| 11/05/21 | Seminario | 16:30 | 18:00 | | Tommaso de Fernex | University of Utah (USA) | On rationality of complex algebraic varieties (online lecture series)
Inizio del ciclo di 12 ore di lezioni on-line (ZOOM) per il Dottorato di Ricerca. Il Ciclo di lezioni è organizzato dal proponente scientifico Prof. Flaminio Flamini nell'ambito dellle attività del PROGETTO DI ECCELLENZA MIUR 2018-2022 MATH@TOV (CUP E83C18000100006).
La cadenza delle lezioni e'
MARTEDI' E GIOVEDI' 16:30-18:00 da
11 Maggio 2021 a 03 Giugno 2021
Per ulteriori informazioni sul corso, visitare la pagina web di riferimento:
https://sites.google.com/view/on-rationality-of-cpx-alg-vars/
Abstract: Rationality has been a central topic in the field since the Luroth problem was formulated at the end of the 18th century. The only rational curve is the projective line, and Castelnuovo's criterion settles the two-dimensional case. However, determining which varieties are rational in higher dimensions can be a challenging problem. In these lectures, I will overview some of the history of the problem and focus on two aspects related to rationality: birational rigidity and deformations of rational varieties. We will prove Iskovskikh-Manin's theorem on quartic threefolds and its generalization to higher dimensions, and Kontsevich-Tschinkel's specialization result on rationality. Along the way, we will also review some classical theorems on surfaces such as Noether-Castelnuovo's factorization theorem of Cremona transformations and Segre and Manin's theorems on rationality of cubic surfaces over non-closed fields.
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| 26/04/21 | Colloquium | 17:00 | 18:00 | | Thomas J.R. Hughes | The University of Texas at Austin | Isogeometric Analysis: Origins, Status, Recent Progress and Structure Preserving Methods
( MS Teams Link for the streaming )
The vision of Isogeometric Analysis (IGA) was first presented in a paper published October 1, 2005 [1]. Since then it has become a focus of research within both the fields of Finite Element Analysis (FEA) and Computer Aided Geometric Design (CAGD) and has become a mainstream analysis methodology and provided a new paradigm for geometric design [2-4]. The key concept utilized in the technical approach is the development of a new foundation for FEA, based on rich geometric descriptions originating in CAGD, more tightly integrating design and analysis. Industrial applications and commercial software developments have expanded recently. In this presentation, I will describe the origins of IGA, its status, recent progress, areas of current activity, and the development of isogeometric structure preserving methods.
Key Words: Computational Mechanics, Computer Aided Design, Finite Element Analysis, Computer Aided Engineering
REFERENCES
[1] T.J.R. Hughes, J.A. Cottrell and Y. Bazilevs, Isogeometric Analysis: CAD, Finite Elements, NURBS, Exact Geometry and Mesh Refinement, Computer Methods in Applied Mechanics and Engineering, 194, (2005) 4135-4195.
[2] J.A. Cottrell, T.J.R. Hughes and Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, Chichester, U.K., 2009.
[3] Special Issue on Isogeometric Analysis, (eds. T.J.R. Hughes, J.T. Oden and M. Papadrakakis), Computer Methods in Applied Mechanics and Engineering, 284, (1 February 2015), 1-1182.
[4] Special Issue on Isogeometric Analysis: Progress and Challenges, (eds. T.J.R. Hughes, J.T. Oden and M. Papadrakakis), Computer Methods in Applied Mechanics and Engineering, 316, (1 April 2017), 1-1270.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
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| 15/04/21 | Seminario | 14:00 | 15:00 | | Roberta Ghezzi | Università di Roma "Tor Vergata" | Regularization of chattering phenomena via bounded variation controls
( MS Teams Link for the streaming )
In control theory, chattering refers to fast oscillations of controls, such as accumulation of switchings in finite time. This behavior is rather typical, as it is the case for the class of single-input control-affine problems, and may be a serious obstacle to convergence of standard numerical methods to detect optimal solutions.
We propose a general regularization procedure, consisting of penalizing the cost functional with a total variation term. Under appropriate assumptions of small-time local controllability, we prove that the optimal cost and any optimal solution of the regularized problem converge respectively to the optimal cost and an optimal solution of the initial problem. Our approach is valid for general classes of nonlinear optimal control problems and applies to chattering phenomena appearing in constrained problems as well as to switching systems. We also quantify the error in terms of the rate of convergence of the sequence of switching times, for systems with regular time-optimal map.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |