## Notiziario Scientifico

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

Settimana dal 29-11-2021 al 5-12-2021

Lunedì 29 novembre 2021
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Paolo Piccione (U. San Paolo del Brasile)
Nonplanar minimal spheres in ellipsoids of revolution
In 1987, Yau posed the question of whether all minimal 2-spheres in a 3-dimensional ellipsoid inside R^4 are planar, i.e., determined by the intersection with a hyperplane. While this is the case if the ellipsoid is nearly round, Haslhofer and Ketover have recently shown the existence of an embedded non-planar minimal 2-sphere in sufficiently elongated ellipsoids, with min-max methods. Using bifurcation theory and the symmetries that arise in the case where at least two semi-axes coincide, we show the existence of arbitrarily many distinct embedded non-planar minimal 2-spheres in sufficiently elongated ellipsoids of revolution. This is based on joint work with R. G. Bettiol (CUNY)

Martedì 30 novembre 2021
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, Universita' di Tor Vergata
Seminario di geometria
Federico Pintore (Universita' di Bari)
Collisions in isogeny graphs, and the security of the SIDH-based identification protocol
The digital signature schemes that have been proposed so far in the setting of the Supersingular Isogeny Diffie-Hellman scheme (SIDH) were obtained by turning an interactive identification protocol by De Feo, Jao and Plût into non-interactive schemes. The security of the resulting schemes is therefore deduced from that of the base identification protocol. In this talk, we revisit the proofs that have appeared in the literature for the special soundness property of the above-mentioned SIDH-based identification protocol. The existence of some special cycles in supersingular isogeny graphs make such previous proofs fail.
Per informazioni, rivolgersi a: onorati@mat.uniroma2.it

Martedì 30 novembre 2021
Ore 16:00, Aula "Dal Passo" e online su questo link, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Joost Hulshof (Vrije Universiteit Amsterdam)
Advancing front solutions in a degenerate reaction-diffusion system
We are interested in planar travelling wave solutions of the system $$u_t=\varepsilon\,\nabla\cdot u\nabla u+uv,\quad v_t=\nabla\cdot\nabla u-uv,$$ with nonnegative profiles  $$U$$ and $$V$$ that satisfy $$U(-\infty)=V(+\infty)=0$$ and $$U(\infty)=V(-\infty)=1$$. The corresponding solutions have (u\to1) and (v\to0) as $$t\to\infty$$. Among these traveling wave profiles there's one with $$U\equiv0$$ on the left and $$U>0$$ on the right. We discuss its existence and an approach towards its stability analysis, using a linearisation technique that we developed for the Porous Medium Fischer equation $$u_t=(uu_x)_x+u(1-u)$$ (PMF). This is part of an ongoing research project with Michiel Bertsch, Lorenzo Giacomelli and others, suggested to us by Mayan Mimura. The ultimate goal is to show that for small $$\varepsilon>0$$ the front solutions are stable in 1D but unstable in 2D. For now it seems that the results for (PMF) are nontrivial and new.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006

Mercoledì 1 dicembre 2021
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Moduli spaces of residueless meromorphic differentials and the KP hierarchy
I'll present a recent joint work with A. Buryak and D. Zvonkine, where we study the moduli spaces of residueless meromorphic differentials, i.e., the closures, in the moduli space of stable curves, of the loci of smooth curves whose marked points are the zeros and poles of prescribed orders of a meromorphic differential with vanishing residues. Our main result is that intersection theory on these spaces is controlled by an integrable system containing the celebrated Kadomtsev-Petviashvili (KP) hierarchy as a reduction to the case of differentials with exactly two zeros and any number of poles. This fact has several deep consequences and in particular it relates the aforementioned moduli spaces with Hurwitz theory, representation theory of sl2(C), integrability and a conjecture of Schmitt and Zvonkine on the r=0 limit of Witten's r-spin classes.
Per informazioni, rivolgersi a: pezzini@mat.uniroma1.it

Mercoledì 01 dicembre 2021
Ore 14:00, Aula 211 - Online a questo link, Dipartimento di Matematica e Fisica, Università degli Studi RomaTre
Seminario di Fisica matematica
Prof. Sébastien Ott (Université de Fribourg)
High temperature Ising model with exponentially decaying interactions: success and failure of Ornstein-Zernike asymptotics
The Ornstein-Zernike theory is a heuristic picture describing the behaviour of correlation functions in high temperature/low density systems. It gives a prediction for the asymptotic behaviour of the (truncated) two-point function: $$G(0,x) = c|x|^{-(d-1)/2}e^{-nu(x)}(1+o(1))$$ where nu is a norm on $$R^d$$. While the OZ picture was made rigorous in various situations, it was recently realized that the belief that the asymptotics holds generically in systems with a finite correlation length was misplaced: indeed the OZ asymptotics can be shown to fail for various systems with exponentially decaying interactions at very high temperature or very low density. In this talk, I will focus on the example of the ferromagnetic Ising model and will review the recent progresses towards the description of the fine asymptotics of G when $$T>T_c$$ and the interaction is exponentially decaying. Based on joint work with Y. Aoun, D. Ioffe, and Y. Velenik.
Per poter partecipare in presenza, sarà necessario esibire il Green Pass. I non affiliati a Roma Tre che fossero interessati a partecipare in presenza, sono pregati di prenotarsi contattando gli organizzatori all'email alessandro.giuliani@uniroma3.it.

