GeCo GeDi Seminarshttps://gecogedi.dimai.unifi.it/seminars/en-usFri, 24 May 2019 16:56:52 +0000Geometry of Monge-Ampère equationshttps://gecogedi.dimai.unifi.it/seminar/1308/2019-05-24: A. Kotov.<p>In this lecture we will show how to use contact geometry for 1st and 2d order PDEs and explain what is a covering of a PDE. The latter will be illustrated on an example of a homogeneous PDE of Monge-Ampere type.</p>https://gecogedi.dimai.unifi.it/seminar/1308/Remarks on some $4$-forms in $\mathbb R^8$ and $\mathbb R^{16}$https://gecogedi.dimai.unifi.it/seminar/1292/2019-05-27: <a href="/person/156/">P. Piccinni</a>.<p>It will be a linear algebra talk, with just a few applications to some classes of Riemannian manifolds of dimension 8 and 16. I will talk about some exterior or differential 4-forms, naturally associated in these dimensions with structures related with quaternions and octonions, as well as with the notions of Clifford system and of even Clifford structure.</p>https://gecogedi.dimai.unifi.it/seminar/1292/Hirzebruch surfaces in a one-parameter familyhttps://gecogedi.dimai.unifi.it/seminar/1293/2019-05-27: F. Battaglia.https://gecogedi.dimai.unifi.it/seminar/1293/coffee breakhttps://gecogedi.dimai.unifi.it/seminar/1294/2019-05-27: .https://gecogedi.dimai.unifi.it/seminar/1294/TBAhttps://gecogedi.dimai.unifi.it/seminar/1295/2019-05-27: <a href="/person/133/">F. Podesta'</a>.https://gecogedi.dimai.unifi.it/seminar/1295/lunch breakhttps://gecogedi.dimai.unifi.it/seminar/1296/2019-05-27: .https://gecogedi.dimai.unifi.it/seminar/1296/Locally conformally K\"ahler surfaces: a surveyhttps://gecogedi.dimai.unifi.it/seminar/1297/2019-05-27: V. Vuletescu.https://gecogedi.dimai.unifi.it/seminar/1297/coffee breakhttps://gecogedi.dimai.unifi.it/seminar/1298/2019-05-27: .https://gecogedi.dimai.unifi.it/seminar/1298/Locally conformally Kähler manifolds with holomorphic Lee fieldhttps://gecogedi.dimai.unifi.it/seminar/1299/2019-05-27: A. Moroianu.https://gecogedi.dimai.unifi.it/seminar/1299/Quotients of twistor spacehttps://gecogedi.dimai.unifi.it/seminar/1300/2019-05-27: S. Salamon.https://gecogedi.dimai.unifi.it/seminar/1300/social dinnerhttps://gecogedi.dimai.unifi.it/seminar/1301/2019-05-27: .https://gecogedi.dimai.unifi.it/seminar/1301/On the $J$-anti-invariant and symplectic cohomologieshttps://gecogedi.dimai.unifi.it/seminar/1302/2019-05-28: A. Tomassini.<p>We will present some recent results obtained in two joint papers with Nicoletta Tardini and Richard Hind, concerning the cohomolgy of symplectic and almost complex manifolds.</p><p>Let $J$ be an almost complex structure on a $2n$-dimensional manifold $M$. Then $J$ acts in a natural way on the bundle of $2$-forms $\Lambda^2(M)$, so that $$\Omega<sup>2</sup>(M)=\Omega<sub>J</sub><sup>+</sup>(M) \oplus \Omega<sub>J</sub><sup></sup>-(M),$$where $\Omega^2(M)$ is the space of smooth sections of $\Lambda^2(M)$ and $\Omega_J^-(M)$ denote the space of $J$-invariant and $J$-anti-invariant forms, respectively. Therefore, it is natural to consider the cohomology subgroups $H^+_J(M)$, $H^-_J(M)$ of $H^2_{dR}(M;R)$ whose elements are de Rham classes represented by $J$-invariant respectively $J$-anti-invariant forms. \newline We will describe some features of the anti-invariant cohomology. Furthermore, we discuss some properties of the Bott-Chern symplectic cohomology.</p>https://gecogedi.dimai.unifi.it/seminar/1302/Hermitian and Complex Geometry of a subclass of Kato manifoldshttps://gecogedi.dimai.unifi.it/seminar/1303/2019-05-28: <a href="/person/218/">A. Otiman</a>.https://gecogedi.dimai.unifi.it/seminar/1303/coffee breakhttps://gecogedi.dimai.unifi.it/seminar/1305/2019-05-28: .https://gecogedi.dimai.unifi.it/seminar/1305/Almost complex structures on quaternion-Kaehler manifoldshttps://gecogedi.dimai.unifi.it/seminar/1304/2019-05-28: P. Gauduchon.https://gecogedi.dimai.unifi.it/seminar/1304/Manifold submetries and polynomial algebrashttps://gecogedi.dimai.unifi.it/seminar/1307/2019-05-29: M. Radeschi.<p>Manifold submetries generalize Riemannian submersions, isometric group actions, and isoparametric maps. The local structure of Riemannian submersions around a point, is determined by Riemannian submersions from round spheres. In this talk, we will prove a surprising equivalence between the class of Riemannian submersions from spheres, and a class of polynomial algebras, with applications, for example, to Invariant Theory. This is based on a joint work with Ricardo Mendes.</p>https://gecogedi.dimai.unifi.it/seminar/1307/An introduction to tensor networkshttps://gecogedi.dimai.unifi.it/seminar/1284/2019-05-31: N. Vannieuwenhoven.<p>I will present an introduction to general tensor networks. We start with the easy case of networks that are a tree and discuss their algebraic and differential geometry. Then, we move to more complicated, general networks that include cycles, discussing their algebraic structure and presenting some open problems.</p>https://gecogedi.dimai.unifi.it/seminar/1284/Monge and Ampère : waiting for pluripotential theoryhttps://gecogedi.dimai.unifi.it/seminar/1282/2019-06-06: <a href="/person/230/">E. Di Nezza</a>.<p>A fundamental problem in Kähler geometry is to look for canonical metrics on a Kähler manifold, where the world “canonical” means that the metric satisfies a curvature condition. Such geometric problem boils down to a complex non-linear PDE of Monge-Ampère type. In the last 50 years the study of the regularity of solutions of such equations has motivated a lot of works. I will give a survey of what is known in this direction (also in singular settings), emphasising how the developments in pluripotential theory were crucial in order to treat (singular) complex Monge-Ampère equations.</p>https://gecogedi.dimai.unifi.it/seminar/1282/TBAhttps://gecogedi.dimai.unifi.it/seminar/1267/2019-06-12: M. Brion.<p>Seminario di geometria algebrica e aritmetica di Pisa</p>https://gecogedi.dimai.unifi.it/seminar/1267/TBAhttps://gecogedi.dimai.unifi.it/seminar/1268/2019-06-12: F. Tonini.<p>Seminario di geometria algebrica e aritmetica di Pisa</p>https://gecogedi.dimai.unifi.it/seminar/1268/Lee classes of locally conformally symplectic complex surfaceshttps://gecogedi.dimai.unifi.it/seminar/1277/2019-06-20: G. Dloussky.https://gecogedi.dimai.unifi.it/seminar/1277/TBAhttps://gecogedi.dimai.unifi.it/seminar/1288/2019-06-27: <a href="/person/266/">A. Cattaneo</a>.https://gecogedi.dimai.unifi.it/seminar/1288/