Notiziario Scientifico
a cura del Dipartimento di Matematica Guido Castelnuovo, Sapienza Università di Roma
Settimana dal 14-10-2024 al 20-10-2024
Lunedì 14 ottobre 2024
Sala di Consiglio, Dipartimento di Matematica "G. Castelnuovo", Sapienza Università di Roma
Conferenza
Hyperkähler varieties and related topics, II
Programma:
- 9:30 - 10:30 Claire Voisin (IMJ-PRG) On a question of Borel and Haefliger
- 11:00 - 12:00 Alessio Bottini (Universität Bonn) The derived category of the variety of lines on a cubic fourfold
- 14:30 - 15:30 Salvatore Floccari (Universität Bielefeld) The hyperKummer construction
- 16:00 - 17:00 Mirko Mauri (IMJ-PRG) The P=W paradigm for compact hyperkähler manifolds
Lunedì 14 ottobre 2024
Ore 16:00, Aula M1, Dipartimento di Matematica e Fisica, Università degli Studi Roma Tre
Colloquium di Teoria dei Numeri
Ken Ono
University of Virginia
This talk presents “partition theoretic” analogs of the classical work of Matiyasevich that resolved Hilbert’s Tenth Problem in the negative. The Diophantine equations we consider involve equations of MacMahon’s partition functions and their natural generalizations. Here we explicitly construct infinitely many Diophantine equations in partition functions whose solutions are precisely the prime numbers. To this end, we produce explicit additive bases of all graded weights of quasimodular forms, which is of independent interest with many further applications. This is joint work with Will Craig and Jan-Willem van Ittersum.
Per informazioni, rivolgersi a: laura.capuano@uniroma3.it
Martedì 15 ottobre 2024
Sala di Consiglio, Dipartimento di Matematica "G. Castelnuovo", Sapienza Università di Roma
Conferenza
Hyperkähler varieties and related topics, II
Programma:
- 9:30 - 10:30 Arend Bayer (University of Edinburgh) Non-commutative abelian surfaces, Kummer-type Hyperkaehler varieties, and Weil-type abelian fourfolds
- 11:00 - 12:00 Laura Pertusi (Università di Milano) Cubic threefolds and noncommutative curves
- 12:00 - 13:00 Giovanni Mongardi (Università di Bologna) Regenerations and applications
- 14:30 - 15:30 Paolo Stellari (Università di Milano) Deformation of t-structures with applications to hyperkaehler geometry, I
- 16:00 - 17:00 Antonio Rapagnetta (Università Tor Vergata) Singular moduli spaces of sheaves on K3 surfaces
Martedì 15 ottobre 2024
Ore 15:00, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
Seminario di Modellistica Differenziale Numerica
Adriano Festa (Politecnico di Torino)
A network model for urban planning
In this seminar we present a mathematical model to describe the evolution of a city, which is determined by the interaction of two large populations of agents, workers and firms. The map of the city is described by a network with the edges representing at the same time residential areas and communication routes. The two populations compete for space while interacting through the labour market. The resulting model is described by a two population Mean-Field Game system coupled with an Optimal Transport problem. We prove existence and uniqueness of the solution and we provide some numerical tools to develop several numerical simulations. This is a joint work with Fabio Camilli (Sapienza Roma) and Luciano Marzufero (Libera Università di Bolzano).
Martedì 15 ottobre 2024
Ore 15:00, aula E, Dipartimento di Matematica, Sapienza Università di Roma
seminario di Fisica Matematica
Suren Poghosyan (Institute of Mathematics, Armenian National Academy of Sciences)
Limit Theorems for Classical Gases
We consider classical continuous system of interacting particles in Euclidean space (classical gas). Our approach to the limit theorems for the particle number is based on the method of cluster expansions which is well known for nite Gibbs processes. In case of the limiting Gibbs process with empty boundary conditions, we use our result on the cluster representation of such processes which goes back to Malyshev and Minlos. We prove integral and local central limit theorems for a large class of stable and regular pair potentials (which include physically relevant interactions) if the activity is small. In case of local central limit theorem we obtain also an estimate of convergence rate.
Per informazioni, rivolgersi a: basile@mat.uniroma1.it, domenico.monaco@uniroma1.it
Mercoledì 16 ottobre 2024
Sala di Consiglio, Dipartimento di Matematica "G. Castelnuovo", Sapienza Università di Roma
Conferenza
Hyperkähler varieties and related topics, II
Programma:
- 9:30 - 10:30 Davesh Maulik (MIT) Algebraic cycles and Hitchin systems
- 11:00 - 12:00 Laure Flapan (Michigan State University) Cones of Noether-Lefschetz divisors and moduli of hyperkähler manifolds
- 12:00 - 13:00: Giulia Saccà (Columbia University) Lefschetz Standard conjecture for Lagrangian fibrations
Mercoledì 16 ottobre 2024
Ore 14:30, Aula B, Dipartimento di Matematica, Sapienza Università di Roma
Minicorso
Emanuele Macrì (Université Paris-Saclay)
Stable bundles on Fano and hyper-Kähler manifolds, lezione 2
The aim of this course is to present some recent advances in the theory of stable sheaves on higher dimensional varieties, in particular Fano and hyper-Kähler manifolds. We will start by reviewing the case of surfaces. We will then turn to Fano threefolds, where the theory is in a certain sense a generalization of the case of curves, by studying in detail the case of cubic threefolds. Finally, we will consider hyper-Kähler fourfolds, where the theory gives a generalization of Mukai's theory on K3 surfaces. This seminar is part of the activities of the Dipartimento di Eccellenza CUP B83C23001390001 and it is funded by the European Union – Next Generation EU.
