Integrals involving rapidly oscillatory factors abound. Quintessential examples include the Fourier transform, integral operators employed in the analysis of wave phenomena, and exponential sums. The concept of stationary phase is a central element of the theory.
The Fourier transform can be viewed as a linear operator, or a bilinear form. We focus on multilinear operators, which are less canonical than the Fourier transform and are open to structural questions reflecting their diversity.
We begin with certain multilinear inequalities which do not involve cancellation, generalizing convolution. We then bring oscillation into the picture, and finally discuss inequalities for multilinear forms in which the oscillation is implicit in the structure of the inequalities, rather than appearing explicitly in the integrals. The notion of stationary phase is reborn in mutated form.
Along the way we will see connections to web geometry, Hilbert's tenth problem, additive combinatorics, convex geometry, Ramsey theory, computer science, weak continuity, and ergodic theory.
Sala P3.10, Pavilhão de Matemática
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).
Room P3.10, Mathematics Building, Instituto Superior Técnico
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.
Sessions on March 19 and 20, 1:00PM to 2:30PM.
@ Instituto Superior Técnico
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)
The event is supported by FCT UIDB/04459/2025 CAMGSD.
@ Instituto Superior Técnico, Department of Mathematics (room 3.10)
From Statistical Mechanics to Quantum Mechanics, Quantum Field Theory or even Hydrodynamics, Probability has progressively become a fundamental toolbox in Mathematical Physics, unifying methods of research in domains that were regarded as separate for a long time. This series of seminars aims to showcase bridges between such domains, including those too recent to be regarded as associated with Theoretical or Mathematical Physics.
Schedule and Abstracts here.
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.
@ Instituto Superior Técnico
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.
@ Universidade de Aveiro
The Workshop on Operator Theory, Complex Analysis, and Applications 2025 - WOTCA 2025 will be held at University of Aveiro, Portugal, on July 7-11, 2025.
It aims to bring together researchers working in Operator Theory, Complex Analysis, and their applications, in particular Mathematical Physics, and to create an opportunity to highlight the current state of the art in these fields, to present open problems and to promote collaborative discussions.
This workshop follows the line of several previous WOTCA meetings.
The programme will consist of several invited 25+5 minute talks and a very small number of contributed talks. A preliminary list of speakers is available here.
WOTCA 2025 has no registration fee and is open to everybody interested, but the number of participants will be limited, in order to foster dialogue in a friendly atmosphere.
This workshop 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: UIDB/04459/2025, UIDP/04459/2025 (CAMGSD, IST-ID) and UIDB/04674/2020 (CIMA).
@ Universidade de Aveiro
The fifth Young Researchers in Functional Analysis and Mathematical Physics meeting, YRFAMP’25, will take place at University of Aveiro, Portugal, on July 9-11, 2025. The previous YRFAMP meetings were YRFAMP’18, YRFAMP’22, YRFAMP’23 and YRFAMP’24.
It will be held aiming to foster contact between leading mathematicians and younger ones.
YRFAMP’25 welcomes students and young researchers in Functional Analysis, Mathematical Physics and related topics. However the number of talks will be limited. Those interested in participating should send an email to one of the organisers.
The program of YRFAMP’25 will consist of a series of invited 15+5 minute talks and a very small number of contributed talks.
This workshop 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: UIDB/04459/2025, UIDP/04459/2025 (CAMGSD, IST-ID) and UIDB/04674/2020 (CIMA).
@ Universidade do Minho, Guimarães, Portugal
This meeting will bring together the large community interested in nonlinear PDEs, including elliptic, parabolic, dispersive and coagulation-fragmentation equations. Participation is free, but registration via the website is required. More information is available there. Limited funding may be available for young researchers.
There is an opportunity for contributed talks. The deadline to submit an abstract is May 5, 2025. Please check the details.
Organizers
- Jean-Baptiste Casteras (CEMS.UL, Universidade de Lisboa)
- Marina Ferreira (CNRS, Université Toulouse)
- Fernando Miranda (CMAT, Universidade do Minho)
- Lisa Santos (CMAT, Universidade do Minho)
- Hugo Tavares (CAMGSD, IST)
- Dmitry Vorotnikov (CMUC, Unversidade do Minho)
News
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