Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 29-01-2024 al 04-02-2024
Lunedì 29 gennaio 2024
Ore 11:00, Aula Conversi, Edificio Marconi, Dipartimento di Fisica, Sapienza Università di Roma
Interdisciplinary workshop
Physics and Topology
Topology has recently found a route from mathematics to physics. Indeed, although within the Landau paradigm, quantum phases of matter differ by their symmetries, a finer classification exists, based on the topological properties of the wavefunctions. This finer classification gave rise to the discovery of new quantum topological phases of matter like quantum spin Hall systems and topological insulators, culminating with the Nobel Prize in 2016 to Haldane, Kousterliz, and Thouless. Today, topological effects are one of the most active and fruitful research areas in physics, and intense efforts have been devoted to the exploration of new topological quantum phases and phenomena. This goal is driven not only by the prediction of fundamentally new physical phenomena but also by the potential technological applications of such systems. In this workshop, after a general discussion of topological effects in physics and mathematics, more focalized talks will be given, touching specific fields like quantum topological materials, topological photonics and acoustic, topological superconductivity, and their applications in devices. In our opinion, this multidisciplinary environment is of fundamental importance for the purposes of a general vision of the topological effects in physics and for cross-fertilization among different research fields.
Detailed information, including the program and the abstract booklet, is available at the webpage: https://sites.google.com/uniroma1.it/physicsandtopology/home All the interested colleagues are welcome. The conference is partly supported by the European Union under Next Generation EU PRIN 2022 project “Interacting Quantum Systems: Topological Phenomena and Effective Theories” (PI Domenico Monaco).
Per informazioni, rivolgersi a: panati@mat.uniroma1.it
Lunedì 29 gennaio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Angelo Zanni (Sapienza Università di Roma)
Decomposizione in profili per operatori astratti: teoria ed applicazione ad un operatore a coefficienti totalmente variabili
in questo seminario vedremo una teoria astratta per una decomposizione in profili di successioni H1 tramite il flusso dell'equazione di Schrödinger. Tale decomposizione verrà poi usata per costruire, sotto opportune ipotesi, una soluzione critica, ossia con flusso precompatto. L'esistenza di tale soluzione critica può essere sfruttata per ottenere lo scattering, come vedremo nel caso di un operatore a coefficienti variabili per l'equazione di Schrödinger defocusing in dimensione 1. This seminar is part of the activities of the Excellence Department Project CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Martedì 30 gennaio 2024
Ore 14:30, aula D'Antoni, Dipartimento di Matematica, Università di Roma Tor Vergata
seminario di Geometria
Luca Battistella (Università di Bologna)
Hyperelliptic curves and differentials
Strata of differentials have been studied from several perspectives, from dynamics to geometry and topology. Algebraic geometers need compactifications. One, which is a posteriori logarithmic, was introduced by Bainbridge--Chen--Gendron--Grushevsky--Möller in terms of multiscale (collections of) differentials (on reducible nodal curves). This natural compactification is unfortunately not irreducible, but they were able to single out the main component in terms of a condition on global residues; their proof rests on transcendental methods. I will mention a conjecturally equivalent condition which is purely algebraic. In joint work with Sebastian Bozlee, we give a proof of concept of this conjecture in the case of hyperelliptic differentials. The technical core of our work is a flexible tool for constructing hyperelliptic Gorenstein contractions of reducible nodal curves, given a hyperelliptic tropical differential, i.e. a suitable piecewise-linear function, on the dual graph.
Per informazioni, rivolgersi a: guidomaria.lido@gmail.com
Martedì 30 gennaio 2024
Ore 16:00, Aula "Dal Passo", Dipartimento di Matematica, Università di Roma "Tor Vergata"
Seminario di Analisi Matematica
Daniele Castorina (Università di Napoli Federico II)
Mean field sparse optimal control of systems with additive white noise
We analyze the problem of controlling a multi-agent system with additive white noise through parsimonious interventions on a selected subset of the agents (leaders). For such a controlled system with a SDE constraint, we introduce a rigorous limit process towards an infinite dimensional optimal control problem constrained by the coupling of a system of ODE for the leaders with a McKean-Vlasov-type SDE, governing the dynamics of the prototypical follower. The latter is, under some assumptions on the distribution of the initial data, equivalent with a (nonlinear parabolic) PDE-ODE system. The derivation of the limit mean-field optimal control problem is achieved by linking the mean-field limit of the governing equations together with the Γ-limit of the cost functionals for the finite dimensional problems. Joint work with Giacomo Ascione (SSM Napoli) and Francesco Solombrino (Napoli Federico II).
