Duality is an important concept in the study of stochastic interacting particle systems. For arbitrary initial measures duality expresses expectations of a family of functions at time $t$ in terms of the transition probability of a dual process which may be simpler to analyse. Focussing on countable state space we discuss duality from the perspective of the generator. Unlike the more traditional approach of looking at duality in a pathwise manner this allows us to understand straightforwardly how dualities arise from symmetries, or more generally, from invariant subspaces of the generator and leads to constructive methods for finding useful dualities. Also the new concept of reverse duality comes out naturally. It yields the full probability measure of the process at time t for a family of initial measures in terms of transition probabilities of the dual process and thus allows for the computation of arbitrary expectation values.
@ Room P3.10, Mathematics Building, Instituto Superior Técnico
A new seminar series starts with three introductory short courses: Introduction to Machine Learning for mathematicians (João Costa, CAMGSD), Universal approximation theorems and reproducing kernel Hilbert spaces (Luís Carvalho, CAMGSD) and Infinitely wide Neural Networks (Gonçalo Oliveira, CAMGSD).
Mathematics doctoral defense 2025-02-27
Francisco Cristóvão Agostinho, supervised by Hugo Ricardo Nabais Tavares (adviser), Simão Fernandes Correia (co-adviser), defended his thesis Classification and Stability Results of Ground State Solutions on Metric Graphs, at Anfiteatro Pa3, Pavilhão de Matemática, Instituto Superior Técnico, and was awarded a doctoral degree in Mathematics.
This conference aims to be a forum for sharing ideas and recent results in this area of mathematics. Previous editions of this conference series have taken place in Brazil, Spain, Italy, Portugal, and Sweden.
Organizers: Ivan Kaygorodov (University of Beira Interior), Lina Oliveira (CAMGSD, IST, University of Lisbon), Pedro Lopes (CAMGSD, IST, University of Lisbon)
Mathematics doctoral defense 2025-01-15
Arber Selimi, supervised by Roger Francis Picken (adviser), defended his thesis Categorical Aspects of 3-Bundles and Local 3-Connections, at Anfiteatro Pa3, Pavilhão de Matemática, Instituto Superior Técnico, and was awarded a doctoral degree in Mathematics.
This meeting celebrates Rui Loja Fernandes’ 60th birthday and his important contributions to these areas. The conference will feature both distinguished speakers and promising young researchers.
