Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 08-02-2021 al 14-02-2021
Lunedì 08 febbraio 2021
Ore 16:00, modalità telematica con Zoom al seguente link: https://uniroma1.zoom.us/j/81656265460?pwd=UmlZQzBDY2VmSUwrNitZbkNWMERIdz09
Seminario di Probabilità e Statistica Matematica
Antonio Agresti (Dottorato in Matematica, Sapienza Università di Roma)
Nonlinear parabolic stochastic evolution equations in critical spaces.
Critical spaces for non-linear equations are important due to scaling invariance, and in particular this plays a central role in fluid dynamics. In this talk we introduce and discuss local/global well-posedness, and blow-up criteria for stochastic parabolic evolution equations in critical spaces. Our results extend the celebrated theory of Prüss, Wilke and Simonett for deterministic PDEs. Due to the presence of noise it is unclear that a stochastic version of the theory is possible, but as we will show a suitable variation of the theory remains valid. We will also explain several features which are new in both the deterministic and stochastic framework. In particular, we discuss a new bootstrap method to prove regularization
of solutions to (S)PDEs, which can also be applied in critical situations. Our theory is applicable to a large class of semilinear and quasilinear parabolic problems which includes many of the classical SPDE. During the talk we give applications to stochastic reaction-diffusion equations and stochastic Navier-Stokes equations with gradient noise. This is a joint work with Mark Veraar (TU Delft).
Martedì 09 febbraio 2021
Ore 14:30, Canale Youtube dell'IAC https://www.youtube.com/watch?v=Og3QdOpjJq4, Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche
Serie di seminari IAC "AIM: Artificial Intelligence and Mathematics, fundamentals and beyond"
Elisa Ricci (Dipartimento di Ingegneria e Scienza dell'Informazione, Università di Trento)
Visual Learning in an Imperfect World
Over the last few years deep learning has enabled unprecedented successes in computer vision. Despite their effectiveness, deep networks rely on large scale, carefully annotated training data. Therefore, when considering complex problems in real world applications, their performances drop since both data and labels can be noisy or difficult and costly to obtain. In this seminar, I will discuss recent approaches and trends in computer vision for addressing the challenge of visual learning in realistic scenarios. I will also focus on recent activities from my research group on this topic, discussing methods for unsupervised and self-supervised learning, domain adaptation and continual learning.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Mercoledì 10 febbraio 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
Alexander Kuznetsov (Steklov Mathematical Institute)
Lefschetz collections and residual categories for Grassmannians
I will try to explain and motivate the notion of Lefschetz (exceptional) collections in derived categories of coherent sheaves and their residual categories and, in particular, its conjectural relation to quantum cohomology. If time permits, I will discuss recent progress in construction of Lefschetz collections for Grassmannians of classical groups. This is joint work with Maxim Smirnov.
Per informazioni, rivolgersi a: pezzini@mat.uniroma1.it
Mercoledì 10 febbraio 2021
Ore 14:30, teleconferenza, https://meet.google.com/pip-kvzt-fkz
Seminario delle Meccaniche
Susanna Terracini (Università di Torino)
Segregation, interaction of species and related free boundary problems
Partial differential equations are often used to describe physical laws governing a complicated system in a confined space with relatively simpler behavior on the boundary. Thus, reaction-diffusion systems with strong interaction terms appear in many multi-species physical problems as well as in population dynamics. A prototypical example appears when looking for solitary wave solutions for Bose-Einstein condensates of two (or more) different hyperfine states which overlap in space. Typically the forces between particles in the same state are attractive while those between particles in different states can be either attractive or repulsive. If the condensates repel, they eventually separate spatially giving rise to a free boundary. This phenomenon is called phase separation and has been described in recent literature, both physical and mathematical. The classification of entire solutions and the geometric aspects of phase separation are of fundamental importance as well. We intend to focus on the most recent development of the theory in connection with problems featuring anomalous diffusions, long-range and non symmetric interactions.
Mercoledì 10 febbraio 2021
Ore 16:00, seminario online a questo link, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Algebre di Operatori
Yoh Tanimoto (University of Rome Tor Vergata)
Towards integral perturbation of two-dimensional CFT
We present some ideas to construct new Haag-Kastler nets starting with a two-dimensional conformal field theory. This is a natural variation of the Barata-Jaekel-Mund construction. It is suggested in physics literature that a similar constructions should lead to integrable models, and we will discuss possible extensions of this programme.
