Notiziario Scientifico
a cura del Dipartimento di Matematica G. Castelnuovo, Sapienza Università di Roma
Settimana dal 13-05-2019 al 19-05-2019
Lunedì 13 maggio 2019
Ore 12:00, Aula 311, Dipartimento di Matematica e Fisica, Largo S. L. Murialdo 1
Seminario di Crittografia
Luca De Feo (Université de Versailles)
Isogeny graphs in cryptography: the good, the bad and the ugly
Isogenies of elliptic curves have recently come under the spotlight thanks to their applications in post quantum cryptography. The two prominent isogeny-based primitives, SIDH and CSIDH, provide, respectively, the key encapsulation with the lowest communication complexity among all candidates to the NIST post-quantum competition, and the only known efficient post-quantum non-interactive key exchange. Computational problems related to isogenies have been studied for more than 30 years, owing to their connections to elliptic curve cryptography. I will thus start by reviewing the relevant computational problems, and highlight some recent results. I will then introduce isogeny graphs, and explain how they are useful in cryptography; in particular I will point out what they are good for, what they are not-so-good at, and what they are absolutely terrible at. Finally, I will present some research perspectives and some important open problems.
Lunedì 13 maggio 2019
Ore 14:15, Aula Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Analisi Matematica
Stephane Junca (University of Nice Sophia Antipolis, Nice, France)
Hyperbolic conservation laws, oscillations and fractional BV spaces
In 1994, a Lions, Perthame and Tadmor conjecture proposes an optimal regularity in fractional Sobolev spaces for entropy solutions of nonlinear multidimensional scalar conservation laws. The first optimal result for uniformly convex fluxes by Lax and Oleinik 1957 is stated in BV ( space of functions with bounded variation) which gives the sharp Sobolev regularity and, moreover, the trace property on each side of a shock wave. Unfortunately, "BV is not enough" to explain this conjecture. Examples of strongly oscillating waves not in BV are presented. Fractional BV spaces seem to be appropriate to encompass these examples and retain the "BV trace property" and the optimal Sobolev exponent conjectured by Lions, Perthame and Tadmor.
Lunedì 13 maggio 2019
Ore 15:30, Aula 5, Università UNINT, Via C. Colombo 200
Seminario
Alexandra Otiman (Università Roma Tre e Institute of Mathematics "Simon Stilov", Romanian Academy)
Geometria Hermitiana e complessa di una sottoclasse di varietà di Kato
Martedì 14 maggio 2019
Ore 14:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Analisi Matematica
Jingang Xiong (Beijing Normal University)
On asymptotic behavior of solutions of conformally invariant equations with isolated singularities.
I will review some classical results of conformally invariant equations with isolated singularities. I will report a recent joint work with Tianling Jin, in which we solved the higher order case. Our approach uses blow up analysis for local integral equations, and is unified for all critical elliptic equations of order smaller than the dimension.
(*) this seminar is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
Martedì 14 maggio 2019
Ore 15:00, 1B1, Pal. RM002, Dipartimento SBAI, Sapienza Università di Roma
Incontri di Algebra e Geometria allo SBAI
Salvatore Stella (University of Haifa (Israel))
Acyclic cluster algebras via Coxeter double Bruhat cells and generalized minors
Cluster algebras come with a canonical partial basis: the cluster monomials. Extending this partial basis to a full basis has been one of the central problems in the theory giving raise to a varied zoo of constructions. In this talk we will explain how Lie theory can be used to relate them. Specifically, after recalling the basic definitions, we will explain how any acyclic cluster algebra can be seen as the ring of coordinates of a suitable double Bruhat cell in the associated Kac-Moody group. Under this identification we will interpret cluster monomials as generalized minors -- certain functions on a Kac-Moody group defined in terms of its representations -- and explain how one can use generalized minors to extend cluster monomials to a continuous family of bases of the cluster algebra in the affine cases. This talk is based on joint works with D. Rupel and H. Williams
Martedì 14 maggio 2019
Ore 15:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Seminario di Analisi Matematica
Yeyao Hu (University of Texas at San Antonio)
Uniqueness and symmetry of solutions to a mean field equation on tori.
We prove a sharp uniqueness result of a mean field equation on arbitrary flat tori. We first establish the evenly symmetry of the solutions by the newly invented sphere covering inequality which is of independent interest. Then we employ a careful nodal line analysis together with a homotopic argument to show the uniqueness.
(*) this seminar is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
Martedì 14 maggio 2019
Ore 15:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Andrea Moiola (Dipartimento di Matematica F. Casorati, Università di Pavia)
Acoustic and electromagnetic transmission problems: wavenumber-explicit bounds and resonance-free regions
We consider the Helmholtz and the time-harmonic Maxwell transmission problems with one penetrable star-shaped Lipschitz obstacle. Under a natural assumption about the ratio of the wavenumbers, we prove bounds on the solution in terms of the data, with these bounds explicit in all parameters. For example, in the case of the Helmholtz equation, the (weighted) \( H^1 \) norm of the solution is bounded by the \( L^2 \) norm of the source term, independently of the wavenumber. Such explicit bounds are key to developing frequency-explicit error analysis for numerical methods such as FEM and BEM. The "shape-robustness" allows to quantify how variations in the shape of the obstacle affect the solution and makes the bounds particularly suitable for uncertainty quantification (UQ) applications. These bounds then imply the existence of a resonance-free strip beneath the real axis. If the assumption on the wavenumbers is lifted, then no bound with polynomial dependence on the wavenumber is possible. Joint work with Euan Spence (University of Bath).
