Doctoral School in Mathematical Science - Opening Day 2015/2016

The opening day of the Doctoral School in Mathematics will take place on October 7, 2015, at
in room 1BC45.

11:30: meeting, brief introduction of Seminario Dottorato 2015/16
11:30-12:30: talk of Daria Ghilli "Rare events in finance by PDE methods"
12:30-13-30: presentation of the activities/courses of PhD Programme 2015/16
13:30: refreshments at the common room of 7th floor

For further information feel free to contact Pierpaolo Soravia.

Rare events in finance by PDE methods

Wednesday 7 October 2015 h.11:30, Room 1BC45
Daria Ghilli (Padova, Dip. Mat.)
“Rare events in finance by PDE methods"

Rare events, or tails events, are events which happen only “rarely", in other words, they are situated in the tails of the distribution. Take for example the well-known experiment of tossing a coin: our experience (and also the law of large numbers) says that, after a big enough number of tosses, the most probable value for the empirical mean of the outcomes is 1/2. But what about the probability of being far from 1/2? This is a typical rare event.
The theory who deals with the estimation of tails events is called "large deviations theory" and has many applications, for example, in risk management and finance.
After an introduction to the theory, we consider applications to financial mathematics, concerning the estimation of price of particular type of options (out-of the money) near their maturity. These are typical financial objects whose value deteriorates quickly in time and then are considered, in this context, as rare events.
Our approach - mainly of analytical nature - is different from the classical probabilistic ones.

This seminar will be held as a special event during the OPENING DAY OF THE DOCTORAL SCHOOL.

Concorso pubblico per l'ammissione al Corso di Dottorato in Scienze Matematiche (XXXI ciclo) (Curriculi: Matematica, Matematica Computazionale) - A.A. 2015/2016

Concorso Pubblico per l’ammissione al
Corso di Dottorato in SCIENZE MATEMATICHE (XXXI ciclo)
(Curriculi: Matematica, Matematica Computazionale) – A.A. 2015/2016

Pubblicazione esito “valutazione titoli”
Si ricorda che la presente graduatoria ha carattere provvisorio. La graduatoria definitiva verrà pubblicata, come da bando di concorso (art. 8) dal 3 agosto 2015 mediante:

ValutazioneTitoli.pdf (Username: risultati2015, Password comunicata privatamente)

Why should people in approximation theory care about (pluri-)potential theory?

Wednesday 24 June 2015 h. 15:00, room 2BC30
Federico Piazzon (Padova, Dip. Mat.)
"Why should people in approximation theory care about (pluri-)potential theory?"

We give an introductory summary of results in (pluri-)potential theory that naturally come into play when considering classical approximation theory issues both in one and (very concisely) in several complex variables. We focus on Fekete points and the asymptotic of orthonormal polynomials for certain $L^2$ counterpart of Fekete measures. No specific knowledge on the topic is assumed.

An introduction to derived categories

Wednesday 10 June 2015 h. 14:30, room 2BC30
Francesco Mattiello (Padova, Dip. Mat.)
"An introduction to derived categories"

Derived categories were introduced in the sixties by Grothendieck and Verdier and have proved to be of fundamental importance in Mathematics.
Starting with a short review of the basic language of category theory, we will first introduce the notion of abelian category with the help of several examples. Then we will spend some time giving a thorough motivation for the construction of the derived category of an abelian category. Finally, we will look at a way to break a derived category into two pieces that permit (among other things) to recover the original abelian category.

Controllability and the numerical approximation of the minimum time function

Wednesday 27 May 2015 h. 14:30, room 2BC30
Thien Thuy Le Thi (Padova, Dip. Mat.)
"Controllability and the numerical approximation of the minimum time function"

In optimal control theory, minimum time problems are of interest since they appear in many applications such as robotics, automotive, car industry, etc.. The scope of this talk is to give a brief introduction of these problems. Controllability conditions under various settings are considered. Such conditions play a vital role in studying the regularity of the minimum time function T(x). Moreover, we will also introduce the HJB equation associated with a minimum time problem and approaches to computing T(x) approximately.

Variational methods in nonlinear elasticity: an introduction

Wednesday 6 May 2015 h. 14:30, room 2BC30
Alice Fiaschi (Padova, Dip. Mat.)
"Variational methods in nonlinear elasticity: an introduction"

After a brief introduction of the variational formulation for the standard model in nonlinear elasticity, we will consider the problem of finding the "right" space to describe the equilibrium configurations of an elastic body, from the point of view of the Calculus of Variations. In this framework, I will introduce the space of Young measures as a suitable space to describe materials exhibiting microstructures.

Preferences in AI

Wednesday 29 April 2015 h. 14:30, room 2BC30
Cristina Cornelio (Padova, Dip. Mat.)
"Preferences in AI"

Artificial Intelligence (AI) is a field that has a long history but still constantly and actively growing and changing. The applications of AI are several, for example web search, speech recognition, face recognition, machine translation, autonomous driving, automatic scheduling etc. These are all complex real-world problems, and the goal of artificial intelligence (AI) is to tackle these with rigorous mathematical tools: machine learning, search, game playing, Markov decision processes, constraint satisfaction, graphical models, and logic.
Recently, a new concept became very important in AI: the use of preferences. Let's think about social networks, online shops, systems that suggest music or films. In this talk it is presented an overview on the main applications of preferences in AI, like recommender systems, multi-agent decision making, computational social choice, stable marriage problems, uncertainty in preferences and qualitative preferences.

Sobolev spaces, differential operators and multipliers

Wednesday 15 April 2015 h. 16:00, room 2BC30
Aigul Myrzagaliyeva (Padova, Dip. Mat. and Eurasian Nat. Univ. Astana)
"Sobolev spaces, differential operators and multipliers"

In this talk, after recalling some basic notions of Sobolev spaces we give some examples, then we introduce differential operators and multipliers in pair of Sobolev spaces. We give the statement and motivation of the problem. Morever, we also present some open problems.

Zooming into p-adic curves

Wednesday 1 April 2015 h. 14:30, room 2BC30
Velibor Bojkovic (Padova, Dip. Mat.)
"Zooming into p-adic curves"

The goal of the seminar is to introduce the audience to the basic notions of Berkovich geometry through a toy example of a p-adic projective curve. After recalling the basic properties of a p-adic field, we motivate Vladimir Berkovich's approach to studying geometry over such fields and go into describing the structure of compact p-adic curves.

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