Prossimi Seminari

Mercoledì 28 Giu ore 11:00
presso Seminario II
seminario di algebra e geometria
Un teorema di compattezza in omologia persistente invariante per gruppi
Nicola Quercioli
Il confronto metrico è una tematica molto importante nell'ambito dell'analisi topologica dei dati (TDA). Uno strumento per tale confronto è la pseudo-distanza naturale, che misura la differenza fra funzioni a valori reali definite su uno spazio topologico X rispetto a un sottogruppo G del gruppo H di tutti gli omeomorfismi da X in X. Limitazioni inferiori di tale metrica possono essere ottenute calcolando l'omologia persistente delle funzioni considerate. Sfortunatamente tali limitazioni hanno un'invarianza troppo estesa, essendo l'omologia persistente classica invariante rispetto all'azione dell'intero gruppo H. Nel nostro seminario esporremo un nuovo metodo per ridurre tale invarianza a quella ristretta all'azione del solo gruppo G. Questo metodo è basato sull'introduzione, sotto opportune ipotesi, di operatori non espansivi invarianti per G. Nella seconda parte del seminario esporremo un teorema di compattezza per lo spazio topologico di tali operatori, che garantisce la possibilità di ottenere approssimazioni arbitrariamente buone della pseudo-distanza naturale senza ricorrere al suo calcolo diretto, che è notoriamente piuttosto difficile.
Mercoledì 28 Giu ore 14:00
presso Palazzo Marchesini, via Marsala 26, Bologna
Adiacente possibile, creatività ed innovazione
Giovedì 29 Giu ore 11:00
presso Seminario I
seminario di analisi numerica
nell'ambito della serie
Topics in Mathematics 2016/2017
Application of sparse data processing
Ivan Selesnick
Giovedì 29 Giu ore 14:15
presso Seminario II
seminario interdisciplinare
nell'ambito della serie
Topics in Mathematics 2016/2017
Una mini-introduzione ai biliardi iperbolici, 1
Marco Lenci
Lunedì 03 Lug ore 14:00
presso Seminario I
seminario di analisi matematica
On pseudo H-type Lie algebras (parte I)
Irina Markina
Abstract: In this mini course we will introduce and study 2-step nilpotent Lie algebras, closely related to the Clifford algeras. The pseudo H-type Lie algebras, are generalisations of the Heisenberg type Lie algebras, introduced by Aroldo Kaplan at 1980 for the study of hypoelliptic operators. The mini course will include the following topics. 1. Definition of pseudo H-type Lie algebras. We give equivalent definitions of the pseudo H-type Lie algebras, that originated from the composition of quadratic forms, the representation of the Clifford algebras and isometric properties of the adjoint operator on the Lie algebra. 2. Relation of pseudo H-type Lie algebras and representations of Clifford algebras. Representations of Clifford algebras can be used for the construction of the Lie algebras if and only if the representation space can be endowed with a non degenerate bi-linear symmetric form, making the representation map skew symmetric with respect to this form. We will explain main difficulties of finding such a non-degenerate bi-linear symmetric form and provide several examples of the construction of the pseudo H-type Lie algebras from the Clifford algebra representations, including those that were introduced by A. Kaplan. 3. We will show the method of construction of a special basis for the pseudo H-type Lie algebras, such that the structural constants of the Lie algebras are always 0, 1 or -1. We show that the Bott periodicity of the Clifford algebras are naturally inherited by the pseudo H-type Lie algebras. It allows to reduce the construction to some basic cases. 4. We will show that infinite number of Clifford algebras leads to the infinite number of pseudo H-type Lie algebras. Moreover, the isomorphism of Clifford algebras is not automatically transmitted to the isomorphism of the Lie algebras. We will provide a complete classification of pseudo H-type Lie algebras. 5. The last topic is the description of automorphism groups of the pseudo H-type Lie algebras. It is not a closed topic still, nevertheless, I will inform on some achieved results.
