Programme
November 25, 2022
14h00 - 14h15 Opening Session
14h15 - 15h15 Filipe Rodrigues (Assistant Professor, ISEG - Univ. Lisbon, and former PDMA student) - Operational Research in Seaside Operations under Uncertainty
15h15 - 15h35 Ivan Pombo (PDMat) - Uniqueness of the Calderón problem in 3D for complex conductivities through quaternionic analysis
15h35 - 15h55 Ivo Sengo (MAP-Fis) - Black holes or the unbearable curvatureness of being
15h55 - 16h30 Coffee-Break
16h30 - 16h50 Manisha Jain (PDMA) - Framing (quantum, fuzzy) transition systems as coalgebras
16h50 - 17h10 Inês Serôdio Costa (PDMA) - Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
17h10 - 17h30 Gabriel Cardoso (PDMA) - An extension of Euclid-Euler Theorem for certain α-perfect numbers
Operational Research in Seaside Operations under Uncertainty
14h15 - 15h15
Filipe Rodrigues [frodrigues@iseg.ulisboa.pt]
Abstract: Operational Research has a wide range of real-world applications. This talk is about one of them: seaside operations. Seaside operations play a critical role in the world; however, they are highly affected by several uncertain factors like weather conditions and mechanical failures of equipment. Therefore, to obtain solutions applied in practice, it is essential to take such uncertainty into account when designing solution methods. This talk focuses on two different problems arising in seaside operations: the maritime inventory routing problem and the berth allocation problem. For both problems, several approaches to handle uncertainty are overviewed, namely: stochastic programming, robust optimization, and risk-measures. The benefits of operational research – in particular, the use of tools to deal with uncertainty – are shown by the computational results.
Uniqueness of the Calderón problem in 3D for complex conductivities through quaternionic analysis
15h15 - 15h35
Ivan Pombo [ivanpombo@ua.pt]
Abstract: In this talk I will introduce a novel approach to solve the uniqueness of Calderón problem. Our proofs rely on the application of quaternionic analysis to mimic the structure of the complex analysis proofs in 2D.
Black holes or the unbearable curvatureness of being
15h35 - 15h55
Ivo Sengo [sengo@ua.pt]
Abstract: In 1915 Einstein published its theory of General Relativity, which is still the most trustworthy theory that we have for the description of all gravitational phenomena. Although mathematically elegant, this theory predicts its own demise: Einstein's equations inform us that from the collapse of very massive stars a black hole must emerge and, inside it, a singularity in the geometry of the spacetime. Black holes are characterized for having an event horizon: a region in the spacetime from which nothing can escape, not even light. For many decades such objects belonged to the realm of mathematics but today, more than a century after the discovery of the Schwarzschild metric, we can not only hear them, through the waves that they generate when colliding, but we can also see them. But what does it mean to see an invisible object, and what do we expect to learn from these images? And, more importantly, do these black holes have hair?
Framing (quantum, fuzzy) transition systems as coalgebras
16h30 - 16h50
Manisha Jain [manishajain@ua.pt]
Abstract: The topic of my PhD project is the development of a fuzzy dynamic logic for quantum programs i.e. a modal logic indexed by quantum programs. The theory of coalgebras provide a generic and elegant way to model arbitrary transition system and derive the underlying modal logics. In this task I will explain the coalgebraic approach, illustrated with classical determinsitic and non deterministic transition system. Then I will describe my current research in framing i) fuzzy transition system and ii) quantum transition system as coalgebras and combining them.
Sharp bounds on the least eigenvalue of a graph determined from edge clique partitions
16h50 - 17h10
Inês Serôdio Costa [inesserodiocosta@ua.pt]
Abstract: In this talk, sharp bounds on the least eigenvalue of an arbitrary graph are presented. Necessary and sufficient (just sufficient) conditions for the lower (upper) bound to be attained are deduced using edge clique partitions. As an application, we prove that the least eigenvalue of the n-Queens' graph is equal to -4 for every n>3 and it is also proven that its multiplicity is (n-3)2.
An extension of Euclid-Euler Theorem for certain α-perfect numbers
17h10-17h30
Gabriel Cardoso [gabriel.cardoso@ua.pt]
Abstract: In a posthumously published work, Euler proved that all even perfect numbers are of the form 2p-1(2p-1), where 2p-1 is a prime number. In this presentation, we extend Euler's method for certain α-perfect numbers for which Euler's result can be generalized. In particular, we use Euler's method to prove that if N is a 3-perfect number divisible by 6; then either 2 exactly divides N or 3 exactly divides N. As well, we prove that if N is a 5/2-perfect number divisible by 5, then 24 exactly divides N, 52 exactly divides N, and 312 divides N. Finally, for p ∈ {17,257,65537} we prove that there are no 2p/(p-1)-perfect numbers divisible by p.