Wednesday 10 June 2015 h. 14:30, room 2BC30
Francesco Mattiello (Padova, Dip. Mat.)
"An introduction to derived categories"
Abstract
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.
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"
Abstract
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.
Wednesday 6 May 2015 h. 14:30, room 2BC30
Alice Fiaschi (Padova, Dip. Mat.)
"Variational methods in nonlinear elasticity: an introduction"
Abstract
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.
Wednesday 29 April 2015 h. 14:30, room 2BC30
Cristina Cornelio (Padova, Dip. Mat.)
"Preferences in AI"
Abstract
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 realworld 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, multiagent decision making, computational social choice, stable marriage problems, uncertainty in preferences and qualitative preferences.
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"
Abstract
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.
Wednesday 1 April 2015 h. 14:30, room 2BC30
Velibor Bojkovic (Padova, Dip. Mat.)
"Zooming into padic curves"
Abstract
The goal of the seminar is to introduce the audience to the basic notions of Berkovich geometry through a toy example of a padic projective curve. After recalling the basic properties of a padic field, we motivate Vladimir Berkovich's approach to studying geometry over such fields and go into describing the structure of compact padic curves.
Wednesday 18 March 2015 h. 14:30, room 2BC30
Gabriele Santin (Padova, Dip. Mat.)
"Introduction to kernelbased methods"
Abstract
In this talk we give an introduction to kernelbased methods and to their application in different fields of applied mathematics.
We consider some examples that motivate the use of kernelbased techniques. Each example can be included in the same framework, but allows to show and discuss different features that arise naturally in the particular application. The examples deal with multivariate scattered data approximation, optimal recovery in Hilbert spaces, numerical solution of PDE, machine learning, and statistics.
After building up the fundamental tools of kernelbased methods, we will introduce the problem of the determination of optimal subspaces for kernelbased multivariate approximation. We will give some insight into the problem and discuss possible applications.
Wednesday 25 February 2015 h. 15:30, room 2BC30
Khanh Tung Nguyen (Padova, Dip. Mat.)
"Automorphisminvariant modules"
Abstract
In this talk, after recalling some basic concepts, we mention the class of injective modules, the class of quasiinjective modules and their generalization, the class of automorphisminvariant modules.
Next, we give some results related to the endomorphism rings of automophisminvariant modules and their injective envelopes.
Finally, we show a connection between automorphisminvariant modules and bolean rings.
Wednesday 11 February 2015 h. 14:30, room 2BC30
Sander Dommers (Bologna, Dip. Mat.)
"Metastability of the Ising model on random graphs at zero temperature"
Abstract
In this talk I will introduce a random graph model known as the configuration model. After this, I will discuss the Ising model, which is a model from statistical physics where a spin is assigned to each vertex in a graph and these spins tend to align, i.e., take the same value as their neighbors. It is especially interesting to study the Ising model on random graphs. I will discuss some properties of this model. In particular, I will talk about the dynamics and metastability in this model when the interaction strength goes to infinity. This corresponds to the zero temperature limit in physical terms.
Wednesday 28 January 2015, h. 14:30, room 2BC30
Davide Buoso (Padova, Dip. Mat.)
"Shape sensitivity analysis for vibrating plate models"
Abstract
In this talk, we consider two different models for the vibration of a clamped plate: the KirchhoffLove model, which leads to the well known biharmonc operator, and the ReissnerMindlin model, which instead gives a system of differential equations. We point out similarities and differences, showing the connections between these two problems. Then we show some results concerning the stability of the spectrum with respect to domain perturbations.
After recalling the known results in shape optimization for the biharmomic operator, we state some analyticity results for the dependence of the eigenvalues upon domain perturbations and Hadamardtype formulas for shape derivatives. Using these formulas, we prove that balls are critical domains for the symmetric functions of the eigenvalues under volume constraint.
