that brings together mathematicians, machine learning researchers and neuroscientists working to uncover the geometric principles shared by brains and machines. In neuroscience, mounting evidence suggests that neural circuits encode task and environmental structure through low-dimensional manifolds, conserved symmetries and structured transformations; in deep learning, sparsity, equivariance and compositionality are guiding the development of more generalisable and interpretable models. Following editions from 2022 to 2025, NeurReps 2026 expands into geometric representation steering and geometric mechanistic interpretability and introduces a Findings track to foster collaboration between experimentalists and theorists, alongside an archival proceedings track published in a dedicated PMLR volume. The programme combines invited talks, contributed papers and a panel session on topology, geometry and neuroscience towards a unified framework. The workshop runs from 8:00 to 17:00 AEDT on Friday 11 December 2026 in Hall 4 of the International Convention Centre (ICC) Sydney. It is organised by Francisco Acosta, David Klindt, Louisa Cornelis, Alison Pouplin, Nina Miolane and Fatih Dinc.

Quantify biological shape variation and its covariation with the physical environment through geometric morphometrics. This introductory workshop develops landmark and semilandmark configurations, data acquisition and digitisation, Generalized Procrustes Analysis and shape space. Participants compare alternative alignment methods, visualise thin-plate-spline deformations in two and three dimensions, and use principal components, multivariate regression and allometry to interpret variation. Practical work uses TPS software and MorphoJ, with emphasis on interpreting biological questions through geometric and statistical methods. 14, 15, 18, 19 and 20 January 2027, each 14:00–19:00, Europe/Madrid (CET, UTC+1); 25 live hours. English; intended for graduates and researchers in biological sciences and related disciplines. No previous morphometrics experience required; familiarity with multivariate statistics recommended. Eighteen places. EUR 476 through 31 October 2026, then EUR 580; Ambassador Institution fees EUR 380.80 and EUR 464, respectively. Live attendance is required for the certificate. Payment follows acceptance; advertised fees include VAT.

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.

Explore path-integration techniques linking quantum mechanics, quantum field theory and gravity. Five themes connect worldline methods, strong external backgrounds, heat-kernel expansions and resurgence, on-shell quantities, and geometry in first quantisation. Discussion includes curved spaces, superspace and nontrivial topology, as well as representations of wavefunctions, scattering amplitudes and gravitational waveforms. Review lectures introduce challenges in each area, followed by invited and contributed talks, two poster sessions and extended collaborative discussions across research communities. 22 March 2027 at 17:00 through 2 April at 13:30, Europe/Paris. The local timezone changes from CET to CEST on 28 March. Expressions of interest close on 15 December 2026 and participation is confirmed by the end of the year. An Indico account is required. Capacity is 70. Estimated fees, including accommodation and meals, are EUR 1,330 for established or senior scientists and EUR 940 for early-career researchers, payable on arrival; limited travel support is being sought.

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.