Zeta functions associated to profinite groups

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.

Secure And Scalable Management of Internet of Things Deployments

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.

Extension fields, and classes in the genus of a lattice

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.

Biologically inspired deduction of Optimal Transport Problems

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.

Products of elementary and idempotent matrices and non-euclidean pids

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.

Doctoral School in Mathematical Science - Opening Day 2016/2017

The opening day of the Doctoral School in Mathematics will take place on October 5, 2016, at
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.

Integer Linear Programming to solve Large-Scale problems

Our first seminar of 2016/17 will be held as a special event
inside the Opening Day of the Doctoral School (15:30, 1BC45)

Wednesday 5 October 2016 h.16:15, Room 1BC45
Veronica Dal Sasso (Padova, Dip. Mat.)
“Integer Linear Programming to solve Large-Scale problems"

Integer linear programming is widely used to find optimal solutions to problems that arouse in the real world and are related to logistics, planning, management, biology and so on. However, if from a theoretical point of view it is easy to give a formulation for these problems, from a computational point of view their implementation can be impractical due to the high number of constraints and variables involved.
During this seminar I will present classical results for dealing with large-scale integer linear programs and their application to a particular bioinformatic problem, related to the study of the human genome, that helps recovering information useful to study diseases and populations' behaviours.

Computed Tomography: a real case example of inverse problem

Wednesday 15 June 2016 h. 15:00, Room 2BC30
Elena Morotti (Dip. Mat.)
"Computed Tomography: a real case example of inverse problem"

X-ray computed tomography (CT) is a well known medical imaging technique, that seeks to reveal internal structures hidden by the skin and bones. Mathematically, the CT process can be modelled as a linear system and the image reconstruction is a challenging inverse problem. In this talk I will show both phisical and mathematical basic concepts, to explain the CT process, and the two possible approaches to solve the problem (leading to analitical or iterative numerical methods). Finally, I will shortly introduce the Digital Breast Tomosynthesis (DBT) technology, that is a 3D emerging technique for the diagnosis of breast tumors, together with numerical results for a simulated problem.

Polyhedral structures in algebraic geometry

Wednesday 1 June 2016 h. 14:30, Room 2BC30
Stefano Urbinati (Dip. Mat.)
"Polyhedral structures in algebraic geometry"

Algebraic geometry studies the zero locus of polynomial equations connecting the related algebraic and geometrical structures. In several cases, nevertheless the theory is extremely precise and elegant, it is hard to read in a simple way the information behind such structures. A possible way of avoiding this problem is that of associating to polynomials some polyhedral structures that immediately give some of the information connected to the zero locus of the polynomial. In relation to this strategy I will introduce Newton-Okounkov bodies and Tropical Geometry.

Fractional Calculus: Numerical Methods and Models

Wednesday 25 May 2016 h. 14:30, Room 2BC30
Abdelsheed Ismail Gad Ameen (Dip. Mat.)
"Fractional Calculus: Numerical Methods and Models"

In this talk, we first give a short introduction of fractional calculus (FC) and its geometrical, physical interpretation. Then, we discuss the differential equations of fractional order (Caputo type) which have recently proved to be valuable tools for modeling of many biological phenomena. Most of fractional ordinary differential equations (FODEs) do not have exact analytic solutions so that numerical techniques must be used. Hence, we present the fractional Euler method to solve systems of nonlinear FODEs and show how to use this method for solving the Susceptible-Infected-Recovered (SIR) model of fractional order.

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