Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 26-04-2021 al 02-05-2021
Lunedì 26 aprile 2021
Ore 14:30, https://meet.google.com/nie-attq-ged
seminario di Analisi Matematica
Alessandro Carlotto (ETH Zurigo)
Free boundary minimal surfaces with connected boundary and arbitrary genus
Besides their self-evident geometric significance, which can be traced back at least to Courant, free boundary minimal surfaces also naturally arise in partitioning problems for convex bodies, in capillarity problems for fluids and, as has significantly emerged in recent years thanks to work of Fraser and Schoen, in connection to extremal metrics for Steklov eigenvalues for manifolds with boundary (i. e. for eigenvalues of the corresponding Dirichlet-to-Neumann map). The theory has been developed in various interesting directions, yet many fundamental questions remain open. One of the most basic ones can be phrased as follows: does the Euclidean unit ball contain free boundary minimal surfaces of any given topological type? In spite of significant advances, the answer to such a question has proven to be very elusive. I will present some joint work with Giada Franz and Mario Schulz where we answer (in the affirmative) the well-known question whether there exist in B^3 (embedded) free boundary minimal surfaces of genus one and one boundary component. In fact, we prove a more general result: for any g there exists in B^3 an embedded free boundary minimal surface of genus g and connected boundary. This result provides a long-awaited analogue of the existence theorem obtained by Lawson in 1970 for closed minimal surfaces in round S^3. The proof builds on global variational methods, in particular on a suitable equivariant counterpart of the Almgren-Pitts min-max theory, and on a striking application of Simon's lifting lemma.
Lunedì 26 aprile 2021
Ore 17:00, Seminario online su questo link, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Colloquium di dipartimento
Thomas J.R. Hughes (The University of Texas at Austin)
Isogeometric Analysis: Origins, Status, Recent Progress and Structure Preserving Methods
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.
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
Per informazioni, rivolgersi a: molle@mat.uniroma2.it, gavarini@mat.uniroma2.it
Mercoledì 28 aprile 2021
Ore 14:00, Seminario telematico via Google Meet all'URL http://meet.google.com/jjt-toji-skw, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Donna Testerman (EPFL)
Overgroups of regular unipotent elements in simple algebraic groups
We consider the question of determining reductive overgroups of regular unipotent elements in simple algebraic groups and in particular give a condition which guarantees that the overgroup does not lie in a proper parabolic subgroup of the ambient simple group. This is joint work with Gunter Malle, and follows on work of Suprunenko, Saxl and Seitz, and Testerman and Zalesski.
Per informazioni, rivolgersi a: pezzini@mat.uniroma1.it
Mercoledì 28 aprile 2021
Ore 14:30, https://meet.google.com/pip-kvzt-fkz, Dipartimento di Fisica, Sapienza Università di Roma
Seminario delle Meccaniche
Giancarlo Benettin ( Università di Padova)
The Fermi-Pasta-Ulam problem and its underlying integrable dynamics
In 1954 Fermi, Pasta and Ulam for the first time used a computer to study the ergodic behavior of a system with many degrees of freedom, aiming to investigate the foundations of Statistical Mechanics. Several branches of physical and mathematical investigations started from that paper. The aim of the talk is to shortly review some main contributions to the problem and then revisit, in the light of some recent numerical results, one of the leading ideas, namely that the model should be understood as a perturbation of the Toda model, well known in Statistical Mechanics, which is nonlinear but integrable. The behavior at the thermodynamic limit turns out to be particularly delicate.
Giovedì 29 aprile 2021
Ore 14:00, Seminario online su questo link, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Aleks Jevnikar (Università di Udine)
Existence results for super-Liouville equations
We consider super-Liouville equations on closed surfaces, which have a variational structure with a strongly-indefinite functional. We obtain the first existence results by making use of min-max methods and bifurcation theory. Joint project with Andrea Malchiodi and Ruijun Wu.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it
Giovedì 29 aprile 2021
Ore 14:30, Canale Youtube Cnr-Iac https://www.youtube.com/watch?v=nYwkplQQbEg, Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche
Seminari Generali IAC 2021
Donatella Granata (Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche)
Interdiction Networks and Critical Disruption Path problem
Many real-life optimization problems can accurately be represented as networks, this talk will be structured in two main parts. In the first one, we will introduce how it is important from interdiction perspectives to predict and evaluate the behavior of the system, via measuring the rules governing individual vertices, edges, or associated substructures, whose malfunctioning prevents the functionality of the network as a whole. In the second part, we will deal with the Critical Disruption Path problem presenting some variants and exact and meta-heuristics procedures to face it.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Giovedì 29 aprile 2021
Ore 14:30, Il seminario sarà tenuto in modalità telematica, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre, Largo San Leonardo Murialdo 1
Seminario di Geometria
Chiara Damiolini (Rutgers University)
Geometric properties of sheaves of conformal blocks from vertex algebras
In this talk I will discuss geometric properties of certain vector bundles on the moduli space of stable n-pointed curves which arise from modules over vertex operator algebras. I will in particular describe conditions on the vertex algebra that guarantee that the factorization property holds for these vector bundles and discuss its consequences and open problems. This is based on a joint work with A. Gibney and N. Tarasca.
