Notiziario Scientifico

Notiziario dei seminari di carattere matematico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma

Settimana dal 14-06-2021 al 20-06-2021

Lunedì 14 giugno 2021
Ore 10:00, Sala consiglio e su zoom, Dipartimento di Matematica, Sapienza Università di Roma
Mini-corso
Nathanael Berestycki
Introduction to GFF, Multiplicative Chaos and Liouville Quantum Gravity
In recent years rigorous approaches to Liouville quantum gravity have been proposed and this has led to extraordinary progress in many different directions, including our understanding of large random planar maps. These approaches are based on the Gaussian free field and its associated Gaussian multiplicative chaos. I will introduce these notions and discuss several related themes, including (time-permitting): Liouville Brownian motion, the quantum zipper and the mating of trees theorem, and applications to random planar maps.
Pagina del corso: https://vittoriasilvestri.wordpress.com/about/978-2/


Lunedì 14 giugno 2021
Ore 12:00, Aula Picone e Google Meet, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Dipartimento
Maria Anna Raspanti
Dalle trasformazioni quadratiche alle trasformazioni cremoniane
Gli sviluppi più notevoli dello studio delle trasformazioni geometriche si ebbero nella seconda metà del XIX secolo e culminarono nell’opera di Luigi Cremona sulle trasformazioni birazionali del piano e dello spazio che, a rendergli merito, presero il nome di cremoniane. Seguendo un percorso segnato dai personaggi che con la loro opera hanno maggiormente contribuito alla genesi e allo sviluppo della teoria delle trasformazioni birazionali del piano, si vedrà come, oltre alla figura centrale di Cremona, se ne distinguano altre – quali G. Bellavitis (1803 – 1880), G. V. Schiaparelli (1835 – 1910) ed E. de Jonquières (1820 -1901) – i cui studi, che precedono quelli di Cremona, risultano avere un ruolo più rilevante di quanto finora emerso.


Mercoledì 16 giugno 2021
Ore 10:30, Sala consiglio e su zoom, Dipartimento di Matematica, Sapienza Università di Roma
Mini-corso
Nathanael Berestycki
Introduction to GFF, Multiplicative Chaos and Liouville Quantum Gravity
In recent years rigorous approaches to Liouville quantum gravity have been proposed and this has led to extraordinary progress in many different directions, including our understanding of large random planar maps. These approaches are based on the Gaussian free field and its associated Gaussian multiplicative chaos. I will introduce these notions and discuss several related themes, including (time-permitting): Liouville Brownian motion, the quantum zipper and the mating of trees theorem, and applications to random planar maps.
Pagina del corso: https://vittoriasilvestri.wordpress.com/about/978-2/


Mercoledì 16 giugno 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
Mihai Păun (Universität Bayreuth)
On extension of twisted canonical forms defined on the central fiber of a Kähler family
We will report on a joint work with J. Cao. Our main result establishes the extension of twisted canonical forms defined on an infinitesimal neighborhood of the central fiber of a Kahler family under a natural \( L^2 \) hypothesis.
Per informazioni, rivolgersi a: diverio@mat.uniroma1.it


Mercoledì 16 giugno 2021
Ore 14:30, https://meet.google.com/pip-kvzt-fkz, Dipartimento di Fisica, Sapienza Università di Roma
Seminario delle Meccaniche
Lorenzo Bertini (Università di Roma La Sapienza)
Large deviations associated to Boltzmann equations: formulation, open problems, and applications.
We consider a system of N particles interacting via stochastic binary collisions, like the celebrated Kac's model. We discuss the large deviations asymptotic of the empirical measure and flow reviewing some relevant results and open problems. In particular, we show that - with probability exponentially small in N - there are paths that do not conserve the total energy. The structure of the large deviations rate function provides a natural gradient flow formulation of the underlying Boltzmann-Kac equation. As an application of this formulation, we finally discuss - in the context of non-homogeneous linear kinetic equations - the diffusive scaling limit.