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C23000330006
Mercoledì 31 gennaio 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Giulio Bresciani (SNS Pisa)
Real versus complex plane curves
We prove that a smooth, complex plane curve of odd degree can be defined by a polynomial with real coefficients if and only if it is isomorphic to its complex conjugate; there are counterexamples in even degree. Even though the statement is completely elementary, it was not known until now. Our proof is stack-theoretic. More generally, we prove a result about fields of moduli of plane curves.
Mercoledì 31 gennaio 2024
Ore 16:00, Aula B, Dipartimento di Matematica e Fisica, Università Roma Tre
Junior seminar
Federico Pieroni (Università degli studi Roma Tre)
An overview on Coble surfaces, their moduli, and the Coble conjecture
Since the late 19th century, a classical problem in Algebraic Geometry was to find a nice description of the group of birational transformations of the projective plane \( \mathbb{P}^2 \) to itself. Coble surfaces were introduced with this aim. After a brief introduction on their definition and main properties, we will reconstruct the moduli space of Coble surfaces \( M_{Coble} \), compute its dimension, and show that every Coble surface \( X \) admits a distinguished Coble curve \( C \subset X \). We will conclude the discussion talking about the Coble conjecture: for a fixed Coble surface \( X \), can we find transformations \( \phi : X \to X \) acting identically on the Coble curve? How many surfaces inside \( M_{Coble} \) have this property?
Mercoledì 31 gennaio 2024
Ore 16:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Luigi Barletti (Università di Firenze)
Nonsingular quantum corrections to electron hydrodynamics in graphene
In recent times the hydrodynamic behaviour of electrons in graphene has attracted much interest from both the theoretical and experimental viewpoints. The usual approach to graphene hydrodynamics is "semiclassical", to the extent that the macroscopic equations are derived from a classical Boltzmann equation with conical momentum-energy relation. However, it would be interesting to obtain quantum corrections, similarly to what is done for traditional semiconductors, which can be achieved by using the quantum maximum entropy principle. However, due to the conical singular point, such procedure proves to be difficult in graphene and, so far, quantum corrections have been computed only for a regularized energy band. In the present work we show that singularities can actually be avoided, at least in the case of inviscid equations.
Finanziato dall'Unione europea – Next Generation EU
Per informazioni, rivolgersi a: basile@mat.uniroma1.it
Giovedì 01 febbraio 2024
Aula Urbano VIII, Argiletum - Roma Tre (Via della Madonna dei Monti, 40)
Mini-Workshop
Stability in Hamiltonian Dynamics and Beyond
Sponsors: PRIN 2022 "Stability in Hamiltonian Dynamics and Beyond", Progetto d'eccellenza Dipartimento di Matematica, Univ. Roma "Tor Vergata".
Program:
- 09:30 - 10:30: Olga Bernardi (Uni. Padova): Symplectic billiards: an overview and recent rigidity results.
- 10:30 - 11:00: coffee break
- 11:00 - 12:00: Stefano Baranzini (Univ. Torino): A variational approach to frozen planet orbits.
- 12:00 - 13:00: Davide Zaccaria (Univ. Roma Tre): Singular KAM Theory for generalized natural systems.
- 13:00 - 14:30: Pausa pranzo
- 14:30 - 15:30: Irene De Blasi (Univ. Torino): Billiards with potentials in Celestial Mechanics: refractive case.
- 15:30 - 16:30: Nicola Sansonetto (Univ. Verona): On integrable Hamiltonian systems on almost-symplectic manifolds.
- 16:30 - 17:00: coffee break
Giovedì 01 febbraio 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Carlo Mercuri (Università di Modena e Reggio Emilia)
Solutions to nonlinear elliptic problems involving Sobolev exponent
In this talk I will review some old and new results on existence, non-existence and multiplicity for nonlinear elliptic PDEs of the type \(-\Delta_pu+a(x)|u|^{p-2}u = |u|^{p^*-2}u\) in \(\Omega\), where \(\Omega\subseteq\mathbb R^N\) may be an unbounded domain, \(1 < p < N,\, p^* = Np/(N-p)\) is the critical Sobolev exponent, and \(-\Delta_pu=div(|\nabla u|^{p-2}\nabla u)\). In particular, I will present some recent progress in collaboration with Riccardo Molle (Tor Vergata).
