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.

Introduction to kernel-based methods

Wednesday 18 March 2015 h. 14:30, room 2BC30
Gabriele Santin (Padova, Dip. Mat.)
"Introduction to kernel-based methods"

In this talk we give an introduction to kernel-based methods and to their application in different fields of applied mathematics.
We consider some examples that motivate the use of kernel-based 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 kernel-based methods, we will introduce the problem of the determination of optimal subspaces for kernel-based multivariate approximation. We will give some insight into the problem and discuss possible applications.

Automorphism-invariant modules

Wednesday 25 February 2015 h. 15:30, room 2BC30
Khanh Tung Nguyen (Padova, Dip. Mat.)
"Automorphism-invariant modules"

In this talk, after recalling some basic concepts, we mention the class of injective modules, the class of quasi-injective modules and their generalization, the class of automorphism-invariant modules.
Next, we give some results related to the endomorphism rings of automophism-invariant modules and their injective envelopes.
Finally, we show a connection between automorphism-invariant modules and bolean rings.

Metastability of the Ising model on random graphs at zero temperature

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"

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.

Shape sensitivity analysis for vibrating plate models

Wednesday 28 January 2015, h. 14:30, room 2BC30
Davide Buoso (Padova, Dip. Mat.)
"Shape sensitivity analysis for vibrating plate models"

In this talk, we consider two different models for the vibration of a clamped plate: the Kirchhoff-Love model, which leads to the well known biharmonc operator, and the Reissner-Mindlin 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 Hadamard-type formulas for shape derivatives. Using these formulas, we prove that balls are critical domains for the symmetric functions of the eigenvalues under volume constraint.

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