| 06/05/21 | Seminario | 16:00 | 17:00 | | Selim Ghazouani | Université Paris-Sud (France) |
DinAmicI: Another Internet Seminar (DAI Seminar)
”Piecewise affine homeomorphisms of the circle and dilation surfaces”
- in streaming mode -
(see the instructions in the abstract)
In this talk I will consider the following question: if one picks a piecewise affine map of the circle “at random”, what dynamical behaviour are we likely to observe? The case of standard circle diffeomorphisms has been studied by Herman in the 80s; in this emblematic case the problem can be reduced to theorems close to KAM theory. For the piecewise affine case, we put forward a geometric approach, inspired by methods from both Teichmüller theory and hyperbolic geometry.
Note:
The zoom link to the seminar will be posted on the DinAmicI website and on Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
|
| 06/05/21 | Seminario | 14:00 | 15:00 | | Margherita Nolasco | Università degli Studi dell'Aqulla | Seminario di Equazioni Differenziali
A variational principle for a charge-normalized solitary wave for the Maxwell-Dirac equations
(MS Teams link for the streaming at the end of the abstract)
In the context of classical field theory, the solitary wave solutions of the Euler-Lagrange equations describe "extended" particles. The existence of a charge-normalized solitary wave solution of the coupled Maxwell-Dirac equations, describing the spin-1/2 charged particle (electron) with self-interaction, has been an open problem for a long time. The first existence result of (not necessarily normalized) solitary waves was given by Esteban, Georgiev and Séré (Calc.Var. PDE (1996)) by using a variational method, as critical points of an energy functional which is strongly indefinite and presents a lack of compactness. In this talk we discuss the existence of a charge-normalized solitary wave obtained with a different variational principle inspired by the min-max characterization of eigenvalues of Dirac operators. In particular, we provide a variational characterization of the normalized solitary wave as a minimizer of an effective "renormalized" energy functional.
MS Teams Link for the streaming
Note:
This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |
| 30/04/21 | Seminario | 15:00 | 16:00 | | Filippo AMBROSIO | EPFL Lausanne |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Birational sheets in linear algebraic groups"
- in streaming mode -
(see the instructions in the abstract)
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.
N.B.: please click HERE to attend the talk in streaming.
|
| 29/04/21 | Seminario | 14:00 | 15:00 | | Aleks Jevnikar | Università di Udine | Existence results for super-Liouville equations
( MS Teams Link for the streaming )
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
|
| 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
|
| 23/04/21 | Seminario | 15:00 | 16:00 | | Kenji IOHARA | Université de Lyon 1 |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Elliptic root systems of non-reduced type"
- in streaming mode -
(see the instructions in the abstract)
After explaining some known basic facts about elliptic root systems (ERS) of reduced type, I will show the classification and automorphism groups of ERS of non-reduced type. Some future problems will be discussed.
These results are obtained in collaboration with A. Fialowski and Y. Saito.
N.B.: please click HERE to attend the talk in streaming
|
| 16/04/21 | Seminario | 15:00 | 16:00 | | Anton MELLIT | Universität Wien |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Old and new identities for the nabla operator and counting affine permutations" (Mellit)
- in streaming mode -
(see the instructions in the abstract)
An amazing nabla operator discovered by Bergeron and Garsia is a cornerstone of the theory of Macdonald polynomials. Applying it to various symmetric functions produces interesting generating functions of Dyck paths and parking functions. These kind of results are sometimes known as "shuffle theorems". I will try to give an overview of these results and explain how working with affine permutations and certain generalized P-tableaux allows to view them from a uniform point of view. The "new" in the title refers to the formula conjectured by Loehr and Warrington giving an explicit expansion of nabla of a Schur function in terms of nested Dyck paths.
This is a joint work with Erik Carlsson.
N.B.: please click HERE to attend the talk in streaming
|
| 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 |
| 09/04/21 | Seminario | 15:00 | 16:00 | | Giovanna CARNOVALE | Università di Padova |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Approximations of a Nichols algebra from a geometric point of view"
- in streaming mode -
(see the instructions in the abstract)
The talk is based on work in progress with Francesco Esposito and Lleonard Rubio y Degrassi.
Recently Kapranov and Schechtman have settled an equivalence between the category of graded connected co-connected bialgebras in a braided monoidal category W and the category of factorizable systems of perverse sheaves on all symmetric products Sym n( C) with values in W. The Nichols (shuffle) algebra associated with an object V corresponds to the system of intersection cohomology extensions of a precise local system on the open strata.
Motivated by the study of Fomin-Kirillov algebras and their relation with Nichols algebras, we describe the factorizable perverse sheaves counterpart of some algebraic constructions, including the n-th approximation of a graded bialgebra, and we translate into geometric statements when a Nichols algebra is quadratic.
N.B.: please click HERE to attend the talk in streaming
|
| 08/04/21 | Seminario | 16:00 | 17:00 | | Eva Miranda & Daniel Peralta-Salas | UPC Barcelona & ICMAT Madrid |
DinAmicI: Another Internet Seminar (DAI Seminar)
Looking at Euler flows through a contact mirror: Universality and Turing completeness
- in streaming mode -
(see the instructions in the abstract)
The dynamics of an inviscid and incompressible fluid flow on a Riemannian manifold is governed by the Euler equations. Recently, Tao launched a programme to address the global existence problem for the Euler and Navier Stokes equations based on the concept of universality. Inspired by this proposal, we show that the stationary Euler equations exhibit several universality features, In the sense that, any non-autonomous flow on a compact manifold can be extended to a smooth stationary solution of the Euler equations on some Riemannian manifold of possibly higher dimension.
These results can be viewed as lending support to the intuition that solutions to the Euler equations can be extremely complicated in nature.
A key point in the proof is looking at the h-principle in contact geometry through a contact mirror, unveiled by Sullivan, Etnyre and Ghrist more than two decades ago.
We end up this talk addressing an apparently different question: What kind of physics might be non-computational? Using the former universality result, we can establish the Turing completeness of the steady Euler flows, i.e., there exist solutions that encode a universal Turing machine and, in particular, these solutions have undecidable trajectories..
This talk is based on joint work with Robert Cardona and Fran Presas.
Note:
The zoom link to the seminar will be posted on the DinAmicI website and on Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
|