Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 12-06-2023 al 18-06-2023
Lunedì 12 giugno 2023
Ore 12:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Geometria
Siye Wu (National Tsing Hua University, Taiwan)
Deformation of the Pre-quantum Action. Part 2.
In geometric quantisation, there is a family of complex polarisations. In this talk, we consider a family of star products in deformation quantisation. We construct the action of a function on a section of the prequantum line bundle. In the case of symplectic vector spaces, the star products are non-formal, and are compatible the projectively flat connection on the bundle of Hilbert spaces. The construction is equivariant with respect to symplectic group actions that can be lifted to metaplectic group actions on the bundles. We also consider the fermionic counterpart, where there is a family of (isomorphic) spinor representations on the Clifford algebra.
Lunedì 12 giugno 2023
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Analisi Matematica
Riccardo Caniato (ETH Zurich)
Variations of Yang-Mills lagrangians in high dimension.
In this talk we will present some analysis aspects of gauge theory in high dimension. First, we will study the completion of the space of arbitrary smooth bundles and connections under L^p-control of their curvature. We will start from the classical theory in critical dimension (i.e. n=2p) and then move to the super-critical dimension (i.e. n>2p), making a digression about the so called “abelian” case and thus showing an analogy between p-Yang-Mills fields on abelian bundles and a special class of singular vector fields. In the last part, we will show how the previous analysis can be used in order to build a Schoen-Uhlenbeck type regularity theory for Yang-Mills fields in supercritical dimension.
Per informazioni, rivolgersi a: azahara.delatorrepedraza@uniroma1.it
Martedì 13 giugno 2023
Sala seminari INdAM, c/o edificio G. Castelnuovo, Sapienza Università di Roma
Convegno
Round meanfield II, crowd-opinion-cells and more
Programma:
- 10.00-11.00 Pierre Degond: Swarming rigid bodies in dimension n
- pausa caffè
- 11.30 Marta Menci: Modelling cell dynamics: a numerical trip across the scales
- pranzo
- 14.30-15.30 Sébastien Motsch: TBA
- pausa caffè
- 16.00 Nathalie Ayi e Nastassia Pouradier Duteil: Graph limit for interacting particles systems on weighted random graph
Martedì 13 giugno 2023
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Federico Pichi (École Polytechnique Fédérale de Lausanne)
Projection-based and data-driven reduced order models for parametric bifurcation problems
Bifurcating phenomena, i.e. sudden changes in the system’s qualitative behavior, are linked to the non-uniqueness of the solution and arise in several physical contexts. This talk discusses intrusive and non-intrusive Reduced Order Models (ROMs) for reconstructing bifurcation diagrams originating from parametrized PDEs. Indeed, when exploiting standard high-fidelity techniques (e.g. Finite Element, Finite Volume), the associated computational cost is unaffordable and compromises the whole investigation. We propose branch-wise POD and deflated-greedy as projection-based approaches to certify the error and obtain consistent speedup. Furthermore, we compare these results with purely data-driven ones obtained by exploiting novel machine learning frameworks. In particular, we introduce linear and nonlinear ROMs, based on feedforward and graph neural networks, to learn the latent dynamics and overcome the curse of dimensionality. We test the proposed methodologies on Coanda’s effect, a bifurcating benchmark in fluid dynamics held by the Navier-Stokes equations. Applications include: (i) Optimal Control problems to steer the bifurcating behavior and (ii) varying geometries giving rise to complex evolutions.
Martedì 13 giugno 2023
Ore 17:00, Aula B, Dipartimento di Matematica
YAMS - Young Algebraist Meetings in Sapienza
Giacomo Hermes Ferraro (Sapienza - Università di Roma)
The quest for a functional equation of L-functions in Drinfeld theory
The theory of Drinfeld modules, pioneered by Anderson and Thakur in th 90's, was conceived as a possible analogue to the theory of complex elliptic curves in finite characteristic, where the role of the ring of integers \(\mathbb{Z}\) is assumed by the ring of regular functions of some curve \(X/\mathbb{F}_q\). We will introduce the analogues of the real and complex numbers, of the period lattices, and of the exponential map in this context. Two novel objects - special functions and Pellarin L-functions - arise in this theory, which have no parallel in characteristic zero, and can be conceived as interpolations of Gauss sums and Dirichlet L-functions, respectively; we will present some results about their relation, and compare them to the classical functional equation for Dirichlet L-functions.
Per informazioni, rivolgersi a: sabino.ditrani@uniroma1.it
Mercoledì 14 giugno 2023
Sala seminari INdAM, c/o edificio G. Castelnuovo, Sapienza Università di Roma
Convegno
Round meanfield II, crowd-opinion-cells and more
Programma:
- 10.00-11.00 Lorenzo Pareschi: Boltzmann legacy in global optimization
- pausa caffè
- 11.30 Laurent Boudin e Francesco Salvarani: Exponential convergence to consensus in finite and infinite dimensions
- pranzo
- 14.30-15.30 Marco Di Francesco TBC: TBA
- pausa caffè
- 16.00 round table introduced by Marco Caponigro (TBC)
Mercoledì 14 giugno 2023
Ore 14:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Algebra e Geometria
Martina Lanini (Università di Roma Tor Vergata)
GKM-Theory for cyclic quiver Grassmannians
After recalling some background on Goresky-Kottwitz-MacPherson (GKM) version of the Localization Theorem for equivariant cohomology, and some of the applications of such a result to (equivariant) Schubert calculus and geometric representation theory, I will explain how it is possible -and why it is desirable- to extend such techniques to the quiver Grassmannian setting. This is joint work with Alex Puetz.
