Representation finite algebras and generalizations

Wednesday 6 December 2017 h.14:30, Room 2BC30
Simone Giovannini (Padova, Dip. Mat.)
“Representation finite algebras and generalizations"

An algebra is called “representation finite” if it has a finite number of indecomposable modules. Finite dimensional hereditary representation finite algebras are classified by Gabriel's Theorem: they are the path algebras of Dynkin quivers of type ADE. Recently, with the development of higher dimensional Auslander-Reiten theory, some interest has been raised by a generalization in dimension n of these algebras, which are called n-representation finite algebras. In this seminar we will recall some basic definitions and results about representation theory of finite dimensional algebras. Then we will give a naive idea of how some classical notions can be generalized to higher dimension and, finally, we will show some examples of 2-representation finite algebras.

Approximation and convergence in finite state Mean Field Games

Wednesday 22 November 2017 h.14:30, Room 2BC30
Alekos Cecchin (Padova, Dip. Mat.)
“Approximation and convergence in finite state Mean Field Games"

Mean Field Games represent limit models for symmetric non-zero sum non-cooperative dynamic games, when the number N of players tend to infinity. We focus on finite time horizon problems where the position of each agent belongs to a finite state space. Relying on a probabilistic representation of the dynamics in terms of Poisson random measures, we first show that a solution of the Mean Field Game provides an approximate symmetric Nash equilibrium for the N-player game. Then, under stronger assumptions for which uniqueness holds, we prove that the sequence on Nash equilibria converges to a Mean Field Game solution. We exploit the so-called Master Equation, which in this framework is a first order quasilinear PDE stated in the symplex of probability measures.

Doctoral School in Mathematical Science - Opening Day 2017/2018

The opening day of the Doctoral School in Mathematics will take place on October 4, 2017, at 15:00 in room 1BC45.

15:00 Room 1BC45: welcome address to the new students
15:10 Presentation of the activities of PhD Programme 2017/18
16:00 Seminario Dottorato - talk of Sebastiano Don: “Fine properties of functions of bounded variation in Carnot-Caratheodory spaces”
about 17:00 Refreshments at the meeting room of 7th floor

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Graduatoria Valutazione Titoli

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Biodiversity: Mathematical Modelling and Statistics

Wednesday 14 June 2017 h.14:30, Room 2BC30
Anna Tovo (Padova, Dip. Mat.)
“Biodiversity: Mathematical Modelling and Statistics"

Ecological systems are characterized by the emergence of universal patterns that are deemed to be insensitive to the details of the system. Such universality motivates the understanding of ecological patterns through mathematical models able to grasp basic mechanisms at work. With this talk, we will try to describe and analyze the elements that underlie these patterns as well as the patterns themselves from a mathematical point of view. In particular we will focus on biodiversity. Identifying and understanding the relationships between all the life on Earth are some of the greatest challenges in science. After a brief introduction aiming to define the basic concepts of biodiversity and its related patterns, we will see different models developed to predict and measure them. We will then tackle the problem of upscaling biodiversity through spatial scales and we will discuss some still open problems that interest the scientific community.
The seminar is intended for a general audience and it will thus be held at an introductory level.

The influence of network structure in neuronal information transmission

Wednesday 31 May 2017 h.14:30, Room 2BC30
Giacomo Baggio (Padova, DEI)
“The influence of network structure in neuronal information transmission"

Understanding how neurons communicate is one of the most challenging open problems in neuroscience. In this talk, I will present some recent results aiming at formulating this problem from a mathematical and information-theoretic viewpoint. After an overview on neuronal network dynamical models, I will introduce a digital communication framework for studying the information transmission problem in a neuronal network driven by linear dynamics. Within this framework, a novel metric for measuring the information capacity of a neuronal network based on Shannon’s capacity and the notion of inter-symbol interference will be discussed. Finally, I will illustrate how the structure of the network matrix and, in particular, its departure from normality, affects the information capacity of a network.
The talk will be introductory in nature and it is intended for a general audience.

Variational Approaches in Shape Partitioning

Wednesday 3 May 2017 h.14:30, Room 2BC30
Martin Huska (Padova, Dip. Mat.)
“Variational Approaches in Shape Partitioning"

The rapid development of 3D scanning technology has incredibly increased the availability of digital models exploited for a wide range of applications varying from computer graphics and medical imaging up to industrial production. One fundamental procedure that processes the raw acquired data for further manipulation, e.g. in product design, animation, deformation and reverse engineering, is the shape partitioning. This process consists in the decomposition of an object into non-overlapping salient sub-parts determined by a shape attribute.
In this seminar, we will introduce the concept of Shape Partitioning together with the wide range of partitioning methods. Next, we will observe a few partitioning/segmentation models in the field providing some results. At last, if the time allows, we will introduce the concept of Convex-Nonconvex segmentation over surfaces.
The seminar will be held at introductory level, thus, general audience is welcome to participate.

An introduction to domain perturbation theory for elliptic eigenvalue problems

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.

Quantized option pricing in Mathematical Finance

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.

Topology, analysis and the Riemann-Hilbert correspondence

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.

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