Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 17-01-2022 al 23-01-2022
Martedì 18 gennaio 2022
Ore 14:30, Aula Dal Passo, Dipartimento di matematica, Universita' di Roma Tor Vergata
Seminario di Geometria
Eleonora Di Nezza (Ecole Polytechnique de Paris)
Families of Kähler-Einstein metrics
In a lot of geometric situations we need to work with families of varieties. In this talk we focus on families of singular Kähler-Einstein metric. In particular we study the case of a family of Kähler varieties and we develop the first steps of pluripotential theory in family, which will allow us to have a control on the C^0 estimate when the complex structure varies. This type of result will be applied in different geometric contexts. This is a joint work with V. Guedj and H. Guenancia.
Per informazioni, rivolgersi a: onorati@mat.uniroma2.it
Mercoledì 19 gennaio 2022
Ore 14:30, Canale Youtube dell'IAC https://www.youtube.com/watch?v=oCzuzztVuZ8, Istituto per le Applicazioni del Calcolo, Consiglio Nazionale delle Ricerche
Seminari generali IAC 2022
Andrea Raiconi (Istituto per le Applicazioni del Calcolo - Cnr)
The Knapsack Problem with Forfeit Sets
The 0/1 Knapsack Problem is one of the most well-known problems in combinatorial optimization, with multiple applications including capital budgeting, loading of goods in transport vehicles, and assignment of tasks or resources, among others. In this presentation we introduce a novel variant of the problem called Knapsack Problem with Forfeit Sets (KPFS), which considers a collection of possibly overlapping sets of items (forfeit sets), representing contrasting choices. Each set has an associated allowance threshold and a penalty cost. The allowance threshold defines how many items can be chosen from each set before paying, in the objective function, the associated cost. A global limit on the number of allowed threshold violations is also considered. We show the problem to generalize two previously proposed variants of the 0/1 Knapsack Problem, and present a polynomially solvable subcase. Finally, we propose three heuristic and metaheuristic approaches to face the problem and present some computational results.
Per informazioni, rivolgersi a: briani@iac.rm.cnr.it
Mercoledì 19 gennaio 2022
Ore 16:15, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Fisica Matematica
Serena Cenatiempo (GSSI, L' Aquila)
A second order upper bound for confined hard sphere bosons
In this talk we present a second order upper bound for the ground state energy of a gas of N bosons confined in the three dimensional unit torus and interacting through a hard sphere potential with radius of order 1/N (Gross-Pitaevskii regime). Our result matches the known expression for the energy in the case of integrable potentials, and represents the first example where an upper bound for a hard sphere Bose gas capturing the second order term is obtained. The proof is based on a suitable modification of the trial state used by Dyson in his pioneering ’57 paper. Joint work with G. Basti, A. Olgiati, G. Pasqualetti and B. Schlein.
Giovedì 20 gennaio 2022
Ore 14:15, online, registrazione disponibile alla pagina https://www.mcqm.it/talks/registration.html
ciclo "Mathematical Challenges in Quantum Mechanics"
Nicolas Rougerie (ENS Lyon)
Two modes approximation for bosons in a double well potential
We study the mean-field limit for the ground state of a gas of bosonic particles in a double-well potential, jointly with the limit of large inter-well separation/large potential energy barrier. Two one-body wave-functions are then macroscopically occupied, one for each well. The physics in this two-modes subspace is usually described by a Bose-Hubbard Hamiltonian, yielding in particular the transition from an uncorrelated "superfluid" state (each particle lives in both potential wells) to a correlated "insulating" state (half of the particles live in each potential well). Through precise energy expansions we prove that the variance of the number of particles within each well is suppressed (violation of the central limit theorem), a signature of a correlated ground state. Quantum fluctuations around the two-modes description are particularly relevant, for they give energy contributions of the same order as the energy difference due to suppressed variances in the two-modes subspace. We describe them in terms of two independent Bogoliubov Hamiltonians, one for each potential well. Joint work with Alessandro Olgiati and Dominique Spehner.
Per informazioni, rivolgersi a: monaco@mat.uniroma1.it
Giovedì 20 gennaio 2022
Ore 15:00. Il seminario sarà tenuto in modalità telematica. Chi è interessato a partecipare può rivolgersi ad Annalisa Cusi (annalisa.cusi@uniroma1.it)
Seminari di Ricerca in Didattica e Storia della Matematica
Claudio Bernardi (Sapienza Università di Roma)
Le dimostrazioni in matematica: esempi e osservazioni
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.
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