Wednesday 29 March 2017 h.14:30, Room 2BC30
Francesco Ferraresso (Padova, Dip. Mat.)
“An introduction to domain perturbation theory for elliptic eigenvalue problems”
How does the sound of a drum depend on its shape? This weak variant of the classical question “Can one hear the shape of a drum?” can be considered in the framework of domain perturbation theory for elliptic differential operators. Starting with easy examples we will see that the answer to this apparently harmless question is rather different in the case of regular perturbations and in the case of singular perturbations. We will focus on the singular case, where the geometry of the problem is deeply mixed with the differential structure, in particular with the boundary conditions. Finally, we will give an account of recent advances in the study of a specific singular perturbation (the dumbbell domain) for the Laplace operator and for the biharmonic operator.
The seminar is intended for a general audience and it aims to introduce basic concepts from spectral theory as well as more advanced research results.
Wednesday 15 March 2017 h.14:30, Room 2BC30
Lucio Fiorin (Padova, Dip. Mat.)
“Quantized option pricing in Mathematical Finance”
Quantization is a widely used tool in Signal Processing and Numerical Probability, and it has been recently applied to Mathematical Finance. The quantization of a continuous random variable consists in finding the “best” discrete version of it, i.e. minimizing the L^2 distance. It is possible, using this technique, to create new algorithms for the pricing of European options under different models of the underlying asset.
In this seminar we introduce the basic tools used in mathematical finance and we will present the most common results in the theory of option pricing. After a brief discussion on the existing models of the price of a financial asset, we will give the audience some ideas on how quantization can be a powerful tool able to overcome existing problems.
Wednesday 1 March 2017 h.14:30, Room 2BC30
Christopher Lazda (Padova, INdAM Marie Curie Fellow)
“Topology, analysis and the Riemann-Hilbert correspondence”
The Riemann-Hilbert correspondence gives a way of passing back and forth between topology and differential geometry, describing the behaviour of differential equations in terms of the monodromy of their local solutions. Starting with the example of the logarithm, I will give an introduction to the ideas behind this correspondence in a concrete and down to earth manner, concentrating on the case of Riemann surfaces. If there is time I will also explain how this gives a completely algebraic way to study topological invariants.
Wednesday 15 February 2017 h.14:30, Room 2BC30
Daniele Tovazzi (Padova, Dip. Mat.)
“Collective periodic behavior in interacting particle systems"
Interacting particle systems constitute a wide class of models, originally motivated by Statistical Mechanics, which in the last decades have become more and more popular, extending their applications to various fields of research such as Biology and Social Sciences. These models are important tools that may be used to study macroscopic behaviors observed in complex systems. Among these phenomena, a very interesting one is collective periodic behavior, in which the system exhibits the emergence of macroscopic rhythmic oscillations even though single components have no natural tendency to behave periodically.
This talk aims to introduce to a general audience some basic tools in the theory of interacting particle systems and some of the mechanisms which can enhance the appearance of self-sustained macroscopic rhythm. After recalling some notions of Probability, we present the classical Curie-Weiss model, which doesn't exhibit periodic behavior, and we show how we can modify it in order to create macroscopic oscillations. This is also the starting point for some recent developments that will be sketched in the last part of the talk.
Wednesday 1 February 2017 h.14:30, Room 2BC30
Leone Cimetta (Padova, Dip. Mat.)
“Zeta functions associated to profinite groups”
In this seminar we will discuss the properties of some Dirichlet series associated to a group G satisfying specific topological properties. These series deal with two important problems arisen in the last century, which both had a great development over the last decades.
The first problem (the subgroup growth of a profinite group G) involves the behaviour of the function a_n(G), that is the number of subgroups of G of index n.
The second problem consists in determining the probability that, randomly choosing n elements of a group, we get a generating set for the whole group.
The second problem, in particular, arises from a famous work by P. Hall, which solved it in 1936 in the finite case.
After recalling some basic definitions, we will present the motivations for the problems; then, starting from some examples and classical results for finite groups, we will give some ideas to develop both problems in the profinite case and show some relations between the series involved.
Wednesday 18 January 2017 h.14:30, Room 2BC30
Moreno Ambrosin (Padova, Dip. Mat.)
“Secure And Scalable Management of Internet of Things Deployments”
In recent years, the advent of Internet of Things (IoT) is populating the world with billions of low cost heterogeneous interconnected devices. IoT devices are quickly penetrating in many aspects of our daily lives, and enabling new innovative services, ranging from fitness tracking, to factory automation. Unfortunately, their wide use, as well as their low-cost nature, makes IoT devices also an attractive target for cyber attackers, which may exploit them to perform various type of attacks, such as Denial of Service (DoS) attacks or privacy violation of end users. Furthermore, the potentially very large scale of IoT systems and deployments, makes the use of existing security solutions practically unfeasible.
In this talk I will give an overview of the problem of secure management, and present our research effort in defining secure and scalable solutions for managing large IoT deployments. Moreover, I will focus in particular on two important parts of the device management process: (1) software updates distribution; and (2) device's software integrity check.
Wednesday 14 December 2016 h.14:30, Room 2BC30
Frances Odumodu (Padova, Dip. Mat.)
“Extension fields, and classes in the genus of a lattice“
In this talk, which will be accessible to a large audience, a first part will be devoted to a basic reminder on extension fields with examples, and a second part to the more specific framework of number fields, i.e. finite degree extensions of rational numbers. Concerning the latter part, the Hasse-Minkowski local-global theorem for quadratic forms fails in general at the integral level, hence there are two levels of classification, the genus (local) and the integral class (global): we shall focus on some results concerning the classes in the genus of a lattice and in particular the trace form.
Wednesday 30 November 2016 h.14:30, Room 2BC30
Enrico Facca (Padova, Dip. Mat.)
“Biologically inspired deduction of Optimal Transport Problems”
In this talk, after a brief introduction on the Optimal Transport Problems and some PDEs based formulation, we will present a recently developed approach, based on an extension of a model proposed by Tero et al (2007), for the simulation of the dynamics of Physarum Polycephalum, a unicellular slime mold showing surprising optimization ability, like finding the shortest path connecting two food sources in a maze.
We conjecture that this model is an original formulation of the PDE-based OT problems. We show some theoretical and numerical evidences supporting our thesis.
Wednesday 16 November 2016 h. 14:30, Room 2BC30
Laura Cossu (Padova, Dip. Mat.)
“Products of elementary and idempotent matrices and non-euclidean pids”
It is well known that Gauss Elimination produces a factorization into elementary matrices of any invertible matrix over a field. Is it possible to characterize integral domains different from fields that satisfy the same property? As a partial answer, in 1993, Ruitenburg proved that in the class of Bézout domains, any invertible matrix can be written as a product of elementary matrices if and only if any singular matrix can be written as a product of idempotents.
In this seminar we present some classical results on these factorization properties and we focus, in particular, on their connection with the notion of weak-Euclidean algorithm. We then conclude with a conjecture on non-Euclidean principal ideal domains, rare and interesting objects in commutative algebra, and some related results.
In order to make the talk understandable to a general audience, we will recall basic definitions of Commutative Ring theory and provide easy examples of the objects involved.
The opening day of the Doctoral School in Mathematics will take place on October 5, 2016, at
15:30 in room 1BC45.
15:30-16:15: presentation of the activities/courses of PhD Programme 2016/2017
16:15-17:15: talk of Veronica Dal Sasso "Integer Linear Programming to solve Large-Scale problems"
17:30: refreshments at the common room of 7th floor
For further information feel free to contact Pierpaolo Soravia.