|18/02/20||16:00||17:00||1101 D'Antoni||Finnur Larusson||Università' di Adelaide||Legendrian holomorphic curves in complex projective 3-space and
superminimal surfaces in the 4-sphere|
I will describe new joint work with Antonio Alarcon and Franc
Forstneric. Complex projective 3-space CP^3 carries an essentially unique
complex contact structure, which is of interest for a number of reasons.
We study holomorphic immersions and general holomorphic maps from Riemann
surfaces to CP^3 that are Legendrian with respect to this structure.
For example, we prove approximation and interpolation theorems for such maps,
and we prove that every Riemann surface admits a complete injective
Legendrian holomorphic immersion into CP^3.
We use the twistor projection from CP^3 onto the 4-sphere to derive corollaries for
superminimal surfaces in the 4-sphere.
|18/02/20||Seminario||14:30||15:30||1201 Dal Passo||Margerita Nolasco||Universita' dell'Aquila||Least energy solution for the relativistic electron in a Coulomb external potential|
We study the normalized solutions of a nonlinear eigenvalue problem for a model of a self-interacting spin-$1/2$ relativistic particle in an external electrostatic field generated by a heavy nucleus. The model is described by the Maxwell-Dirac equations coupled with an external Coulomb potential term. The first (positive) eigenvalue is the Lagrange multiplier lying in the positive part of the spectral gap of the essential spectrum of the Dirac-Coulomb operator. We prove the existence of a normalized least (positive) energy solution and we give a variational characterization for the lowest (positive) energy critical value (the "ground state" of the system).
|14/02/20||Seminario||14:00||15:00||1200 Biblioteca Storica||Paolo PAPI||"Sapienza" Università di Roma||Yangians vs. minimal W-algebras: a surprising coincidence
I will discuss a proof of the fact that the singularities of the R-matrix R(k) of the minimal quantization of the adjoint representation of the Yangian associated with a Lie algebra g are opposite to the roots of the monic polynomial that expresses the OPE of conformal fields with conformal weight 3/2 in the affine W-algebra of level k associated with g. I will then explain some interesting consequences.
This is a joint work with V. G. Kac and P. Moseneder-Frajria.
|14/02/20||Seminario||10:00||13:00||1201 Dal Passo||Workshop||Workshop: Regular and stochastic behaviour in dynamical systems |
|13/02/20||Seminario||10:00||17:00||1201 Dal Passo||Workshop||Workshop: Regular and stochastic behaviour in dynamical systems|
|12/02/20||16:00||17:00||1101 D'Antoni||Yasuyuki Kawahigashi||University of Tokyo||"Relative boundary-bulk duality and orbifold subfactors"
Minicorso di Dottorato - prima lezione
|12/02/20||Seminario||10:00||17:00||1201 Dal Passo||Workshop||Workshop: Regular and stochastic behaviour in dynamical systems
|11/02/20||Seminario||14:30||15:30||1201 Dal Passo||Beatrice Pelloni||Heriot-Watt University||The mathematical theory of some geophysical flow models
The mathematical and numerical analysis of models for atmospheric flows is still a formidable mathematical challenge. The semi-geostrophic equations are a particular system of partial differential equations, widely used in the modelling of large-scale atmospheric flows. In this talk I will review the mathematical ideas and results that have enabled spectacular progress in the past 25 years, as well as discuss the many problems that are still open.
Note: This talk is part of the activity of the MIUR Department of Excellence Grant 2018-2022, CUP E83C18000100006.
|07/02/20||Seminario||15:15||16:15||1101 D'Antoni||Luigi Lombardi||Università di Milano||Fibrazioni di varietà algebriche ed equivalenze derivate
In questo seminario descriverò il comportamento di alcune classi di fibrazioni di varietà complesse su varietà di dimensione di Albanese massima sotto equivalenze derivate.
Il primo risultato principale è che ogni equivalenza derivata induce una corrispondenza biunivoca tra gli
insiemi delle classi di isomorfismo di fibrazioni su curve lisce proiettive di genere maggiore od uguale a 2. Inoltre questa corrispondenza preserva le basi delle fibrazioni. Infine presenterò il caso di fibrazioni su varietà di dimensione superiore, relazionandolo alla congetturata invarianza derivata dei numeri di Hodge.
|07/02/20||Seminario||14:00||15:00||1101 D'Antoni||Riccardo ARAGONA||Università de L'Aquila||Group theoretical approach for symmetric encryption
In 1949 Shannon gave the first abstract definition of cipher as a set of transformations on a message space. In 1975, Coppersmith and Grossman studied the group generated by a set of bijective transformations defining a cipher and the link of some properties of this group with the security of the corresponding cipher. From this work a new research sector in algebraic crypto-graphy arises, that of the study of the properties of the group generated by the encryption functions of a cipher that can reveal weaknesses in the cipher itself.
In the first part of the talk, after presenting the algebraic background describing the structure of block ciphers, we will explain the link between the study of permutation groups and the study of the security of symmetric cryptosystems.
In the second part of the talk we will present some new results that characterize the properties of the components of a block cipher which imply that the group generated by its encryption functions has those properties that make it resistant against known algebraic attacks.