|19/06/18||Seminario||14:30||15:30||1201 Dal Passo||Patrick Martinez||Universite' Toulouse III||Inverse problems for energy balance models in climate science|
|15/06/18||Seminario||11:00||12:00||1201 Dal Passo||Patrick Martinez||Universite' Toulouse III||Control cost for degenerate parabolic equations|
|12/06/18||Seminario||16:00||17:00||1101 D'Antoni||Yaacov Kopeliovich||University of Connecticut||Thomae formulas for general Abelian covers of CP^1|
100 years and a change: Thomae designed a formula
calculating certain value of theta functions as polynomial up to a
constant. I will explain the generalization of these formulas for
General Abelian Covers.
|08/06/18||Seminario||17:00||18:00||1101 D'Antoni||Jacinta TORRES||KIT - Karlsruher Institut für Technologie||Kostant Convexity and the Affine Grassmannian
We present some ideas and results towards a building-theoretical affine Grassmannian. One of our aims is to substitute many proofs carried out using relations in the Kac-Moody group using certain retractions. This is joint work in progress with Petra Schwer.
|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 |
|“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.