For more information about this event visit this <a href="http://www.mat.uniroma2.it/may12.php"> <strong> webpage </strong></a> (which contains also the link for the streaming of the event). <br> <br> This is part of the international initiative <a href="https://may12.womeninmaths.org/"> <strong> May 12: Celebrating women in Mathematics </strong> </a> <br> <br> Note: </strong> This talk is part of the activity of the MIUR Department of Excellence Project MATH@TOV CUP E83C18000100006

We present some recent results obtain in collaboration with Denis Bonheure (Bruxelles, Belgium) and Silvia Cingolani (Bari, Italy) about a semiclassical analysis for a planar Schroedinger-Poisson system with potential functions. <br> <b>NB</b>:<i>This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006</i>

Motivated by analogies with the case of SL(2,Z), we introduce a method for the study of possible variants of the Akemann-Ostrand property for SL(3,Z). This is a joint work in progress with Florin Radulescu. <br> This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006. <br> <a href="https://teams.microsoft.com/l/meetup-join/19%3a428ea736adc6424c8ae37f187c91b51b%40thread.tacv2/1620301003085?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22e6325df7-3e74-4c88-ab0b-65ff8a758e69%22%7d">MS Teams link</a>

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.

&nbsp; After recalling the most important results about Kazhdan-Lusztig cells for symmetric groups, I will introduce the <em>p</em>-Kazhdan-Lusztig basis and give a complete description of <em>p</em>-cells for symmetric groups. After that I will mention important consequences of the Perron-Frobenius theorem for <em>p</em>-cells which provide one of the last missing ingredients for the proof of the cellularity of the <em>p</em>-Kazhdan-Lusztig basis in finite type <em>A</em>. <br> &nbsp; <strong>N.B.:</strong> please <a href="https://teams.microsoft.com/l/meetup-join/19%3a342c23eced2540e4bcbb6f938e999db6%40thread.tacv2/1614163430980?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22cf31dbee-7758-4272-af72-503d7694f2ea%22%7d" target="Teams">click <strong>HERE</strong> to attend the talk</a> in streaming

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. <br> <br> <a href="https://teams.microsoft.com/l/meetup-join/19%3a7f273a2aff1145dfae91372d186b1cd9%40thread.tacv2/1619704157047?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22d37d6fea-2e4d-4c35-88e4-99bf4cf68fe9%22%7d"> <strong> MS Teams Link for the streaming </strong> <em> </strong> </a> <br> <strong> Note: </strong> This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

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. <br> <br> <strong> Note: </strong> <em> </strong> <em> The zoom link to the seminar will be posted on the <a href="https://www.dinamici.org/dai-seminar/"> DinAmicI website </a> and on <a href="https://mathseminars.org/seminar/DinAmicI"> Mathseminars.org</a>. Moreover, it will be also streamed live via the youtube <a href="https://www.youtube.com/channel/UCyNNg155G3iLS7l-qZjboyg"> DinAmicI channel</a>. </em> </em>

&nbsp; The sheets of a variety <em>X</em> under the action of an algebraic group <em>G</em> are the irreducible components of subsets of elements of <em>X</em> with equidimensional <em>G</em>-orbits. For <em>G</em> complex connected reductive, the sheets for the adjoint action of <em>G</em> on its Lie algebra <strong>g</strong> were studied by Borho and Kraft in 1979. In 2016, Losev introduced finitely many subvarieties of <strong>g</strong> 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. <br> &nbsp; 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 <strong>g</strong>. <br> &nbsp; The main part is aimed at investigating analogues of birational sheets of conjugacy classes in <em>G</em>. To conclude, assuming that the derived subgroup of <em>G</em> is simply connected, we illustrate the main features of these varieties, comparing them with the objects defined by Losev. <br> &nbsp; Part of the talk is based on joint works with G. Carnovale and F. Esposito, and M. Costantini. <br> <strong>N.B.:</strong> please <a href="https://teams.microsoft.com/l/meetup-join/19%3a342c23eced2540e4bcbb6f938e999db6%40thread.tacv2/1614163430980?context=%7b%22Tid%22%3a%2224c5be2a-d764-40c5-9975-82d08ae47d0e%22%2c%22Oid%22%3a%22cf31dbee-7758-4272-af72-503d7694f2ea%22%7d" target="Teams">click <strong>HERE</strong> to attend the talk</a> in 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. <br> <b>NB</b>:<i>This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006</i>

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. <br> <br> <b>Key Words</b>: <i>Computational Mechanics, Computer Aided Design, Finite Element Analysis, Computer Aided Engineering</i> <br> <br> <b>REFERENCES</b> <br> [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. <br> [2]  J.A. Cottrell, T.J.R. Hughes and Y. Bazilevs, Isogeometric Analysis: Toward Integration of CAD and FEA, Wiley, Chichester, U.K., 2009. <br> [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. <br> [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.<br> <br> <br> <b>NB</b>:<i>This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006</i>