Notiziario Scientifico
Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica G. Castelnuovo
Sapienza Università di Roma
Settimana dal 9 al 15 aprile 2018
Lunedì 9 aprile 2018
Ore 14:15, aula di Consiglio
seminario di Analisi Matematica
Carlo Mantegazza (Università di Napoli Federico II)
Evolution by curvature of networks in the plane
We will present the state-of-the-art of the problem of the motion by curvature of a
network of curves in the plane, discussing existence, uniqueness, singularity formation
and asymptotic behavior of the flow.
Martedì 10 aprile 2018
Ore 10:00, aula 2E, Dipartimento di Scienze di Base e Applicate per Ingegneria
(SBAI), via A. Scarpa 14
corso di dottorato
Giovanni Cerulli Irelli (Sapienza Università di Roma)
Quiver representations and cluster algebras, I
We will give an introduction to the representation theory of quivers and finite dimensional
algebras. We will then apply the theory to study the geometry of quiver Grassmannians.
Time permitting we will see applications to the Fomin-Zelevinsky theory of cluster algebras.
The course is intended for non--expert with standard background in mathematics.
Martedì 10 aprile 2018
Ore 14:30, aula Dal Passo, dipartimento di Matematica,
Università di Roma Tor Vergata, via della Ricerca Scientifica 1
seminario di Equazioni Differenziali
Massimo Grossi (Sapienza Università di Roma)
Radial nodal solution for Moser-Trudinger problems
We study the asymptotic behavior of least-energy nodal solutions for suitable
Moser-Trudinger problems. We will show that appear different phenomena with respect
to other nonlinearities (for example power or sinh-type nonlinearites).
Martedì 10 aprile 2018
Ore 14:30, aula 311, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Probabilità
Hubert Lacoin (IMPA, Rio de Janeiro)
Wetting and Layering for Solid-and-Solid
Solid-on-Solid (SOS) was introduced in the early 50s as a simplified model for lattice interfaces.
It is believed to display the same low temperature behavior as three-dimensiona systems with phase
coexistence while being considerably easier to analyze.
The objective of this talk is to present the result we recently obtained for SOS interacting with
a solid substrate, which is the problem associated with the following energy functional
\[
V(\phi)= ta \sum_{x\sim y} |\phi(x)-\phi(y)|
-\sum_{x} \left(h{f 1}_{{\phi(x)=0}}-\infty{f1}_{{\phi(x)<0}}
ight)
\]
for \((\phi(x))_{x\in\mathbf{Z}^2}\) (the graph of \(\phi\) representing the interface).
We prove that for \(ta\) sufficiently large, there exists a decreasing sequence
\((h^*_n(ta))_{n\ge 0}\), satisfying \(\lim_{n o\infty}h^*_n(ta)=h_w(ta)\),
and such that:
(A) The free energy associated with the system is infinitely differentiable on
\(\mathbf{R} \setminus \left( {h^*_n}_{n\ge 1}\cup h_w( ta )
ight)\), and not
differentiable on \({h^*_n}_{n\ge 1}\).
(B) For each \(n\ge0\) within the interval \((h^*_{n+1},h^*_n)\) (with the convention
\(h^*_0=\infty\)), there exists a unique translation invariant Gibbs state which is localized
around height \(n\), while at a point of non-differentiability, at least two ergodic Gibbs states
coexist. The respective typical heights of these two Gibbs states are \(n-1\) and \(n\).
The value \(h^*_n\) corresponds thus to a first order layering transition from level
\(n\) to level \(n-1\).
Mercoledì 11 aprile 2018
Ore 14:00, aula di Consiglio
seminario di Algebra e Geometria
Thomas Schick (Georg-August-Universität Göttingen)
Minimal hypersurfaces and positive scalar curvature
There is a long history to find relations between the topology of a smooth manifold and its
(Riemannian) geometry. The first such is the Gauss-Bonnet theorem which says that the Euler
characterestic of a compact 2-dimensional surface without boundary is (upto a positive constant)
the scalar curvature of that manifold. Particular conclusion: if the Euler characterestic is not
positive (i.e. if the surface is not a sphere or a real projective plane) then there is no metric
such that the scalar curvature is everywhere positive.
The use of the Dirac operator allows to obtain similar obstructions to the existence of positive
scalar curvature in higher dimension; but only for spin manifolds (as otherwise this operator
doesn't exist). There is one further approach -invented by Schoen and Yau, which does not rely
on the spin condition, but rather uses minimal hypersurfaces. We will present this approach and
its main implications. There are two crucial problems with this approach:
* in its initial incarnation, it requires regularity results on minimial hypersurfaces which are
available only in dimension less than 8,
* it needs a large integral first homology.
We will report on current work which aims to overcome part of these problems, due to Schoen-Yau
for the first problem, and developped in joint work with
Simone Cecchini for some aspects of the second problem. Specifically, we will introduce
and discuss the case of 'enlargeable manfolds' (as introduced by Gromov and Lawson).
