Graduate Seminar 2018/2019
The Graduate Seminar ("Seminario Dottorato" in Italian) started in 2006. It runs about twice per month, usually on Wednesday afternoon, except in Summer. Seminars are usually given by PhD students and PostDocs of the Department of Mathematics, but occasionally also by Senior Researchers. It is assumed that each Student of the Doctoral School will give a talk in the Seminar during his/her doctoral studies.
The Graduate Seminar is a doubleaimed activity. On the one hand, speakers have the opportunity to think how to communicate their researches to a public of mathematically welleducated but not specialist people, by preserving both understandability and the flavour of a research report. On the other hand, people in the audience enjoy a rare opportunity to get an accessiblebutprecise idea of what's going on in areas of mathematics that they might not know very well.
All speakers are required to prepare a short report on the the topic of their talk, which are collected in a booklet at the end of the year.
The Graduate Student is organized by Corrado Marastoni and Tiziano Vargiolu.
List of 20182019 Seminars
(Click on title for abstract)
 [21 November 2018] Yan HU (Padova, Dip. Mat.) “Congruent numbers, Heegner method and BSD conjecture"
 [3 October 2018] Nicola Gastaldon (Padova, Dip. Mat., and TransCel, Albignasego) "Exact and MetaHeuristic Approach for Vehicle Routing Problems"

[5 December 2018] Paolo Luzzini (Padova, Dip. Mat.) “Regular domain perturbation problems"

[19 December 2018] Dimitrios Zormpas (Padova, Dip. Mat.) “Real Options: An overview"

[30 January 2019] Maria Teresa Chiri (Padova, Dip. Mat.) “Conservation law models for supply chains"

[13 Febuary 2019] Guglielmo Pelino (Padova, Dip. Mat.) “Mean field interacting particle systems and games"
Abstracts of 20182019 Seminars
Yan Hu, Congruent numbers, Heegner method and BSD conjecture
Abstract. The “Congruent number problem” is an old unsolved major problem in number theory. In this seminar we provide a brief introduction to it. We will start from the original version of the problem, and lots of objects will be introduced during the talk. If time permits, some current progresses relateted to the BSD conjecture will also be described.
Nicola Gastaldon, Exact and MetaHeuristic Approach for Vehicle Routing Problems
Abstract. The Vehicle Routing Problem (VRP) includes a wide class of problems studied in Operations Research and relevant from both theoretical and practical perspectives. In its basic formulation, the problem is to find a set of routes for a given fleet of vehicles through a set of locations, so that each location is visited by exactly one vehicle and the total travel cost is minimized. Such problem is often enriched with many attributes rising from realworld applications, such as capacity constraints, pickup and delivery operations, time windows, etc. VRP belongs to the class of combinatorial optimization problems, and it is very hard to solve efficiently and researchers have developed many exact and (meta)heuristic algorithms. The former takes advantage of the structure of the mathematical model to obtain a speedup through decomposition methods. The latter exploits heuristic techniques to obtain solutions that trade off quality and computational burden, such as evolutionary algorithms and neighborhood search routines. In our research, we consider the VRP arising at TransCel, a freight transportation company based in Padova. We devised a Tabu Search heuristic implementing different neighborhood search policies, and now embedded in the tool supporting the operation manager at TransCel. The algorithm runs in an acceptable amount of time both in static and dynamic settings, and the quality of the solutions is assessed through comparison with results obtained by a Column Generation algorithm that solves a mathematical programming formulation of the problem. Current research aims at developing datadriven techniques that exploit the information available from the company's repositories to support stochastic transportation demand arising in real time.
Paolo Luzzini, Regular domain perturbation problems
Abstract. The study of the dependence of functionals related to partial differential equations and of quantities of physical relevance upon smooth domain perturbations is a classical topic and has been carried out by several authors. In this talk we will give an introductory overview about regular domain perturbation problems. We will provide concrete examples, highlight the motivations and the possible applications, and present an outline of some new results obtained in collaboration with P. Musolino and R. Pukhtaievych.
Dimitrios Zormpas, Real Options: An overview
Abstract. Financial options are contracts that derive their value from the performance of an underlying asset. They give to their holder the right, but not the obligation, to buy/sell an asset at a predetermined price and time. Contracts similar to options have been used since ancient times. However, the most basic model for their pricing was proposed in the early 1970’s leading to a Nobel prize in 1997. In the late 1970's the term Real Options is coined by Stewart Myers. According to the real options approach an investment characterized by uncertainty and irreversibility is like a financial option on a real asset. For instance, a potential investor has the right but not the obligation to pay a given amount of money in order to make an investment and gain access to the corresponding profit flow. Using standard option pricing tools one can also study the option to leave a market, outsource production, mothball a production plant etc. In this seminar, I will refer to the correspondence between financial and real options and then present the simplest model in the real options literature that has to do with a potential investor who is considering undertaking an uncertain and irreversible investment. Then I will present a number of applications of the real options approach from the broad literature of operations management and finally make a reference to applications of the real options approach in energy economics.
Maria Teresa Chiri, Conservation law models for supply chains
Abstract. Abstract. Many real situations are modelled by nonlinear hyperbolic first order partial differential equations (PDEs) in the form of conservation or balance laws. Beside the classical case of Euler equations of gas dynamics, such PDEs arise for instance in traffic flow, gas pipelines, telecommunication networks, blood flow in arteries. In this talk, after a short review on the basic theory of scalar conservation laws, we introduce a new model for supply chains. Here, we are considering large volume production that allows a continuous description of the product flow in terms of conservation laws, accompanied by ordinary differential equations describing the processing capacities. A key feature of this model is the behaviour of solutions in presence of a discontinuous dynamics with respect to the unknown conserved quantity (number of parts being processed). This is a joint work with Prof. Fabio Ancona from University of Padova.
Pelino Guglielmo, Mean field interacting particle systems and games
Abstract. Abstract. Mean field theory studies the behaviour of stochastic systems with a large number of interacting microscopic units. Under the meanfield hypothesis, it is often possible to give a macroscopic easier description of the phenomena, which still allows to catch the main characteristics of the complex prelimit model. The main purpose of the talk is to motivate a system of two coupled forwardbackward partial differential equations, known as the mean field game system, which serves as a limit model for a particular class of stochastic differential games with N players. For reaching this goal, an introductive overview on macroscopic limits for mean field interacting particle systems and games under diffusive dynamics will be presented. In the last part of the talk I will briefly review my contributions in the context of finite state mean field games.