Per partecipare al seminario cliccare sul seguente link
Giovedì 29 aprile 2021
Ore 15:00, Il seminario sarà tenuto in modalità telematica, Link per partecipare: https://uniroma1.zoom.us/j/85943796292?pwd=dDliSTJBTFVmazRNYXZGV0lBVUJCZz09
Seminari di Ricerca in Didattica e Storia della Matematica
Samuele Antonini (Università di Pavia)
Analisi di alcuni processi argomentativi nella pratica matematica
Venerdì 30 aprile 2021
Ore 15:00, Il seminario sarà tenuto in modalità telematica, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre, Largo San Leonardo Murialdo 1
Seminario di Logica e Informatica Teorica
Blerina Sinaimeri (LUISS)
A family of tree-based generators for bubbles in directed graphs
Bubbles are pairs of internally vertex-disjoint (s, t)-paths in a directed graph. In de Bruijn graphs built from reads of RNA and DNA data, bubbles represent interesting biological events, such as alternative splicing (AS) and allelic differences (SNPs and indels). However, the set of all bubbles in a de Bruijn graph built from real data is usually too large to be efficiently enumerated and analysed in practice. In particular, despite significant research done in this area, listing bubbles still remains the main bottleneck for tools that detect AS events in a reference-free context. In this talk we present a notion of bubble generator set, i.e., a polynomial-sized subset of bubbles from which all the other bubbles can be obtained through a suitable application of a specific symmetric difference operator. This set provides a compact representation of the bubble space of a graph. We provide a polynomial-time algorithm to decompose any bubble of a graph into the bubbles of such a generator in a tree-like fashion. We present some applications of the bubble generator on a real RNA-seq dataset and we conclude with some open problems. [1] V. Acuña, R. Grossi, G. Italiano, L. De Lima, R. Rizzi, G. Sacomoto, M.-F. Sagot and B. Sinaimeri. On Bubble Generators in Directed Graphs, Algorithmica , 82(4): 898-914, 2020. [2] V. Acuña, G. Italiano, L. De Lima, L. Pepè Sciarria, M.-F. Sagot and B. Sinaimeri. A family of tree-based generators for bubbles in directed graphs, 31rd International Workshop on Combinatorial Algorithms, IWOCA 2020 , Bordeaux, France, June 8-10, 2020.
Per partecipare al seminario cliccare sul seguente link
Venerdì 30 aprile 2021
Ore 15:00, Seminario Telematico, link
Online Representation Theory Seminar
Filippo Ambrosio (EPFL Lausanne)
Birational sheets in linear algebraic groups
The sheets of a variety X under the action of an algebraic group G are the irreducible components of subsets of elements of X with equidimensional G-orbits. For G complex connected reductive, the sheets for the adjoint action of G on its Lie algebra g were studied by Borho and Kraft in 1979. In 2016, Losev introduced finitely many subvarieties of g consisting of equidimensional orbits, called birational sheets: their definition is less immediate than the one of a sheet, but they enjoy better geometric and representation-theoretic properties and are central in Losev's suggestion of an Orbit method for semisimple Lie algebras. In the opening part of the seminar we give a brief overview of sheets and recall some basics about Lusztig-Spaltenstein induction of conjugacy classes in terms of the so-called Springer generalized map and analyse its interplay with birationality. This will give the instruments to introduce Losev's birational sheets in g. The main part is aimed at investigating analogues of birational sheets of conjugacy classes in G. To conclude, assuming that the derived subgroup of G is simply connected, we illustrate the main features of these varieties, comparing them with the objects defined by Losev. Part of the talk is based on joint works with G. Carnovale and F. Esposito, and M. Costantini.
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