Tilting approach to the theorem of Fontaine-Wintenberger

Wednesday 14 March 2018 h. 14:30, Room 2BC30
Yangyu Fan (Univ. Milano)
“Tilting approach to the theorem of Fontaine-Wintenberger”

In this basic notion talk, I will explain an approach to the Fontaine-Winterberger isomorphism between Galois groups in characteristic 0 and characteristic p using the tilting equivalence developed by Scholze and Kedlaya-Liu.

Optimal cross-border electricity trading

Wednesday 28 February 2018 h. 15:00, Room 2BC30
Maria Flora (Padova, dSEA)
“Optimal cross-border electricity trading”

Using econometric tools, we show statistical evidence of cross-effects on the price of electricity in neighbouring countries, due to electricity flows across interconnected locations. We build on this result to set up an optimal trading strategy, based not only on the price spreads observed over time among the selected interconnected countries, but also on the market impacts caused by the flows of electricity among them. Using the previous econometric analysis findings, we model the joint dynamics of electricity prices as including both temporary and permanent impacts of electricity trades, as well as driven by a common co-integration factor. We then pose an optimal control problem, and solve the resulting dynamic programming equation up to a system of Riccati equations, which we solve numerically to evaluate the performance of the strategy. We show that including cross-border effects in the trading strategy specification significantly improves the performance.

Effective conductivity of a composit material and its series expansion

Wednesday 14 February 2018 h. 14:30, Room 2BC30
Roman Pukhtaievych (Padova, Dip. Mat.)
“Effective conductivity of a composit material and its series expansion"

In this talk we discuss the asymptotic behavior of the effective conductivity in a dilute two-phase composite with non-ideal contact conditions at the interface. The composite is obtained by introducing into an infinite homogeneous planar matrix a periodic set of inclusions of a different material and the diameter of each inclusion is proportional to a real positive parameter.
After a brief introduction on composit materials, transmission boundary conditions, and the effective conductivity, we will discuss the way how to obtain the series expansion for the effective conductivity, and a fully constructive method to compute explicitly the coefficients of such series by solving recursive systems of integral equations. Also, we will solve some of them in case the inclusions are in the form of a disk.
The talk will be of an introductory type and is intended for a general audience.

Norm attaining mappings

Wednesday 17 January 2018 h. 14:30, Room 2BC30
Marija Soloviova (Padova, Dip. Mat.)
“Norm attaining mappings”

This talk is about approximation by norm attaining mappings.
We start with some basic notions of Functional Analysis. In the first part we recall the classical results in this field, like Bishop-Phelps-Bollobas' theorem, James' weak compactness theorem.
In the second part we present our joint with Vladimir Kadets and Miguel Martin results of the paper “Norm-attaining Lipschitz functionals” (2016), where we introduce a concept of norm attainment for Lipschitz functionals.
The seminar will be of introductory type.

Stochastic models for energy forward markets

Wednesday 20 December 2017 h.14:30, Room 2BC30
Marco Piccirilli (Padova, Dip. Mat.)
“Stochastic models for energy forward markets”

I will present a probabilistic modeling framework for forward prices, specifically designed for energy markets. Most of the presentation will be kept at an intuitive level, as far as this is possible and sensible. I will start by explaining the general framework of the talk and then move to our contribution, of course describing the underlying mathematical theory as well.
This talk is based on joint work with Fred Espen Benth, Luca Latini and Tiziano Vargiolu.

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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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.

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