Martedì 14 maggio 2019
Ore 15:00, Aula primo piano, IAC-CNR, Via dei Taurini 19
Seminario IAC
Alberto Saracco (Università di Parma)
Fighting Gerrymandering: a discrete approach
Whenever an election is run dividing the population into electoral districts, each based on winner-takes-all, the Gerrymangdering phenomenon appears. Over 2 centuries ago, Massachusetts' Governor Gerry modified the boundaries of his own ellectoral district in order to assure his re-election. Indeed, whenever two parties (or candidates) run for an election, if one of them has more then one third of the votes, the electoral districts can be shaped in order to assure its electoral win. Thus a double-faced problem arises: on one hand a method is needed to measure how gerrymandered a district is; on the other hand it would be useful to have an objective method to shape districts and avoiding the possibility of gerrymandering. A great part of the mathematical studies on the problem have been devoted either to geometrical propertiesof the district or on the application of the theory of isoperimetrical problems in this area. Recently it has been pointed out that it would be more realistic a discrete geometry approach, based on graphs and nets. In this talk I will present a discrete districting plan proposed by Giorgio Saracco and myself and analyse its properties.
Mercoledì 15 maggio 2019
Ore 14:00, Aula di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Francesco Bonsante (Università di Pavia)
Energia \( L^1 \) di mappe tra superfici iperboliche e teoria di Teichmüller
Nel seminario parlerò di una energia \( L^1 \) di mappe tra superfici iperboliche, introdotta da Trapani e Valli. I punti critici di tali mappe sono caratterizzati da essere mappe che preservano l’area e il cui grafico è una superficie minima. Schoen ha mostrato che in ogni classe di omotopia di mappe esiste sempre un unico rappresentante minimizzante per questa energia \( L^1 \). Considerando lo spazio di Teichmüller \( T(S) \) come lo spazio delle metriche iperboliche su \( S \) a meno dell’azione dei diffeomorfismi isotopi all’identità, considererò la funzione su \( T(S) \times T(S) \) ottenuta minimizzando l’energia \( L^1 \) dell’identità sulle orbite. In particolare discuterò come tale funzione degenera quando una delle variabili diverge ad un punto del bordo di Thurston di \( T(S) \). Nella seconda parte del seminario proporrò una generalizzazione del funzionale nel caso di mappe da una superficie iperbolica in una tre varietà, ricavandone l’equazione di Eulero-Lagrange e studiando lo spazio delle immersioni minimizzanti. Il lavoro presentato è in collaborazione con Gabriele Mondello e Jean-Marc Schlenker.
Giovedì 16 maggio 2019
Ore 14:30, Aula 211, Dipartimento di Matematica e Fisica, Largo S. L. Murialdo 1
Seminario di Geometria
Alex Kuronya (University of Frankfurt)
Effective global generation on manifolds with numerically trivial canonical bundle
If L is a line bundle on a projective manifold, then the existence of effective bounds for its tensor powers to have global sections or become globally generated have been a central problem in algebaic geometry for the last 150 years. While the case of curves follows from Riemann-Roch, satsifactory answers for surfaces only arrived about thirty years ago. Research in the area has been mostly motivated by Fujita's conjectures predicting the global generation and very ampleness of certain adjoint line bundles. In this talk we will consider the case of effective global generation for projective manifolds with numerically trivial canonical bundle. This is an account of joint work with Yusuf Mustopa.
Giovedì 16 maggio 2019
Ore 14:30, Aula di consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Tommaso Leonori (Sapienza)
Large solution for an equation involving the p-Laplacian with p diverging
In this talk we deal with explosive solutions to an equation of p-Laplacian type involving a nonlinear gradient term in a smooth bounded domain. We are interested in studying the behavior of the large solutions (i.e. solutions that blow-up at the boundary) as p diverges and in particular we will focus on how the limit depends on the domain.
Venerdì 17 maggio 2019
Ore 11:30, Aula 311, Dipartimento di Matematica e Fisica, Largo S. L. Murialdo 1
Seminario di Logica Matematica
Le Thanh Dung Nguyen (Université Paris 13)
Proof Nets Through the Lens of Graph Theory
One of the main innovations introduced by linear logic at its birth is a representation of proofs as graph-like structures called "proof nets", instead of trees as in natural deductions. However, there have been very few attempts to connect these proof nets with mainstream graph theory. In this talk, we will discuss the benefits of such connections: * Using a relationship between unique perfect matchings and MLL+Mix proof nets first noticed by Retoré, we obtain the best known algorithms for MLL+Mix correctness and sequentialization, and discover some purely graph-theoretical results inspired by linear logic.
(Reference for this part: https://arxiv.org/abs/1901.10247 )
* The notion of combinatorial map (already applied to the combinatorics of the lambda-calculus by Bodini-Gardy-Jacquot, Zeilberger-Giorgetti...) allows us to recast Girard's "long trip" criterion in terms of topology of surfaces, and also induces some clarifications in the theory of cyclic linear logic.
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