Mercoledì 14 giugno 2023
Ore 16:15, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Giovanna Marcelli (Università di Aalborg)
Adiabatic evolution of low-temperature many-body quantum systems
We consider finite-range, many-body fermionic lattice models and we study the evolution of their thermal equilibrium state after introducing a weak and slowly-varying time-dependent perturbation. Under suitable assumptions on the external driving, we derive a representation for the average of the evolution of local observables via a convergent expansion in the perturbation, for small enough temperatures. Convergence holds for a range of parameters that is uniform in the size of the system. Under a spectral gap assumption on the unperturbed Hamiltonian, convergence is also uniform in temperature. As an application, our expansion allows to prove closeness of the time-evolved state to the instantaneous Gibbs state of the perturbed system, in the sense of expectation of local observables, at zero and at small temperatures. In particular, we recover the zero temperature many-body adiabatic theorem by first taking the thermodynamic limit and then the zero temperature limit. As a corollary, we also establish the validity of linear response. Our strategy is based on a rigorous version of the Wick rotation and fermionic cluster expansion. This talk is based on a joint work with R. L. Greenblatt, M. Lange and M. Porta.
Per informazioni, rivolgersi a: basile@mat.uniroma1.it
Giovedì 15 giugno 2023
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Geometria
Sara Angela Filippini (Salento)
Residual intersections and Schubert varieties
he notion of residual intersections was introduced by Artin and Nagata. Roughly speaking, given an algebraic variety X and a closed subscheme Y in X, which is contained in another closed subscheme Z, then a closed subscheme W such that \(W \cup Y = Z\) is a residual intersection of Y in Z. This idea can be formalized as follows: Let I be an ideal in a local Cohen-Macaulay ring R, and \(A = (a_1, \ldots, a_s) \subsetneq I\). Then \(J = A:I\) is called an s-residual intersection of I if \(ht(J) \geq s \geq ht(I)\). Residual intersections provide a generalization of linkage. Indeed, if \(J = A:I\) and \(I = A:J\) for A a regular sequence, I and J are said to be linked. I will show how results of Huneke and of Kustin and Ulrich on residual intersections for standard deteminantal ideals and Pfaffian ideals respectively arise in the context of ideals of Schubert varieties in the big opposite cell of homogeneous spaces. This is joint work with J. Torres and J. Weyman.
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Venerdì 16 giugno 2023
Ore 11:00, Aula 1B1, pal. RM002, Dipartimento SBAI, Sapienza Università di Roma
Algebra e Geometria allo SBAI
Francesco Guaraldo (Sapienza Università di Roma)
Strutture algebriche su varietà differenziabili e variazioni sul tema.
Le varietà differenziabili possono essere descritte da polinomi? Nel Seminario parleremo di risultati sull'argomento e mostreremo come esso sia collegato allo studio delle varietà di Nash.
Venerdì 16 giugno 2023
Ore 16:00, Aula 311, Dipartimento di Matematica e Fisica, Università Roma Tre
Seminario di Logica
Fabio Massaioli (Scuola Normale Superiore, Pisa)
On the semantics of proofs in classical sequent calculus
I recall briefly the peculiar features of cut-reduction procedures in classical sequent calculus and the challenges they pose to the development of a satisfying notion of proof semantics. A common approach in the literature has been to adopt techniques like polarization or embeddings into intuitionistic or linear logic, which solve the difficulties by breaking the simmetry of the cut-reduction procedure. In this talk I shall explore an alternative approach that refrains from breaking symmetry, based upon the idea of tracking the presence of axioms pairing atomic formula occurrences in the conclusion of a proof. A first unrefined formulation fails to be invariant under cut-reduction, but the counter-examples suggest that the difficulty is related to the invertibility of conjunctions. This observation warrants a move to the negative formulation of classical propositional sequent calculus — also known as GS4 — where all parallel logical rule applications permute freely and the structural rules are implicit. I introduce a refined interpretation of GS4 derivations and show that it is preserved under arbitrary permutations of logical rules; then I exploit those permutations to define a global normalization procedure that preserves the interpretation (partially based on a normalization-by-evaluation technique), thus yielding a non-trivial invariant of cut-elimination in GS4. The invariants can be presented as a graphical proof-system, akin to proof-nets, enjoying a polynomial time correctness criterion and very good properties. Finally, I discuss the shortcomings of this approach and assess its ability to solve the problems described at the beginning of the talk.
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