Graduate Seminar 2022-2023
List of Seminars
Video recordings at Unipd's portal "Mediaspace"
(Click on title for abstract)
5 October 2022 h. 17:00, Giacomo Lanaro (Padova, Dip. Mat.), Interest rate market: how economic changes affect mathematical modeling video
16 November 2022 h. 14:30, Muhanna Ali H. ALRASHDI (Padova, Dip. Mat.), “Shear flows and viscoelastic fluids" video
30 November 2022 h. 14:30, Mohammad KARIMNEJAD ESFAHANI (Padova, Dip. Mat.), “Moving Least Square Approximation using Variably Scaled Discontinuous Weight Function" video
14 December 2022 h. 15:30, room 2BC30, Riccardo Gilblas (Padova, Dip. Mat.), “Binomial coefficients in modular arithmetic - A mathematical solution to musical questions" video
18 January 2023 h. 15:30, room 2BC30, Sara Venturini (Padova, Dip. Mat.), “Complex Networks: a highly interdisciplinary field. Theory and Applications" video
8 February 2023 h. 15:30, room 2BC30, Shilun Wang (Padova, Dip. Mat.), “A brief introduction to Bloch-Kato conjecture" video
1 March 2023 h. 15:30, room 2BC30, Mohamed Bentaibi (Padova, Dip. Mat.), “Micro-Macro Limit: From the Follow-the-Leader Model to the Lighthill-Whitham-Richards Model" video
15 March 2023 h. 14:30, room 2BC30, Tania Bossio (Padova, Dip. Mat.), “On the volume of (half-)tubular neighborhoods of surfaces in sub-Riemannian geometry" video
29 March 2023 h. 14:30, room 2BC30, Chiara Bernardini (Padova, Dip. Mat.), “Ergodic Mean-Field Games with Riesz-type aggregation" video
19 April 2023 h. 14:30, room 2BC30, Eduardo Rocha Walchek (Padova, Dip. Mat.), “Reciprocity Laws" video
3 May 2023 h. 14:30, room 2BC30, Maddalena Muttoni (Padova, Dip. Mat.), “Optimal control with a stochastic switching time: introduction and solution approaches" video
17 May 2023 h. 15:30 , room 2BC30, Daniele Nemmi (Padova, Dip. Mat.), “Symmetries, groups and graphs: from the origins to today's research" video
31 May 2023 h. 14:30, room 2BC30, Enrico Vicario (Padova, Dip. Mat.), “Cutting pattern optimization in sawmill" video
Giacomo Lanaro, "Interest rate market: how economic changes affect mathematical modeling"
Abstract. In the last fifteen years many changes in the economic and financial world have caused a great modification in the way in which every financial market is studied by the analysists. One market that has been most affected by these changes is the interest-rate market. We will present how this market worked before the 2007 crisis and what has no longer hold after that date. Moreover, we will show how the mathematical modeling has been adapted to correctly represent the new tasks that have arisen in those years. Finally, we will present how the problem of parameters recalibration for an interest-rate model can be faced in a geometric framework through the computation of the Lie algebra generated by a suitable set of vector fields in an infinite-dimensional setting.
Muhanna Ali H. Alarashdi, "Shear flows and viscoelastic fluids"
Abstract.In this seminar I will give a brief overview on viscoelastic fluids and rheology. Rheology is the science that deals with the way materials deform when forces are applied to them. To learn anything about the rheological properties of a material, we must either measure the deformation resulting from a given force or measure the force required to produce a given deformation. So, we study rheological properties through some experiments such ad steady shear, Small amplitude oscillatory shear, stress growth upon inception of steady shear flow and stress relaxation after a sudden shearing displacement. Moreover, we present a new model that includes logarithmic strains. Finally, comparisons between the new model and a classical one (the upper-convected Maxwell model) will be given to illustrate similarities and differences. />
Mohammad Karimnejad Esfahani, "Moving Least Square Approximation using Variably Scaled Discontinuous Weight Function"
Abstract.Functions with discontinuities appear in many application such as image reconstruction, interface problems, and etc. Accurate approximation and interpolation of these functions are therefore of great importance. After giving an introduction on the required notions, we present an approximation method of discontinuous function f, which incorporates the discontinuities into the approximant s. In a nutshell, the idea is to control the influence of the data on the approximant, not only with regards to their distance, but also with regards to the discontinuities of the underlying function. The numerical experiments show an improvement on the accuracy of the approximation compared with the conventional schemes. />
Riccardo Gilblas, "Binomial coefficients in modular arithmetic - A mathematical solution to musical questions"
Abstract.In this seminar we are linking modular binomial coefficients to periodic sequences with modular integer values. In the context of serialism, the romanian composer Anatol Vieru used such sequences to compose several musical pieces. We will introduce the main properties of periodic sequences and we will explain the link between them and the binomial coefficients in Z/mZ. This allows to use tools such as Kummer's Theorem to answer some questions arisen from Vieru's observations./>
Sara Venturini, "Complex Networks: a highly interdisciplinary field. Theory and Applications"
Abstract.Networks and graph models have become a nearly ubiquitous abstraction and an extremely useful tool to represent a variety of real systems in different fields. They can help us to better understand and analyze different types of interactions and dynamics. Recent researches have shown that real world interactions, in many cases, cannot be fully described by standard graphs. Therefore, there is the need to study more complex structures such as multilayer networks, which enable to take into account different types of information, as well as simplicial complexes and hypergraphs, which consider group interactions. We will give a brief introduction to modern mathematical and computational tools for complex networks, their applications, and their extension to multilayer and hypergraphs.