Mercoledì 16 giugno 2021
Ore 16:00, Online seminar, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Algebre di Operatori
Nicola Pinamonti (Università di Genova)
Sine-Gordon fields with non vanishing mass on Minkowski spacetime and equilibrium states
During this talk we shall discuss the construction of the massive Sine-Gordon field in the ultraviolet finite regime when the background is a two-dimensional Minkowski spacetime. The correlation functions of the model in the adiabatic limit will be obtained combining recently developed methods of perturbative algebraic quantum field theory with techniques developed in the realm of constructive quantum field theory over Euclidean spacetimes. More precisely, perturbation theory is used to represent interacting fields as power series in the coupling constant over the free theory. Adapting techniques like conditioning and inverse conditioning to spacetimes with Lorentzian signature, we shall see that these power series converge if the interaction Lagrangian has generic compact support. Finally, adapting the cluster expansion technique to the Lorentzian case, we shall see that the adiabatic limit of the correlation functions of the interacting equilibrium state at finite temperature is finite. The talk is based on a joint work with D. Bahns and K. Rejzner [arxiv.org:2103.09328] This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006. Link
Per informazioni, rivolgersi a: v.morinelli@gmail.com


Giovedì 17 giugno 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
Jorgen Rennemo (Oslo)
Fixed-point loci in the Hilbert schemes of points in the plane
The Betti numbers of Hilbert schemes of points in the plane were first computed by Ellingsrud and Strømme. In this talk, we'll let a finite cyclic group act on the plane, and consider the analogous problem of computing the Betti numbers of the fixed loci under the induced action on the Hilbert scheme of points. The main result is a new product formula for the Betti numbers in the case where no element of the group fixes the symplectic form on the plane. This is joint work with Paul Johnson.
Per partecipare al seminario cliccare sul seguente link.


Giovedì 17 giugno 2021
Ore 16:00, Streaming via Zoom and Youtube channel, Web site for information: https://www.dinamici.org/dai-seminar/
DinAmicI: Another Internet Seminar (DAI Seminar)
Mauro Artigiani (Universidad del Rosario (Colombia))
Double rotations and their ergodic properties
Double rotations are the simplest subclass of interval translation mappings. A double rotation is of finite type if its attractor is an interval and of infinite type if it is a Cantor set. It is easy to see that the restriction of a double rotation of finite type to its attractor is simply a rotation. It is known due to Suzuki - Ito - Aihara and Bruin - Clark that double rotations of infinite type are defined by a subset of zero measure in the parameter set. We introduce a new renormalization procedure on double rotations, which is reminiscent of the classical Rauzy induction. Using this renormalization, we prove that the set of parameters which induce infinite type double rotations has Hausdorff dimension strictly smaller than 3. Moreover, we construct a natural invariant measure supported on these parameters and show that, with respect to this measure, almost all double rotations are uniquely ergodic. In my talk I plan to outline this proof that is based on the recent result by Fougeron for simplicial systems. I also hope to discuss briefly some challenging open questions and further research plans related to double rotations. The talk is based on a joint work with Charles Fougeron, Pascal Hubert and Sasha Skripchenko. 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 18 giugno 2021
Ore 15:00, Seminario Telematico, link
Online Representation Theory Seminar
Lara Bossinger (UNAM Oaxaca)
Newton--Okounkov bodies for cluster varieties
Cluster varieties are schemes glued from algebraic tori. Just as tori themselves, they come in dual pairs and it is good to think of them as generalizing tori. Just as compactifications of tori give rise to interesting varieties, (partial) compactifications of cluster varieties include examples such as Grassmannians, partial flag varieties or configurations spaces. A few years ago Gross--Hacking--Keel--Kontsevich developed a mirror symmetry inspired program for cluster varieties. I will explain how their tools can be used to obtain valuations and Newton--Okounkov bodies for their (partial) compactifications. The rich structure of cluster varieties however can be exploited even further in this context which leads us to an intrinsic definition of a Newton--Okounkov body. The theory of cluster varieties interacts beautifully with representation theory and algebraic groups. I will exhibit this connection by comparing GHKK's technology with known mirror symmetry constructions such as those by Givental, Baytev--Ciocan-Fontanini--Kim--van Straten, Rietsch and Marsh--Rietsch. (joint work in progress with M.Cheung, T. Magee and A. Nájera Chávez.)


Le comunicazioni relative a seminari da includere in questo notiziario devono pervenire esclusivamente mediante apposita form da compilare online, entro le ore 24 del giovedì precedente la settimana interessata. Le comunicazioni pervenute in ritardo saranno ignorate. Per informazioni, rivolgersi all'indirizzo di posta elettronica seminari@mat.uniroma1.it.
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