Mercoledì 1 dicembre 2021
Ore 14:30, Canale Youtube dell'IAC https://www.youtube.com/watch?v=tq-71BgF8es, Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche
Seminari Generali IAC 2021/2022
Simone Melchionna (Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche)
AI-driven biomechanics to quantify the impact of Covid disease on breathing
The Covid disease causes pneumonia in many patients that in the most serious cases evolves into the Acute Distress Respiratory Syndrome (ARDS), requiring assisted ventilation and intensive care. In this context, identification of patients at high risk of developing ARDS is a key point for early clinical management, better clinical outcome and optimization of resources available in intensive care units. We are currently developing an AI-based computational framework that aims at predicting the ventilation efficiency of patients by using as input lung Computed Tomography (CT), the air flux in lungs obtained from biomechanical simulations and Arterial Blood Gas analysis. By using a dual approach from AI and computer simulations we investigated the feasibility of the approach on a small clinical database of proven Covid cases where the initial CT and various reports were available. We studied the time evolution of the clinical parameters and found correlation with the morphological information extracted from CT scans and disease outcome. Promising results illustrate the ability to predict the evolution of respiratory efficiency an aspect that would be of crucial importance for disease management.
roberto.natalini@cnr.it

Giovedì 2 dicembre 2021
Ore 14:15, Aula M1, Dipartimento Matematica e Fisica, Università di Roma Tre
Seminario di Geometria
Laura Capuano (Roma Tre)
Unlikely intersections in families of semiabelian varieties and applications to a conjecture of Silverman
What makes an intersection likely or unlikely? A simple dimension count shows that two varieties of dimension r and s are non "likely" to intersect if r < codim s, unless there is some special geometrical relation among them. A series of conjectures due to Bombieri-Masser-Zannier, Zilber and Pink rely on this philosophy. After a small survey on these problems, I will present a recent application to a conjecture of Silverman on the greatest common divisor of divisibility sequences coming from certain algebraic groups. This is a joint work with F. Barroero and A. Turchet.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it

Venerdì 3 dicembre 2021
Ore 15:00, Aula Dal Passo (in blended mode), Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Algebre di Operatori
Luca Giorgetti (Università di Roma Tor Vergata)
A planar algebraic description of conditional expectations
Jones' notion of index was introduced for II_1 subfactors and soon after generalized to arbitrary inclusions of von Neumann algebras, not necessarily tracial nor with trivial centers, in several ways. A unital inclusion of von Neumann algebras N < M is said to have finite Jones index if it admits at least one normal faithful conditional expectation of M onto N with finite index. In the talk, I will report on a representation formula for such finite index expectations and their dual expectations (as defined by Haagerup and Kosaki) by means of the solutions of the conjugate equations for the inclusion morphism of N into M and its conjugate morphism. In particular, this provides a 2-categorical formulation of the theory of index in this general setting. Another consequence is that an arbitrary inclusion of von Neumann algebras with a prescribed finite index expectation can be described by a Q-system. These results are both originally due to Longo in the subfactor case. Based on https://arxiv.org/abs/2111.04488. Supported by EU MSCA-IF beyondRCFT grant n. 795151 and by MIUR Excellence Department Project awarded to the Department of Mathematics of the University of Rome Tor Vergata, CUP E83C18000100006. This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006.
Per informazioni, rivolgersi a: v.morinelli@gmail.com

Venerdì 3 dicembre 2021
Ore 16:30, Il seminario sarà svolto in modalità telematica, Chi è interessato a partecipare può rivolgersi a alessandro.gambini@uniroma1.it
Seminario PLS per insegnanti
Claudio Bernardi e Alessandro Gambini (Sapienza Università di Roma)
Questioni di aritmetica e algebra
Per informazioni, rivolgersi a: v.morinelli@gmail.com

Sabato 4 dicembre 2021
Ore 14:30, Sala del chiostro, Facoltà di Ingegneria Civile e Industriale, via Eudossiana 18, Roma
Conferenza nell'ambito del Progetto del Dipartimento di Scienze di Base e Applicate per l'Ingegneria "Il fascino della Matematica e delle sue Applicazioni"
Elena Bonetti (Ministro per le pari opportunità e Università degli Studi di Milano)
La trama invisibile. La matematica che scrive la storia
La conferenza mostra come la matematica è stata e sarà strategica nei passaggi cruciali della storia.
Per informazioni, rivolgersi a: Sandra.Carillo@uniroma1.it

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