Giovedì 11 febbraio 2021
Ore 14:00, seminario online a questo link, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Luca Martinazzi (Università di Padova)
Entire solutions to a prescribed curvature equation in \(\mathbb R^4\) and the Nirenberg problem
Several existence and non-existence results for the Nirenberg problem of prescribing the Gauss curvature on a closed surface are classically known. In higher dimension, analog results hold with the Q-curvature replacing the Gauss curvature. In many cases a non-existence result is associated with a blow-up phenomenon which leads to entire solutions of the Liouville equation \(-\Delta u = e^{2u}\) in dimension 2 or higher-dimensional analogs. On the other hand, Borer, Galimberti and Struwe studied a blow-up phenomenon which could lead to solutions to the equation \(-\Delta u =(1-|x|^2)e^{2u}\) in \(\mathbb R^2\) (1) or \(\Delta^2 u =(1-|x|^2)e^{4u}\) in \(\mathbb R^4\) (2). While non-existence results have been shown for (1) by Struwe, the question remained opened for (2). We recently gave a positive answer with A. Hyder, giving sharp conditions under which (2) admits solutions with controlled behaviour at infinity, hence answering an open question by Struwe. More related open questions will be discussed.
Note: This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
Per informazioni, rivolgersi a: molle@mat.uniroma2.it
Giovedì 11 febbraio 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
Madeline Brandt (ICERM)
Top Weight Cohomology of \(A_g\)
I will discuss a recent project in computing the top weight cohomology of the moduli space \(A_g\) of principally polarized abelian varieties of dimension \(g\) for small values of \(g\). This piece of the cohomology is controlled by the combinatorics of the boundary strata of a compactification of \(A_g\). Thus, it can be computed combinatorially. This is joint work with Juliette Bruce, Melody Chan, Margarida Melo, Gwyneth Moreland, and Corey Wolfe.
Per partecipare al Seminario cliccare sul seguente link.
Giovedì 11 febbraio 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
Marta Menghini (Sapienza Università di Roma)
Le difficoltà di una riforma: La matematica moderna in Italia
Giovedì 11 febbraio 2021
Ore 16:00, On-line seminar, Web site for information: https://www.dinamici.org/dai-seminar/
DinAmicI: Another Internet Seminar (DAI Seminar)
Misha Bialy (Tel Aviv University)
Birkhoff-Poritsky conjecture for centrally-symmetric billiards
In this talk I shall discuss Birkhoff-Poritsky conjecture for centrally-symmetric \(C^2\)-smooth convex planar billiards. We assume that the domain \(\mathcal A\) between the invariant curve of \(4\)-periodic orbits and the boundary of the phase cylinder is foliated by \(C^0\)-invariant curves. Under this assumption we prove that the billiard curve is an ellipse. Other versions of Birkhoff-Poritsky conjecture follow from this result. For the original Birkhoff-Poritsky formulation we show that if a neighborhood of the boundary of billiard domain has a \(C^1\)-smooth foliation by convex caustics of rotation numbers in the interval \((0, 1/4]\) then the boundary curve is an ellipse. The main ingredients of the proof are: (1) the non-standard generating function for convex billiards; (2) the remarkable structure of the invariant curve consisting of \(4\)-periodic orbits; and (3) the integral-geometry approach initiated in [B0], [B1] for rigidity results of circular billiards. Surprisingly, we establish a Hopf-type rigidity for billiards in the ellipse. Based on a joint work with Andrey E. Mironov (Novosibirsk). Note: The zoom link to the seminar will be posted on https://www.dinamici.org/dai-seminar/ and on https://mathseminars.org/seminar/DinAmicI. Moreover, it will be streamed live on youtube via the DinAmicI channel: https://www.youtube.com/channel/UCyNNg155G3iLS7l-qZjboyg
Per informazioni, rivolgersi a: sorrentino@mat.uniroma2.it
Venerdì 12 febbraio 2021
Ore 16:00, Il seminario sarà tenuto in modalità telematica, Link per partecipare: https://uniroma1.zoom.us/meeting/register/tZwtcOGqqzkpE9yen93NMtuUttv031ZmB9lt
Seminari per docenti (PLS)
Francesca Tovena (Università di Tor Vergata)
Frazioni e approssimazioni
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interessata. Le comunicazioni pervenute in ritardo saranno ignorate.
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