| 08/06/18 | Seminario | 15:30 | 16:30 | 1101 D'Antoni | Gabriele GULLÀ | Università di Roma "Tor Vergata" | Logical methods across mathematics: three examples in algebra
In this seminar I will talk about three well known examples of algebraic problems which have been engaged with logical tools (in particular set theoretic tools).
The first one, due to Patrick Dehornoy, is about the use of very high Large Cardinals Axioms to solve problems linked to Laver Tables, which are objects closely related to Braids theory.
The second one is about the study of relations among Forcing Axioms (which are extensions of Baire Category Theorem) and Operator Algebras, in particular C*-algebra problems. This field of research has particularly grown thanks to Ilijas Farah and Nick Weaver.
The last one concerns the proof (by Saharon Shelah, 1974) of the independence of Whitehead Problem (a group theory problem from the '50s) from ZFC (the usual Zermelo-Fraenkel set theory with the Axiom of Choice). In this example in particular the set theoretic ideas which are useful are the Continuum Hypothesis (which can be considered as a cardinal assumption), Martin's Axiom (a specific Forcing Axiom) and the Axiom of Constructibility which is, in a certain way, an anti-Large Cardinal axiom. |
| 08/06/18 | Seminario | 14:30 | 16:00 | 1201 Dal Passo | Leticia Brambila-Paz | CIMAT, Guanajuato, Mexico | "Coherent systems and Butler's conjecture" (Algebraic Geometry Seminar - in the framework of the Excellence Project Math@TOV awarded to the Departement of Mathematics)
(Seminar - in the framework of the Excellence Project Math@TOV awarded to the Departement of Mathematics https://www.mat.uniroma2.it/Progetto/ ) Let (E, V) be a general generated coherent system of type (n, d, n+m) on a general non-singular irreducible complex projective curve. A conjecture of D. C. Butler relates the semistability of E to the semistability of the kernel of the evaluation map V x O_X -> E. In this talk, some results will be given about the existence of generated coherent systems and a necessary condition is given for the Butler conjecture to be satisfied. |
| 07/06/18 | Seminario | 14:30 | 16:00 | 1101 D'Antoni | Leticia Brambila-Paz | CIMAT, Guanajuato, Mexico | "Moduli Spaces" (Department Seminar - in the framework of the Excellence Project Math@TOV awarded to the Departement of Mathematics)
(Department Seminar - in the framework of the Excellence Project Math@TOV awarded to the Departement of Mathematics https://www.mat.uniroma2.it/Progetto/)
The concept of 'moduli space' arises in connection with classification problems. The basic ingredients of a classification problem are a collection of objects A and an equivalence relation * on A. We would like to give A/* a structure that reflects how the objects vary in families. In this talk I will explain the concept of moduli spaces with some examples and see how the study of some moduli spaces gives an interaction with different areas of mathematics like algebraic geometry, differential geometry, topology, representation theory etc., and also with other disciplines like theoretical physics. |
| 05/06/18 | Seminario | 14:30 | 15:30 | 1201 Dal Passo | Gabriele Grillo | Politecnico di Milano | On some nonlinear diffusions on manifolds
I shall discuss recent results on the porous medium and fast diffusion equations on negatively curved manifolds. Among the main problems considered I mention detailed asymptotics of positive solutions, that depend in a crucial way on curvature assumptions. Uniqueness of solutions in suitable classes is another critical issue, and I shall discuss how in the fast diffusion case this turns out to be related to parabolicity, a purely linear concept. |
| 31/05/18 | Seminario | 13:30 | 15:00 | 1201 Dal Passo | Oleg Davydov | University of Giessen | Local Approximation with Polynomials and Kernels
Many numerical algorithms for data fitting and numerical PDEs require local approximation of unknown function values or
derivatives from the data at arbitrary locations in R^d.
