Pagina 34

11/05/21Seminario16:3018:00Tommaso de FernexUniversity 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: 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.
(free lance)
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Cellularity of the p-Kazhdan-Lusztig basis for symmetric groups"
- in streaming mode -
(see the instructions in the abstract)

  After recalling the most important results about Kazhdan-Lusztig cells for symmetric groups, I will introduce the p-Kazhdan-Lusztig basis and give a complete description of p-cells for symmetric groups. After that I will mention important consequences of the Perron-Frobenius theorem for p-cells which provide one of the last missing ingredients for the proof of the cellularity of the p-Kazhdan-Lusztig basis in finite type A.
  N.B.: please click HERE to attend the talk in streaming
06/05/21Seminario16:0017:00Selim GhazouaniUniversité 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 Moreover, it will be also streamed live via the youtube DinAmicI channel.
06/05/21Seminario14:0015:00Margherita NolascoUniversità 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
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.
29/04/21Seminario14:0015:00Aleks JevnikarUniversità di UdineExistence 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
26/04/21Colloquium17:0018:00Thomas J.R. HughesThe University of Texas at AustinIsogeometric 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 WordsComputational Mechanics, Computer Aided Design, Finite Element Analysis, Computer Aided Engineering

[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
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
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
15/04/21Seminario14:0015:00Roberta GhezziUniversità 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

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