Mercoledì 16 ottobre 2024
Ore 15:00, Aula Dal Passo, Dipartimento di Matematica, Università di Roma Tor Vergata
Colloquium di Levi Civita
Silvia Pappalardi (University of Cologne)
Free probability approaches to quantum many-body dynamics
Understanding how to characterize quantum chaotic dynamics is a longstanding question. The universality of chaotic many-body dynamics has long been identified by random matrix theory, which led to the well-established framework of the Eigenstate Thermalization Hypothesis. In this talk, I will discuss recent developments that identify Free Probability - a generalization of probability theory to non-commuting objects - as a unifying mathematical framework to describe correlations of chaotic many-body systems. I will show how the full version of the Eigenstate Thermalization Hypothesis, which encompasses all the correlations, can be rationalized and simplified using the language of Free Probability. This approach uncovers unexpected connections between quantum chaos and concepts in quantum information theory, such as unitary designs. Note: This talk is part of the activity of the MUR Excellence Department Project MatMod@TOV (CUP E83C23000330006). Sponsored by the European Research Council by the Advanced Grant 669240 QUEST “Quantum Algebraic Structures and Models”
Per informazioni, rivolgersi a: pizzo@axp.mat.uniroma2.it
Mercoledì 16 ottobre 2024
Ore 16:30, Aula Picone, Dipartimento di Matematica, Sapienza Università di Roma
Colloquium Guido Castelnuovo
Corinna Ulcigrai (Università di Zurigo)
Flows on surfaces: dynamics and rigidity
lows on surfaces are one of the most studied examples of dynamical systems, starting from the work of Poincaré at the end of the 19th century. Many models of systems of physical origin are described by flows on surfaces, e.g. in celestial mechanics, polygonal billiard dynamics, or solid-state physics. While the topological structure of trajectories has been well understood already in the last century, the ergodic theory and the fine chaotic properties of flows which preserve area have been an active area of research in the last decades. In this talk, we will survey some of the results, as well as recent breakthroughs on linearisation and rigidity questions in higher genus.
Giovedì 17 ottobre 2024
Sala di Consiglio, Dipartimento di Matematica "G. Castelnuovo", Sapienza Università di Roma
Conferenza
Hyperkähler varieties and related topics, II
Programma:
- 9:30 - 10:30 Eyal Markman (University of Massachusetts) Algebraic Weil classes on abelian 2n-folds from secant sheaves on abelian n-folds
- 11:00 - 12:00 Ignacio Barros (University of Antwerp) Theta-extension and extremal divisors on moduli spaces of HK varieties
- 12:00 - 13:00 Georg Oberdieck (KTH) Towards refined curve counting on the Enriques surface
- 14:30 - 15:30 Qizheng Yin (Peking University) D-equivalence conjecture for \(K3^{[n]}\)
- 16:00 - 17:00 Nick Addington (University of Oregon) The Quillen-Lichtenbaum dimension of complex varieties
Giovedì 17 ottobre 2024
Ore 14:15, Aula M1, Dipartimento di Matematica e Fisica, Università Roma 3
Seminario di Geometria
Francesco Tropeano (Roma 3)
Relative monodromy of abelian logarithms for finite covers of universal families
Let us consider a complex abelian scheme endowed with a non-torsion section. On some suitable open subsets of the base it is possible to define the period map, i.e. a holomorphic map which marks a basis of the period lattice for each fiber. Since the abelian exponential map of the associated Lie algebra bundle is locally invertible, one can define a notion of abelian logarithm attached to the section. In general, the period map and the abelian logarithm cannot be globally defined on the base, in fact after analytic continuation they turn out to be multivalued functions: the obstruction to the global existence of such functions is measured by some monodromy groups. In the case when the abelian scheme is endowed with a finite surjective modular map onto some suitable universal family of abelian varieties, we show that the relative monodromy group of the abelian logarithm is non-trivial and of full rank. As a consequence we deduce a new proof of Manin's kernel theorem and of the algebraic independence of the coordinates of abelian logarithms with respect to the coordinates of periods. (Joint work with Paolo Dolce, Westlake University.)
Per informazioni, rivolgersi a: amos.turchet@uniroma3.it
Giovedì 17 ottobre 2024
Ore 14:30, Sala di Consiglio, Dipartimento di Matematica, Sapienza Università di Roma
P(n)/N(p) : Problemi differenziali nonlineari/Nonlinear differential problems
Paolo Cosentino (Università di Roma Tor Vergata)
A Harnack type inequality for singular Liouville type equations
We are concerned with a generalization to the singular case of a result of C.C. Chen e C.S. Lin [Comm. An. Geom. 1998] for Liouville-type equations with rough potentials. The singular problem is actually more delicate and results in a nontrivial variation of the regular case. Part of the arguments of Chen-Lin can be adapted to the singular case by means of an isoperimetric inequality for surfaces with conical singularities. The rest of the proof actually requires a different approach, due to the loss of translation invariance of the problem.
Per informazioni, rivolgersi a: galise@mat.uniroma1.it
Venerdì 18 ottobre 2024
Sala di Consiglio, Dipartimento di Matematica "G. Castelnuovo", Sapienza Università di Roma
Conferenza
Hyperkähler varieties and related topics, II
Programma:
- 9:30 - 10:30 Olivier Debarre (Université Paris Cité) On a conjecture of Kazhdan and Polishchuk
- 11:00 - 12:00 Robert Laterveer (Université de Strasbourg) On the Chow ring of double EPW sextics
- 14:30 - 15:30 Alina Marian (ICTP) The geometry of Quot schemes of zero-dimensional quotients on a curve
- 16:00 - 17:00 Emanuele Macrì (Université Paris-Saclay) Deformation of t-structures with applications to hyperkaehler geometry, II
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