I will present recent results (joint work with Robert Schaback) on the error bounds for both polynomial and kernel-based methods of local approximation and numerical differentiation, and their applications |
| 25/05/18 | Seminario | 16:30 | 17:30 | 1101 D'Antoni | Giovanni
CERULLI
IRELLI | “Sapienza” Università di Roma | Cellular decomposition of quiver Grassmannians
I will report on a joint project with F. Esposito, H. Franzen and M. Reineke – cf. arXiv:1804.07736. Quiver Grassmannians are projective varieties parametrizing subrepresentations of quiver representations of a fixed dimension vector. The geometry of such projective varieties can be studied via the representation theory of quivers (or of finite dimensional algebras). Quiver Grassmannians appeared in the theory of cluster algebras. As a consequence of the positivity conjecture of Fomin and Zelevinsky, the Euler characteristic of quiver Grassmannians associated with rigid quiver representations must be positive; this fact was proved by Nakajima.
We explore the geometry of quiver Grassmannians associated with rigid quiver representations: we show that they have property (S) meaning that: (1) there is no odd cohomology, (2) the cycle map is an isomorphism, (3) the Chow ring admits explicit generators defined over any field. As a consequence, we deduce that they have polynomial point count. If we restrict to quivers which are of finite or affine type (i.e. orientation of simply-laced extended Dynkin diagrams) we can prove much more: in this case, every quiver Grassmannian associated with an indecomposable representation (not necessarily rigid) admits a cellular decomposition. |
| 25/05/18 | Seminario | 15:00 | 16:00 | 1101 D'Antoni | Ernesto
SPINELLI | “Sapienza” Università di Roma | Codimension growth and minimal varieties
In characteristic zero an effective way of measuring the polynomial identities satisfied by an algebra is provided by the sequence of its codimensions introduced by Regev. In this talk we review some features of the codimension growth of PI algebras, including the deep contribution of Giambruno and Zaicev on the existence of the PI-exponent, and discuss some recent developments in the framework of group graded algebras. In particular, a characterisation of minimal supervarieties of fixed superexponent will be given. The last result is part of a joint work with O.M. Di Vincenzo and V. da Silva. |
| 22/05/18 | Seminario | 14:00 | 15:00 | 1201 Dal Passo | Filippo Giuliani | Università degli Studi "Roma Tre" | On the integrability and quasi-periodic dynamics of the dispersive Degasperis-Procesi equation
The Degasperis-Procesi equation
$$
u_t + c_0 u_x + gamma u_{xxx} -alpha^2 u_{xxt} = left( c_2 (u^2_x+uu_{xx}) - frac{2c_3}{alpha^2}u^2
ight)_x
$$
has been extensively studied by many authors, especially in its dispersionless form, since it presents interesting phenomena such as breaking waves and existence of peakon-like solutions. Degasperis-Holm-Hone proved the integrability of this equation and they provided an iterative method to compute infinite conserved quantities.
Since the Degasperis-Procesi equation is a quasi-linear equation the presence of dispersive terms depends on the chosen frame. In absence of dispersive terms there are no constants of motion even controlling the $H^1$-norm.
We show that, in the dispersive case, we can construct infinitely many constants of motion which are analytic and control the Sobolev norms in a neighborhood of the origin.
Moreover, thanks to the analysis of the algebraic structure of the quadratic parts of these conserved quantities we show that the (formal) Birkhoff normal form is action-preserving (integrable) at any order. This fact is used to prove the first existence result of quasi-periodic solutions for the Degasperis-Procesi equation on the circle.
These results have been obtained in collaboration with R. Feola, S. Pasquali and M. Procesi. |
| 21/05/18 | Seminario | 14:30 | 15:30 | 1101 D'Antoni | Andrew Zimmer | William & Mary University | Smoothly bounded domains covering finite volume manifolds
In this talk we will discuss the following
result: if a bounded domain with C^2 boundary covers a
manifold which has finite volume with respect to either the
Bergman volume, the K\"ahler-Einstein volume, or the
Kobayashi-Eisenman volume, then the domain is biholomorphic
to the unit ball. The proof uses a variety of tools from Riemannian geometry and several complex variables including
the squeezing function, Busemann functions, estimates on
invariant distances, and a version of E. Cartan's fixed point
theorem. |
| 18/05/18 | Seminario | 15:00 | 16:00 | 1101 D'Antoni | Herve' Gaussier | Universita' di Grenoble | Local and Global Properties of strongly pseudoconvex domains.
I will try to explain how the geometry
of such domains imposes curvature estimates of invariant
metrics and I will discuss global equivalence problems. This
is a joint work with H.Seshadri and results obtained by
S.Gontard.
|