The Riemann Hypothesis is probably the most important open problem in Mathematics. In this talk we will briefly explain some recent unconventional approaches to the problem, including one which has unexpectedly popped up in the author's research.
How can we include complex environmental considerations like fragmentation into problems of forest management for timber production with restrictions in the areas of clearcuts? In this presentation, I briefly describe some works in which I participated that set out to solve this open problem.
We give an overview of the main developments over the last decade in the study of the Laplacian with Robin (third) boundary conditions on Euclidean domains. Our emphasis will be on the dependence of the eigenvalues and eigenfunctions on the Robin parameter in the boundary condition, and also on the geometry of the underlying domain.
Ecological Statistics is a fast growing area where statistics is put at work to solve problems within an ecological background. In this talk I will showcase some of my work covering examples from - some would say- each of the 5 sub-areas in the field: species distribution modelling, measuring biodiversity, investigating population dynamics, understanding animal movements and interpreting citizen science data.
TAM thanks partial support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UIDB/00006/2020).
Riordan arrays and a generalized Narayana identity
The classical Catalan numbers can be written as sum of the Narayana numbers. We will show how it is possible to use Riordan arrays to generalize this identity obtaining new identities to a family of numbers which includes ballot numbers and several generalized Catalan numbers.
The classification of shapes and spaces (for example, differential manifolds) is one of the key problems in Geometry and Topology (as well as in Theoretical Physics). Discrete invariants (eg, Euler characteristic) and continuous invariants (eg. curvature, complex structure) can be studied with algebraic Topology, and with moduli space theory, respectively. In this talk, we present a few examples of moduli spaces and their geometries, from classical Greek Geometry (eg. plane conics) to spaces of polygons in R^3, which were recently addressed via symplectic and algebraic geometry.
Stochastic capacitated facility location: coping with uncertain uncertainty
This work investigates the application of adaptative distributionally robust optimization to a general class of capacitated facility location problems. State-dependent uncertainty is considered together with additional distributional information such as the possible correlation between random variables. Modeling aspects and solution algorithms (exact and approximate) are presented. Computational results are reported.
Mathematical modelling in Solid mechanics : an example with fracking
I will present the various steps of mathematical modelling on a practical case: presentation and setting of the problem (hydraulic fracture), choice of the approach (energetical and variational), choice of the method (topological differentiation), design of the algorithm (quasi-static and incremental), choice of the discretization (finite elements), choice of the computational language (Matlab), presentation of the numerical results and discussion. This work is part of a long-term research programme with André Novotny (LNCC, Brasil) and Marcel Xavier (UFF, Niterói, Brasil)
In this short talk we present some recent contributions of model theory (logic) to algebraic geometry in non-archimedean setting, improving and extending results by Berkovich.
Going back and forth, and up and down: a recipe for chaos
By using a fairly simple method, we show that the oscillatory behavior of a simple pendulum with oscillating support is unpredictable.
In a steel plant, electric arc furnaces can be operated at different power levels, affecting energy efficiency, duration of the scrap melting tasks and the rate of electrode degradation. We propose a mixed-integer linear programming discrete-time formulation under time-of-use electricity pricing that captures the tradeoffs involved. Results for a real-life Italian case study, show that electrode replacement plays an important role in total cost minimization, with the high-power mode, which allows for faster execution and to fit more tasks in low-price periods but is the least energy efficient and consumes the largest mass of electrode, being mostly avoided.
Lyapunov Exponents: Problems and Applications
Lyapunov Exponents measure the sensitivity of a dynamical system to initial conditions, many times associated with the concept of chaos and its butterfly effect allegory. We will outline the origin, evolution, problems and applications of this concept.