vi annuncio il seguente seminario:
Giovedi' 20 novembre 2014, ore 14.30
Aula 3, Dipartimento di Matematica e Informatica,
via Machiavelli 30
Massimiliano ROSINI (ICM, University of Warsaw-Polonia)
"Conservation laws with point constraints on the flow"
Tutti gli interessati sono invitati a partecipare. Cordiali saluti,
Michele Miranda.
]]>speaker: Davide ADDONA (Universita' di Milano Bicocca)
title: "A Semi-Linear Backward Parabolic Cauchy Problem with Unbounded Coefficients of Hamilton-Jacobi-Bellman Type and Applications to optimal control"
Abstract: We obtain weighted uniform estimates for the gradient of the solutions to a class of linear parabolic Cauchy problems with unbounded coefficients. Such estimates are then used to prove existence and uniqueness of the mild solution to a semi-linear backward parabolic Cauchy problem, where the differential equation is the Hamilton-Jacobi-Bellman equation of a suitable optimal control problem. Via backward stochastic differential equations, we show that the mild solution is indeed the Value Function of the controlled equation and that the feedback law is verified.
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We establish that the Lavrentiev phenomenon does not occur for autonomous
problems in the multiple integrals Calculus of Variations, provided that the inte-
grand is convex with respect to the gradient variable. The main novelty is that
no other (artificial) restriction is assumed on the integrand or on the domain. The
core of the proof is based on a new approximation result for a parametric version
of the variational problem.
Abstract: Efficient enumeration of small objects in an abstract class may require deep structure theory (for instance, for groups) or smart combinatorial tricks (for instance, for quasigroups). I will talk about two important classes of quandles, where both approaches find their place. Certain configurations in transitive groups are used to describe algebraically connected quandles (these are the ones used for coloring knots). Then the deep theory of transitive groups can be exploited to enumerate connected quandles, currently up to size 47 and of sizes p, p^2, p^3, 2p for a prime p. Another class, medial quandles, is described using a heterogeneous affine structure over the orbit decomposition. A few combinatorial tricks then allow for enumeration of small medial quandles. For example, we can calculate that the number of isomorphism classes of 15-element medial quadles is 563753074951.
Il primo seminario avrà luogo Martedì 18 novembre alle ore 16 in aula 1. Seguono titolo e Abstract.
We shall review the basic properties of Ext and Tor functors of a graded R-ring, where R denotes a semisimple ring. A key tool in our investigation will be played by the bar resolution of R. The dual case, corresponding to a graded $R$-coring, will also be discussed.
Koszul rings were introduced by Beilinson, Ginzburg and Soergel, as natural generalization of Koszul algebras, which play a fundamental role in Representation Theory. Our aim is to present the most important properties of this class of rings, using a new method which based on the so called Koszul pairs. By duality, Koszul corings are introduced and investigated. Several examples and applications will be presented.
ABSTRACT:
"In this talk, we show under what additional ingredients a left module in negative degrees over an operad with multiplication can be given the structure of a cyclic k-module and how the underlying simplicial homology gives rise to a calculus structure (or Batalin-Vilkovisky module) over the cohomology of the operad, which is in some sense a dual picture to the relationship between cyclic operads and Batalin-Vilkovisky algebras. In particular, we obtain explicit expressions for a generalised Lie derivative as well as a generalised (cyclic) cap product that obey a Cartan-Rinehart homotopy formula. Examples include the calculi known for the Hochschild theory of associative algebras, for Poisson structures, but above all the calculus for a general left Hopf algebroid with respect to general coefficients (in which the classical calculus of vector fields and differential forms is contained)."
Claudia Menini
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Abstract: We develop a strategy to compute all liftings of a Nichols
algebra over a finite dimensional cosemisimple Hopf algebra. We produce
them as cocycle deformations of the bosonization of these two. The
process also produces new examples of (infinite dimensional) Hopf
algebras, as well as bi-Galois objects associated to bosonizations of
(pre-)Nichols algebras and their liftings.
Il primo seminario avrà luogo Martedì 18 novembre alle ore 16 in aula 1. Seguono titolo e Abstract.
We shall review the basic properties of Ext and Tor functors of a graded R-ring, where R denotes a semisimple ring. A key tool in our investigation will be played by the bar resolution of R. The dual case, corresponding to a graded $R$-coring, will also be discussed.
Koszul rings were introduced by Beilinson, Ginzburg and Soergel, as natural generalization of Koszul algebras, which play a fundamental role in Representation Theory. Our aim is to present the most important properties of this class of rings, using a new method which based on the so called Koszul pairs. By duality, Koszul corings are introduced and investigated. Several examples and applications will be presented.
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Abstract: We prove that for n>2 there exists a quandle of cyclic type of size n
if and only if n is a power of a prime number. This establishes a
conjecture of S. Kamada, H. Tamaru and K. Wada. As a corollary, every
finite quandle of cyclic type is an Alexander quandle. We also prove
that finite doubly transitive quandles are of cyclic type. This
establishes a conjecture of H. Tamaru.
Claudia Menini
]]>Claudia Menini
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Dopo l'iscrizione, verrà inviata una email di conferma con le informazioni necessarie per entrare nella riunione.
Contatto di riferimento: Maria Teresa BORGATO
Per informazioni scrivere a: federica.ferretti5@gmail.com