Shilun Wang, "A brief introduction to Bloch-Kato conjecture"
Abstract. The Bloch-Kato conjecture (BKC) is an important and difficult problem in number theory and arithmetic geometry, which came up with Bloch and Kato in 90s, and was then refined by Fontaine and Perrin-Riou later. It is a natural generalization of the Birch and Swinnerton-Dyer conjecture (BSD), which is one of Millennium Problems. However, we only know BKC is true in few cases. The seminar will give a brief introduction to the motivation and historical development of BKC by some explicit examples and explain its relation with the BSD conjecture. In the second part, we will talk about some progresses in BKC.
Mohamed Bentaibi, "Micro-Macro Limit: From the Follow-the-Leader Model to the Lighthill-Whitham-Richards Model"
Abstract. The Lighthill-Whitham-Richards (LWR) model is a hyperbolic conservation law where the solution is a macroscopic density that typically represents the average spatial concentration of vehicles. The Follow-the-Leader model (FtL) instead can be thought as a dynamical system of N cars in which each car travels with a velocity that depends on its relative distance with respect to the car immediately in front. With the FtL model we build a microscopic density which approximates the macroscopic one. After briefly introducing both the LWR and the FtL models, we prove that the microscopic density converges to the macroscopic one in a suitable topology. We also present new results regarding the microscopic stability of the FtL model and its applications to the analysis of the micro-macro limit problem.
Tania Bossio, “On the volume of (half-)tubular neighborhoods of surfaces in sub-Riemannian geometry"
Abstract. In 1840 Steiner proved that the volume of the tubular neighborhood of a convex set in R^n is a polynomial of degree n in the size of the tube. The coefficients of such a polynomial carry information about the curvature of the set. In this talk we present Steiner-like formulas in the framework of sub-Riemannian geometry. In particular, we introduce the three-dimensional sub-Riemannian contact manifolds, which the first Heisenberg group is a special case of. Then, we show the asymptotic expansion of the volume of the half-tubular neighborhood of a surface and provide a geometric interpretation of the coefficients in terms of sub-Riemannian curvature objects.
Chiara Bernardini, “Ergodic Mean-Field Games with Riesz-type aggregation"
Abstract. In this seminar we introduce second-order ergodic Mean-Field Games systems defined in the whole space R^n with coercive potential and aggregating nonlocal coupling, defined in terms of a Riesz interaction kernel. From a PDE viewpoint, equilibria of the differential game solve a system of PDEs where an Hamilton-Jacobi-Bellman equation is combined with a Kolmogorov-Fokker-Planck equation for the mass distribution. Due to the interplay between the strength of the attractive term and the behavior of the diffusive part, we obtain three different regimes for existence and nonexistence of classical solutions to the MFG system. After briefly introducing the model, we present the main ideas underlying the proof of our results. Finally, we study the behavior of solutions in the vanishing viscosity limit, namely when the diffusion becomes negligible.
Eduardo Rocha Walchek, “Reciprocity Laws"
Abstract.In this seminar, we give an introduction to reciprocity laws in number theory, since its origins in solving quadratic equations over finite fields to how it evolved -- like ever more complex variations on the original theme -- to the almost unrecognizable, yet still somehow related, modern explicit reciprocity laws. Our focus will be on the succession of the many results tied by this same name, introducing the relevant concepts and ideas along the way.
Maddalena Muttoni, “Optimal control with a stochastic switching time: introduction and solution approaches"
Abstract.When planning an optimal policy, a farsighted decision-maker should account for the possibile occurrence of disruptive events over the course of the time horizon. For example, when planning the optimal emission abatement policy, account for a possible climate catastrophe; when planning industrial production, account for an unpredictable disruption that may affect the producer’s profit. In the optimal control framework, a stochastic switching time is a random instant, modeled as a positive random variable, which marks a regime shift – i.e., an abrupt and irreversible change in the system – which splits the planning horizon into two stages. The shift may affect the payoff and/or the state trajectory in several ways, all of which are included in the analysis of the most general scenario. In search for the optimal policy under this kind of uncertainty, two methods are featured in the literature: the “backward” approach and the “heterogeneous” one. The two approaches will be described, compared, and then applied to a marketing toy model.
Daniele Nemmi, “Symmetries, groups and graphs: from the origins to today's research"
Abstract. Symmetries are everywhere: we can find them in nature, art, music, poetry... we can find them in equations, geometrical objects, mechanical systems, molecules and more generally, all over mathematics and science. But what are they? Why are they so important? Every mathematician, even without noticing it, has used symmetries to solve problems which otherwise would have been more difficult or even impossible to solve. The talk will be a journey into group theory: the branch of mathematics which studies the concept of symmetries and how they relate to one another. We will focus in particular on finite groups and how they are built by fundamental blocks: the finite simple groups, whose classification is considered one of the most remarkable achievements in the mathematics of the last century. We will talk about how some of today's research problems, such as generation problems, can be encoded in the language of graphs which help us to better understand the structure of finite groups.
Enrico Vicario, “Cutting pattern optimization in sawmill"
Abstract. Optimizing the cutting of wood from log to board is a step within the lumber production chain that has great potential for optimization. This processing in industry is carried out in lines with machines that are increasingly automated and have varying degrees of flexibility in cutting execution. In this work, a specific problem of generating optimal cutting patterns was modeled in order to address it as a Mixed Integer Linear Problem (MILP). The mathematica formulation has been tested on real instances and the result was compared, in terms of obtained value and computation time, with an ad-hoc greedy heuristics. An original method is also presented to approach a more general cutting pattern problem, based on the integration of optimization techniques and the use of Convolutional Neural Networks (CNN) for reliable board valorization..