Lunedì 03 Lug ore 14:15
presso Aula Arzelà
seminario di algebra e geometria
On the number and boundedness of minimal models of a variety of general type
Diletta Martinelli
Finding minimal models is the first step in the birational classification of smooth projective varieties. After it is established that a minimal model exists some natural questions arise such as: is it the minimal model unique? If not, how many are they? After recalling all the necessary notions of the Minimal Model Program, I will explain that varieties of general type admit a finite number of minimal models. I will talk about a recent joint project with Stefan Schreieder and Luca Tasin where we prove that this number is bounded by a constant depending only on the canonical volume. It follows that in any dimension, minimal models of general type and bounded volume form a bounded family. I will also show that in some cases for threefolds, it is possible to compute this constant explicitly.
Martedì 04 Lug ore 14:15
presso Seminario II
seminario interdisciplinare
nell'ambito della serie
Topics in Mathematics 2016/2017
Una mini-introduzione ai biliardi iperbolici, 2
Marco Lenci
Mercoledì 05 Lug ore 11:00
presso Seminario I
seminario di analisi numerica
Sparse-regularized Least Squares and Nonlinear Smoothing
Ivan Selesnick
In this talk, we describe how certain signal smoothing problems can be formulated using sparse-regularized least squares. The L1 norm is often used for this purpose because it preserves the convexity of the objective function to be minimized. We describe novel non-convex regularizers that outperform the L1 norm, yet preserve the convexity of the objective function.
Giovedì 06 Lug ore 10:00
presso Seminario I
seminario di analisi numerica
Sparse regularization: applications in image processing
Ivan Selesnick
Seminario riservato al gruppo di ricerca di Image Processing di Analisi Numerica
Giovedì 06 Lug ore 11:15
presso Seminario II
seminario interdisciplinare
nell'ambito della serie
Topics in Mathematics 2016/2017
Una mini-introduzione ai biliardi iperbolici
Marco Lenci
Giovedì 06 Lug ore 14:00
presso Seminario I
seminario di analisi matematica
On pseudo H-type Lie algebra (parte II)
Irina Markina
Martedì 25 Lug ore 10:00
presso Seminario II
seminario interdisciplinare
Periodic direct problem for the self-focusing Nonlinear Schrodinger equation
Petr Grinevich
We present some recent results obtained in collaboration with P.M. Santini (Universiy of Roma I). We consider the periodic direct spectral problem for the self-focusing NLS equation in a special situation corresponding to a small perturbation of the constant solution. This model is actively used now as a model for generation of the rogue waves in nonlinear medias. We show that in this special situation all ingredients of the theta-functional formulas can be efficiently calculated as explicit power series with respect to the amplitude of the perturbation.
Martedì 25 Lug ore 10:00
presso Seminario II
seminario di analisi matematica
Periodic direct problem for the self-focusing Nonlinear Schrodinger equationa
Petr Grinevich
The results presented have been obtained in collaboration with P.M. Santini (University of Roma I). We consider the periodic direct spectral problem for the self-focusing NLS equation in a special situation corresponding to a small perturbation of the constant solution. This model is actively used now as a model for generation of the rogue waves in nonlinear medias. We show that in this special situation all ingredients of the theta-functional formulas can be efficiently calculated as explicit power series with respect to the amplitude of the perturbation.
Venerdì 28 Lug ore 15:00
presso Seminario II
seminario di analisi matematica
Spectral theory of the periodic spectral-meromorphic singular operators and the Bloch varieties
Petr Grinevich
We present some recent results obtained in collaboration with S.P. Novikov (Steklov Institute and University of Maryland). We study the spectral theory for ordinary differential operators with special singularities such that all eigenfunctions are locally meromorphic near all real singular points. Such operators are called spectrally-meromorphic. In particular, all singular finite-gap operators satisfy this condition. We show that for periodic spectrally-meromorphic operators the Bloch variety is well-defined, and this observation provides a natural way to show that at least locally our operators can be approximated by the finite-gap ones.