Pedro Nunes' Lectures 2026

The 2026 Pedro Nunes Lectures will be given by Professor Ulrike Tillmann FRS, in October.

Professor Ulrike Tillmann is a leading figure in algebraic topology, with internationally recognised contributions to topology, geometry, and their connections with mathematical physics. Her research on moduli spaces of Riemann surfaces has played an important role in the development of modern algebraic topology and has revealed deep links with ideas arising in quantum field theory and string theory. In recent years, she has also contributed to the emerging field of topological data analysis, exploring how concepts from pure mathematics can provide new insights into problems motivated by data science.

Professor Tillmann is Professor of Mathematics at the University of Oxford.  She served as President of the London Mathematical Society (2021–2023) and has been elected President of the International Mathematical Union (IMU). Among many distinctions, she was elected a Fellow of the Royal Society in 2008, a Fellow of the American Mathematical Society in 2013, received the Whitehead Prize of the London Mathematical Society, the Bessel Research Award of the Alexander von Humboldt Foundation, and was an invited speaker at the International Congress of Mathematicians (ICM 2002).

Title:  From topology via complex data to representation theory 

Abstract:  Topological data analysis (TDA) has proved an effective tool to study complex data. A most prominent method is persistent homology and its multi-parameter variant. Assuming little more than linear algebra I will introduce these theories and present recent applications.  I will then explain how this led to the introduction and study of a new invariant of quiver representations building on ideas coming from geometric invariant theory.

Among other we hope to exemplify with this talk how ideas from pure mathematics have provided new tools for data analysis and led to interesting applications,  and vice versa, how these applications have driven new theory which may be of interest also from a purely mathematical point of view.

October 27, 2026
14.30, Auditório B2, Edifício 2, Universidade do Minho, Braga (partially supported by CMAT)
 

Title: TQFTs and the renaissance of the algebraic topology of manifolds

Abstract: Topological quantum field theory was introduced as a mathematical theory in the 1980s, motivated by physics. A central underlying concept is cobordism of manifolds, a notion originally introduced by Poincare. We will recall some of the early Fields Medal winning work on the subject and explain how the TQFTs and their study via homotopy led to new calculations in physics but also to a new approach to the algebraic topology of manifolds.

This event is funded by national funds through the FCT - Fundação para a Ciência e a Tecnologia, I.P.,under FCT Multi-Annual Financing Program and the projects UID/04459/2025 (CAMGSD, IST-ID), UID/00208/2025 (GFM, IST-ID) and UID/04621/2025 (CEMAT, IST-ID).