Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 05-04-2021 al 11-04-2021
Martedì 06 aprile 2021
Ore 14:30, canale youtube IAC CNR https://www.youtube.com/watch?v=c5eZfeZmHEY, Istituto per le Applicazioni del Calcolo - Consiglio Nazionale delle Ricerche
AIM: Artificial Intelligence and Mathematics, fundamentals and beyond
Pietro Liò (Department of Computer Science and Technology, University of Cambridge)
How Graph neural networks are revolutionizing artificial intelligence
In this talk I will introduce the fundamentals of graph neural networks and I will describe interesting applications in computer science, engineering, biology and medicine. I will also describe the relationships with other important methodologies used in artificial intelligence.
Per informazioni, rivolgersi a: roberto.natalini@cnr.it
Mercoledì 07 aprile 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
Johan Martens (University of Edinburgh)
Sporadic behaviour of quantum representations and rank-level duality
The theory of conformal blocks provides us with projective representations of the mapping class group. These can equivalently also be constructed from the point of view of non-abelian theta functions, via the Hitchin connection. It has been known for some time that, for SL(2), these representations have infinite order, with the exception of some sporadic low levels. We will discuss how some of these sporadic cases can be understood via rank-level duality. This is joint work with Baier, Bolognesi and Pauly.
Per informazioni, rivolgersi a: pezzini@mat.uniroma1.it
Mercoledì 07 aprile 2021
Ore 14:15, Zoom Meeting Meeting ID: 993 9908 8921 Passcode: OCA_2021, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Michele Palladino (Gran Sasso Science Institute)
Introduction to Reinforcement Learning in discrete time (I)
We will briefly provide an introduction on Reinforcement Learning. Then, we will start to review Markov Chains and Markov Decision Processes.
Per informazioni, rivolgersi a: carlini@mat.uniroma1.it
Mercoledì 07 aprile 2021
Ore 14:30, https://meet.google.com/pip-kvzt-fkz, Dipartimento di Fisica, Sapienza Università di Roma
Seminario delle Meccaniche
Antonio Giorgilli (Università di Milano)
The unaccomplished perfection of Kepler's world
This talks aims at answering a question: "How did Kepler discover his celebrated laws?". The answer is somehow hidden in the main works of Kepler: "Mysterium cosmographicum", "Astronomia Nova" and "Harmonice mundi". Kepler's aim was to discover the plan of God when He created the Universe; hence it is a continuous and perseverant search for the perfection of the world. The first two laws, namely the ellipse and the second law that we now call "law of areas", are found in "Astronomia nova". The discovery of the third law in "Harmonice Mundi" comes ten years later, and appears as the conclusive answer to the search of perfection. However, while working on the compilation of the "Rudolphine tables" Keper himself realized that there are inequalities in the motions of Jupiter and Saturn (and possibly of the other planets) which are not in full agreement with the elliptic shape pf the orbits. The case of Jupiter and Saturn is now known as "the great inequality". In this sense the search of perfection should be considered as unaccomplished.
Giovedì 08 aprile 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
Cristina Sabena (Università di Torino)
L'apprendimento della matematica in una prospettiva semiotica multimodale: dalla ricerca empirica alla costruzione di strumenti teorici (e viceversa)
Giovedì 08 aprile 2021
Ore 16:00, On-line seminar (via Zoom and youtube), Web site for information: https://www.dinamici.org/dai-seminar/
DinAmicI: Another Internet Seminar (DAI Seminar)
Eva Miranda and Daniel Peralta-Salas (UPC Barcelona and ICMAT Madrid)
Looking at Euler flows through a contact mirror: Universality and Turing completeness
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.. But, in view of the increase of dimension yielded by our proof. The question is can this be done in dimension 3? We will prove the existence of Turing complete fluid flows on a 3-dimensional geometric domain. Our novel strategy uses the computational power of symbolic dynamics and the contact mirror again. This talk is based on joint work with Robert Cardona and Fran Presas ( arXiv:1911.01963 and arXiv:2012.12828 ) 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
Giovedì 08 aprile 2021
Ore 18:00, link Teams, Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre
Seminario di Geometria
Karl Schwede (University of Utah)
Recent progress in mixed characteristic higher dimensional algebraic geometry
In characteristic zero birational algebraic geometry, Kawamata-Viehweg vanishing is a centrally important tool. For some applications in characteristic p > 0, one may use Frobenius and perturbations as a replacement for resolution of singularities and Kawamata-Viehweg vanishing. This talk will show how to use Bhatt's vanishing theorem for absolute integral closures mixed characteristic as a replacement for resolutions and Kawamata-Viehweg vanishing theorems in a number of applications. This is joint work with B. Bhatt, L. Ma, Z. Patakfalvi, K. Tucker, J. Waldron and J. Witaszek.
Venerdì 09 aprile 2021
Ore 15:00, Il seminario sarà tenuto in modalità telematica, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre, Largo San Leonardo Murialdo 1
Seminario di Logica e Informatica Teorica
Emilio Cruciani (Universitaet Salzburg)
Step-by-step community detection in volume-regular graphs
Spectral techniques have proved amongst the most effective approaches to graph clustering. However, in general they require explicit computation of the main eigenvectors of a suitable matrix (usually the Laplacian matrix of the graph). Recent work (e.g., Becchetti et al., SODA 2017) suggests that observing the temporal evolution of the power method applied to an initial random vector may, at least in some cases, provide enough information on the space spanned by the first two eigenvectors, so as to allow recovery of a hidden partition without explicit eigenvector computations. While the results of Becchetti et al. apply to perfectly balanced partitions and/or graphs that exhibit very strong forms of regularity, we extend their approach to graphs containing a hidden k-partition and characterized by a milder form of volume-regularity. We show that the class of k-volume regular graphs is the largest class of undirected (possibly weighted) graphs whose transition matrix admits k “stepwise” eigenvectors (i.e., vectors that have constant entries over the components corresponding to the same set of the hidden partition). To obtain this result, we highlight a connection between volume regularity and lumpability of Markov chains. Moreover, we prove that if the stepwise eigenvectors are those associated to the first k largest eigenvalues of the transition matrix of a random walk on the graph and the gap between the k-th and the (k+1)-th eigenvalues is sufficiently large, the Averaging dynamics of Becchetti et al. recovers the underlying community structure of the graph in logarithmic time, with high probability. Based on a joint work with Luca Becchetti, Francesco Pasquale, and Sara Rizzo. Link to the paper: https://arxiv.org/abs/1907.07149
Per partecipare al seminario cliccare sul seguente link Teams
Venerdì 09 aprile 2021
Ore 15:00, Seminario Telematico, link
Online Representation Theory Seminar
Giovanna Carnovale (Università di Padova)
Approximations of a Nichols algebra from a geometric point of view
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 Symn(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.
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