Prossimi Seminari di Geometria a
10 Maggio 2018,
ore 14, Aula A1.4, Coppito 0
Conferenziere: Eugenio Vecchi
Titolo: Gauss Curvature in The Heisenberg Group.
The notion of Gauss and mean curvature
play a crucial role in the study of differential geometry of
smooth Euclidean surfaces embedded in the Euclidean space.
In the first
Heisenberg group H there is a currently well accepted notion of
horizontal mean curvature for smooth Euclidean surfaces, but it
is still not understood what could be a reasonable candidate for
the notion of horizontal Gauss curvature. In this talk I will
suggest a possible definition based on the so called Riemannian
approximation scheme. I will also present a Heisenberg version
of the well known Gauss-Bonnet theorem for Euclidean C2-smooth,
oriented and compact surfaces in H. If time permits, I will also
show the connection to a localized Steiner-type formula which
holds in H.
The talk is
based on a joint work with Z.M. Balogh and J.T. Tyson.
Seminari (passati) di Geometria a
19 Aprile 2018, ore 14,
Aula A1.4, Coppito 0
Conferenziere: Joan Pons-Llopis
Titolo: Ulrich bundles on projective varieties.
Abstract: For a vector bundle E on a projective variety X, the
condition of having no intermediate cohomology- namely being
"arithmetically Cohen-Macaulay" - imposes very
strong restictions on E. For istances, thanks to Horrocks'
theorem, we know that any aCM bundle on the projective space
should totally split.
Ulrich proved that, for aCM bundles, there exists a bound on the
dimension of their space of global sections. Therefore, we can
even strengthen the requirements and pay attention to
those aCM bundles attaining this bound (i.e., Ulrich bundles).
Despite all of these constraints, it was asked by Eisenbud and
Schreyer wheter any projective variety supports an Ulrich
bundle. In this talk I intend to report on the history of this
problem as well as to explain the contributions that
I have obtained.
20 Febbraio 2018, ore 12,30, Aula A1.3,
Conferenziere: Ricardo Sa Earp, PUC-Rio (RJ-Brasil)
Titolo: On the reflection principle for minimal surfaces.
Abstract: We present a reflection principle for minimal surfaces in
smooth three manifolds, joint work with Eric Toubiana, Univ Paris
5 Dicembre, ore 12,30, Aula A1.3, Coppito 0
Conferenziere: Luciano Mari, Scuola Normale Superiore
Titolo: Maximum principles at infinity and the
Abstract: Maximum principles at infinity (or "almost maximum
principles"), such as for instance Ekeland and Omori-Yau principles,
are a powerful tool to investigate the geometry of Riemannian
Their validity is intimately related to the geometry of the
underlying space M, and exhibits deep relations with the theory of
stochastic processes on M and to potential theory. In the first part
of the talk, I will present a survey of a few geometric applications
to motivate the study of these principles, and discuss their link
with probability. Then, I will discuss a recent underlying duality
with the existence of suitable exhaustion functions called
Khas'minskii potentials. Indeed, duality holds for a broad class of
fully-nonlinear operators of geometric interest.
This is joint work with Leandro F. Pessoa
28 Novembre, ore 12,30 Laboratorio di Matematica Applicata
Conferenziere: Luigi Vezzoni, Università Di Torino
Titolo: Alexandrov's theorem and its generalizations
Abstract: The celebrated “Soap Bubble Theorem” of
Alexandrov affirms that the spheres are the unique compact embedded
hypersurfaces of the Euclidean space having constant mean curvature.
Alexandrov proved the theorem introducing the method of moving
planes, a very powerful technique which has been the source of many
insights in analysis and differential geometry. Furthermore in the
statement of the theorem the compactness and the embeddedness
assumptions cannot be removed, due to some examples in literature
(such as the Wente torus and some surfaces of Kapouleas). The talk
aims to give a wide and basic exposition of these topics, as well as
an introduction to some recent generalizations which I have obtained
in collaboration with Giulio Ciraolo.
24 Ottobre, ore 12:30 aula
A1.3, Coppito 0
Conferenziere: Giuseppe Pipoli, Università dell'Aquila
Titolo: Inverse mean curvature flow in complex hyperbolic
Abstract: During last decades, the study of geometric flows is a
very active field in geometry and analysis. The inverse mean
curvature flow is perhaps the most important among the expanding
flows, with deep meaning in general relativity too. We will
discuss the evolution of a star-shaped closed and mean convex
hypersurface in the complex hyperbolic space, showing
similarities and differences with the previous cases. The main
new phenomenon is that, in our case, the induced metric, even
after a rescaling, degenerates in a special direction and
converges to a sub-Riemannian limit.
3 Ottobre, ore 12:30, aula
A1.3, Coppito 0
Conferenziere: Margherita Lelli Chiesa, Università dell'Aquila
Titolo: Curves on K3 surfaces
Abstract: I will report on both classical and more recent
results concerning curves lying on K3 surfaces, highlighting
their relevance in the study of the birational geometry of the
moduli space of algebraic curves of fixed genus. Nikulin
surfaces, that is, K3 surfaces endowed with a nontrivial double
cover branched along eight disjoint rational curves, play a
similar role at the level of the moduli space of Prym curves
parametrizing étale double covers of curves of fixed genus. I
will mention current work in this direction joint with Knutsen
13 Giugno, ore 14.30 aula C1.9 (Coppito 2)
Conferenziere: Francesco Mercuri, Universidade Estadual
de Campinas & Università dell'Aquila
Titolo: Una breve storia della congettura generalizzata di
Poincaré e questioni connesse
Sunto: La congettura generalizzata di Poincaré puó essere
enunciata come segue:
Sia M^n una varietà omotopicamente equivalente alla sfera S^n.
Allora M^n = S^n.
In questo seminario discuteremo alcune risposte note per
questa questione ed alcuni problemi aperti,
specialmente relazionati al significato di varietà ed a
quello di M^n = S^n.
30 Maggio, ore 14.30 aula C1.10 (Coppito 2)
Conferenziere: Giuseppe Tinaglia, King's College London
Titolo: The geometry of constant mean curvature surfaces in
Sunto: In this talk I will begin by reviewing classical
properties of constant mean curvature surfaces, H>0, in
R^3. I will then
talk about several geometric results for surfaces embedded in
constant mean curvature, such as curvature and radius
simply-connected surfaces embedded in R^3 with constant mean
Finally I will show applications of such estimates including a
characterisation of the round sphere as the only
surface embedded in R^3 with constant mean curvature and area
for compact surfaces embedded in a flat torus with constant
curvature and finite genus. This is joint work with Meeks.
16 Maggio 2017, ore 14.30, aula A1.4 (Coppito 0)
Conferenziere: Vlad Moraru, Universita' dell'Aquila
Titolo: Interaction between minimal surfaces and scalar curvature.
Sunto: In the late 1970s R. Schoen and S.T. Yau discovered a deep
connection between the sign of the scalar curvature of a
and the topology of stable minimal surfaces contained in M; namely
non-negative ambient scalar curvature is an obstruction to the
topological richness of stable minimal surfaces contained in M. I
explain this relationship and survey various old and new rigidity
results following from it. Among these, I will discuss recent
with O. Chodosh and M. Eichmair. which confirms a conjecture by
Fischer-Colbrie-Schoen and Cai-Galloway: A complete 3-manifold
non-negative scalar curvature and containing an area-minimising