This issue of the bulletin pays tribute to Isabel Figueiredo, highlighting her contributions as President of CIM and Professor. It includes scientific papers on various topics such as Diophantine equations and Bayesian analysis. Additionally, there's an article on Francisco de Melo's work in optics, interviews with Richard Davis and Bruno Loff, and summaries of CIM-supported activities. The bulletin welcomes submissions on mathematics and its applications.
Isabel Narra de Figueiredo was a distinguished figure in the field of Applied Analysis, known for her significant contributions to areas like mechanics and medical applications. Over her career, she built a remarkable body of scientific work, earning recognition both nationally and internationally. She demonstrated youthful energy and remained active in research throughout her life. Additionally, she served the academic community, holding positions in scientific societies and leading organizations such as CIM. Her efforts and dynamism earned her high recognition in Portugal and beyond.
The SPA2023 conference was held at the University of Lisbon from July 24 to 28, 2023, under the patronage of the Bernoulli Society. It featured 257 talks across various sessions, with 496 participants from 44 countries. The event received support from several institutions and research centers in the Lisbon area.
Bruno Loff, a Mathematician and Computer Scientist at the University of Lisbon, received one of the prestigious European Research Council grants. He completed his education at Instituto Superior Técnico and University of Amsterdam, focusing on computational complexity. After postdoc positions in Prague and Porto, he secured a tenure track at the University of Porto. Now, with his ERC grant, he's establishing a computational complexity group at Research Center LASIGE, FCUL. He's highly recognized internationally.
The 14th and 15th centuries were relatively quiet in the history of optics. Francisco de Melo's theory of vision is influenced by medieval theories, notably by Ibn-al Haytham and Witelo. Melo, influenced by the Renaissance, retrieved concepts from Greek authors. His work, "Corollary to Euclid’s Perspective," synthesizes various optic currents and emphasizes abstract thinking and mathematical tools. Melo extensively revised unclear demonstrations in his version of Euclid’s Optics, showing remarkable precision. Though not highly original, Melo's work demonstrates significant differences compared to previous works in optics.
The Seventh International Workshop New Trends in Quaternions and Octonions — NTQO 2023 was held from October 27th to 28th, 2023, at the School of Technology and Management (ESTG) of the Polytechnic of Leiria (IPLeiria) and at the M|I|MO Museum in Leiria. Organized by the Department of Mathematics of ESTG and the Center for Research and Development in Mathematics of the University of Aveiro, in collaboration with other institutions, it aimed to bring together researchers from various fields to discuss recent advances and applications of quaternions and octonions.
Richard A. Davis is a renowned expert in Time Series Analysis and Extreme Value Theory, currently serving as the Howard Levene Professor of Statistics at Columbia University. He obtained his PhD from the University of California at San Diego in 1979 and has held various academic positions at institutions like MIT and Colorado State University. Davis is a Fellow of the Institute of Mathematical Statistics and the American Statistical Association and has authored/co-authored several influential books in the field. He has also been involved in software development for time series analysis and has mentored over 30 PhD students. Davis's research focuses on time series, applied probability, extreme value theory, and heavy-tailed modeling, with particular emphasis on network models and spatial-temporal modeling.
The V Non-Associative Day in Barcelos aimed to unite researchers interested in non-associative algebras, enhance research quality, foster collaboration, and explore future directions. Organized by members from CMUP, CMA-UBI, and CMUC, representing Portuguese institutions, the workshop featured seven invited speakers and took place at the Polytechnic Institute of Cávado and Ave on January 20.
There are three complete plane geometries of constant curvature: spherical, Euclidean, and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focusing on the hyperbolic case, we describe how to obtain all hyperbolic structures on a given topological surface, and how to parameterize them. Finally, we introduce Higgs bundles and explain how they relate to hyperbolic surfaces.
The Global Portuguese Mathematicians Conference's third edition was held at the University of Coimbra from July 26 to 28. It attracted over 60 participants and featured 12 invited speakers. The event facilitated research sharing, idea exchange, and networking among Portuguese mathematicians worldwide. Presentations covered various mathematical areas, showcasing the work of the Portuguese mathematical community.
The purpose of this short note is to present some results regarding the study of Diophantine equations, ranging from very old problems (well-known results to most mathematicians) to some quite new results in the area. Most of the time, the techniques developed to solve particular problems are more interesting than the results themselves. The last section contains our humble contribution.
The LxDS Spring School 2023, organized by LxDS-Lisbon Dynamical Systems Group, CEMAPRE, and CMAF-CIO, took place from May 29-31, 2023, at ISEG-Lisbon School of Economics & Management, Universidade de Lisboa. It featured three courses on dynamical systems by international experts. The school had about 20 participants, including some international attendees, and included oral presentations by PhD students and researchers.
The International Conference on Particle Systems and Partial Differential Equations XI took place at Instituto Superior Técnico (IST), University of Lisbon, from November 6th to 10th, 2023. It aimed to bring together leading researchers in these fields to share their latest findings, foster discussion, and encourage collaborations. The program featured mini-courses by distinguished researchers, talks by invited speakers, and poster sessions. The conference attracted fifty participants from fourteen countries and was supported by various institutions.
Bayes’ theorem is a central result of Statistics and related fields, such as Artificial Intelligence and Machine Learning. In this note, we offer a gentle introduction to a geometric interpretation of Bayesian inference that allows one to think of priors, likelihoods, and posteriors as vectors in a Hilbert space. The given framework can be conceptualized as a geometry of learning from data, and it can be used to construct measures of agreement between these vectors. Conceptually, the geometry is tantamount to that of Pearson correlation, but where an inner product is considered over the parameter space—rather than over the sample space.
I will introduce some concepts in linear control theory and how to adapt and use them to control some problems modeled by nonlinear partial differential equations appearing in a canonical fluid dynamics setting, showcasing how some simple results tailored for ODEs or linear PDEs can be explored to solve nonlinear complex problems from applications.
The Atlantic Conference in Nonlinear PDEs: Dispersive and Elliptic Equations and Systems occurred from October 30 to November 3, 2023, at Instituto Superior Técnico, Universidade de Lisboa, with 74 participants. The event featured plenary talks, contributed talks split into Dispersive and Elliptic PDEs sessions, and poster sessions. It brought together experts and early career mathematicians from both communities, encouraging idea exchange and collaboration.
The ENUMATH 2023 Conference was held in Lisbon, Portugal, featuring plenary talks by experts in various fields of numerical mathematics and industrial applications. The conference included minisymposia, contributed talks, and poster presentations. Charlotte Milano won the Best Poster Award for her work on electromagnetic cartography in medical imaging. The conference facilitated scientific interactions among experts and young scientists from 31 countries, with a focus on contributions from Europe. Proceedings of the conference will be published by Springer in the Lecture Notes in Computational Science and Engineering series.
The third Women in Mathematics Meeting (WM23) was held at the University of Coimbra from July 24th to 26th, 2023. The conference aims to promote women's roles in mathematics and build a supportive community. It gathered 68 participants from various countries, including experts, post-docs, and graduate students. Special sessions addressed the gender gap and the role of Mathematical Societies in promoting gender parity. The event also featured the exhibition "Women of Mathematics from around the world." Attendance was free, with support from several institutions.