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Giovedì 01 febbraio 2024
Ore 16:00, Sala di Consiglio (e anche a distanza, tramite la piattaforma Zoom), Dipartimento di Matematica, Sapienza Università di Roma
Seminari di Ricerca in Didattica della Matematica
Annalisa Cusi (Sapienza Università di Roma)
La creazione di stralci di discussioni di classe come strumento per la formazione degli insegnanti: dall’internalizzazione di un costrutto teorico allo sviluppo di nuove identità
Chi è interessato a partecipare a distanza può rivolgersi ad Annalisa Cusi (annalisa.cusi@uniroma1.it)
Venerdì 02 febbraio 2024
Aula Urbano VIII, Argiletum - Roma Tre (Via della Madonna dei Monti, 40)
Mini-Workshop
Stability in Hamiltonian Dynamics and Beyond
Sponsors: PRIN 2022 "Stability in Hamiltonian Dynamics and Beyond", Progetto d'eccellenza Dipartimento di Matematica, Univ. Roma "Tor Vergata".
Program:
- 09:30 - 10:30: Jessica Elisa Massetti (Univ. Roma Tor Vergata): Attractive invariant circles through elliptic methods.
- 10:30 - 11:00: coffee break
- 11:00 - 12:00: Gian Marco Canneori (Univ. Torino): The N-centre problem on surfaces: complex and chaotic behaviours.
- 12:00 - 13:00: Luis Garcia-Naranjo (Univ. Padova): Determination of stable branches of relative equilibria of the N-vortex problem on the sphere.
Venerdì 02 febbraio 2024
Ore 11:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma "Tor Vergata"
Kirill Zaynullin (University of Ottawa)
Algebraic Cycles and Flag Varieties
This course is a general introduction to the theory of algebraic cycles and motives of twisted flag varieties. Part 1: We first recall basic concepts related to root systems, (lectures 1-2). Chevalley groups, linear algebraic groups, and the associated projective homogeneous varieties (lectures 2-3). Part 2: We then discuss twisted flag varieties - our main object of study, e.g., generalized Severi-Brauer varieties, anisotropic quadrics, and twisted flag varieties (lecture 4). As the next step, we introduce their Chow groups, and the associated category of Grothendieck-Chow motives (lecture 5). Part 3: We provide several classical examples of motivic decompositions of twisted flag varieties (lecture 6). At the end of our course, we intend to demonstrate how a modern Schubert calculus technique (e.g. nil-Hecke modules) can be applied to obtain new/different proofs of motivic decompositions (lecture 7).
Venerdì 02 febbraio 2024
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Probabilità
Leonardo Lelli (Sapienza Università di Roma)
Zero-temperature stochastic Ising model on quasi-transitive graphs
We examine the question of fixation for zero-temperature stochastic Ising model on some connected quasi-transitive graphs. The initial spin configuration is distributed according to a Bernoulli product measure with parameter \( p\in (0,1) \). We prove that the shrink property for the underlying graph is a necessary condition for all sites to flip infinitely often almost surely (in this case the model is said of type I). Our main result shows that if \( p=1/2 \) and the graph is connected and invariant under rotations and translations, then a strengthening of the shrink property, called the planar shrink property, implies that the model is of type I. We provide an infinite class of graphs having the planar shrink property. Finally, we prove that for one-dimensional translation invariant graphs, the shrink property is a necessary and sufficient condition for the model to be of type I. This talk is based on joint work with my thesis advisor Emilio De Santis.
Venerdì 02 febbraio 2024
Ore 14:30, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar
Roberto Fringuelli (U Roma La Sapienza)
Zastava Spaces via non-degenerate maps
Let k be a field, G be a reductive group over k, B be a Borel subgroup of G, and C be a smooth curve over k. The B-orbit stratification of the flag variety G/B induces a natural stratification on the moduli space of maps from C to G/B. The open stratum is strictly related to the so-called Zastava spaces. In this talk, we give an overview of the main properties of these spaces. If time permits, we also present some consequences on the moduli space of G-bundles.
Venerdì 02 febbraio 2024
Ore 16:00, Aula Dal Passo, Dipartimento di Matematica, U Roma Tor Vergata
Algebra and Representation Theory Seminar
Giovanni Cerulli Irelli (U Roma La Sapienza)
Specialization map for quiver Grassmannians
We define a specialization map for quiver Grassmannians of Dynkin type and prove that it is surjective in type A. This generalizes a beautiful theorem of Lanini and Strickland concerning the cohomology of degenerate flag varieties. Joint ongoing work with Francesco Esposito, Ghislain Fourier, and Fang Xin.
Venerdì 02 febbraio 2024
Ore 16:00, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Seminari per i docenti a.a. 2023-2024
Paola Magrone
Preparazione dei giovsni alla scienza, alfabetizzazione matematica: la visione di Mary Everest Boole all'inizio del Novecento.
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