Mercoledì 11 aprile 2018
Ore 14:30, aula F, Università di Roma Tre,
largo san Leonardo Murialdo 1
colloquium di Matematica
Massimiliano Sala (Università di Trento)
Optimal non-linear Boolean functions as multivariable polynomials: the even case
To guarantee security w.r.t. known attacks (especially differential cryptanalysis) it is necessary
to design a block cypher very carefully. One type of component which is often used is the so-called
S-Box (Substitution Box). It turns out that the ideal situation would be to have an APN (Almost Perfect
Nonlinear) permutation of dimension d even, possible 4, 8 or another power of 2. The experimental results
show that: there is no APN permutation for d=4, there is one APN permutation for d=6 (but there could
be more) and none has been found so far for d=8, being any higher dimension intractable with a computer
nowadays. In recent papers, we have investigated the situation by considering APN permutations as
multivariable polynomials (vectorial Boolean functions). In other words, they are polynomial maps from
a binary space of dimension d to itself. We have proved several theoretical results (that partially
explain the computational findings): no component can have degree less than three (for any d even),
no APN permutations exist for d=4, no pure cubic APN permutations exist for d=6.
This is joint work with M. Calderini, I. Villa and M. Zaninelli.
Mercoledì 11 aprile 2018
Ore 17:00, aula di Consiglio
seminario di Fisica Matematica
Vojkan Jaksic (McGill University, Montreal)
Time and Entropy
This talk concerns mathematical theory of the so-called Fluctuation Relation (FR) and Fluctuation
Theorem (FT) in context of dynamical systems relevant to physics. The FR refers to a certain universal
identity linked to statistics of entropy production generated by a reversal operation and FT to the
related mathematical large deviations result. The discovery of FR goes back to numerical experiments
and Evans, Cohen and Morris (1993) and theoretical works of Evans and Searles (1994), Gallavotti and
Cohen (1995). These discoveries generated an enormous body of numerical, theoretical and experimental
works which have fundamentally altered our understanding of non-equilibrium physics, with applications
extending to chemistry and biology. In this talk I will introduce modern theory of FR and FT on an
example and comment on a current research program on this topic.
Giovedì 12 aprile 2018
Ore 14:30, aula 311, Università di Roma Tre,
largo san Leonardo Murialdo 1
seminario di Fisica Matematica
A. Sorrentino (Università di Roma Tor Vergata)
On Birkhoff conjecture for convex billiards
A mathematical billiard is a system describing the inertial motion of a point mass inside a domain,
with elastic reflections at the boundary. This simple model has been first proposed by G.D. Birkhoff
as a mathematical playground where 'it the formal side, usually so formidable in dynamics, almost
completely disappears and only the interesting qualitative questions need to be considered'.
Since then billiards have captured much attention in many different contexts, becoming a very popular
subject of investigation. Despite their apparently simple (local) dynamics, their qualitative dynamical
properties are extremely non-local. This global influence on the dynamics translates into several
intriguing rigidity phenomena, which are at the basis of several unanswered questions and conjectures.
In this talk I shall focus on some of these questions. In particular, I shall describe some recent
results related to the classification of integrable billiards (also known as Birkhoff conjecture).
Giovedì 12 aprile 2018
Ore 15:00, aula 7, Università UNINT, via Cristoforo Colombo 200
seminario
Liviu Ornea (Università di Bucarest)
Potenziali positivi su varietà localmente conformemente kaehleriane compatte
Verrà mostrato che, se una varietà LCK compatta ammette un potenziale sul rivestimento
universale, sul quale il gruppo delle trasformazioni del rivestimento agisce in modo naturale (automorfo),
allora la varietà ammette anche un potenziale positivo, sempre automorfo. Questo è un
risultato ottenuto assieme a Misha Verbitsky.
Venerdì 13 aprile 2018
Ore 14:30, aula D'Antoni, dipartimento di Matematica,
Università di Roma Tor Vergata, via della Ricerca Scientifica 1
seminario
Velleda Baldoni (Università di Roma Tor Vergata)
Multiplicities & Kronecker coefficients
Multiplicities of representations appear naturally in different contexts and as such their description
could use different languages. The computation of Kronecker coefficients is in particular a very
interesting problem which has many applications.
I will describe an approach based on methods from symplectic geometry and residue calculus (joint work
with M. Vergne and M. Walter). I will state the general formula for computing Kronecker coefficients and
then give many examples computed using an algorithm that implements the formula.
The algorithm does not only compute individual Kronecker coefficients, but also symbolic formulas that
are valid on an entire polyhedral chamber. As a byproduct, it is possible to compute several Hilbert series.
Venerdì 13 aprile 2018
Ore 16:00, aula Picone
seminario per insegnanti (Piano Lauree Scientifiche)
Fabio Spizzichino (Sapienza Università di Roma)
Il calcolo combinatorio nel Liceo matematico
Venerdì 13 aprile 2018
Ore 16:00, aula D'Antoni, dipartimento di Matematica,
Università di Roma Tor Vergata, via della Ricerca Scientifica 1
seminario
René Schoof (Università di Roma Tor Vergata)
Il teorema di Lagrange per schemi in gruppi piatti e finiti
Il teorema di Lagrange dice che in un gruppo di cardinalità n la potenza n-esima di ogni elemento
è uguale all'elemento neutro. Una congettura classica afferma che un risultato simile vale per
schemi in gruppi piatti e finiti. Spiegherò la dimostrazione di un caso speciale della congettura.
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