Notiziario Scientifico
Notiziario dei Seminari di carattere matematico
a cura del Dipartimento 'G. Castelnuovo'
Sapienza Università di Roma
Settimana dal 12 al 18 ottobre 2015
Lunedì 12 ottobre 2015
Ore 09.15, aula di Consiglio
Tullio Levi-Civita Lectures 2015
09:15 Laudatio for Tullio Levi Civita Prize 2015 to Andrea Braides
09:30 Andrea Braides Discrete-to-continuum variational methods
10:30 coffee-break
10:45 Alessia Nota From macroscopic dynamics to macroscopic equations:
the Lorentz gas
11:45 Luca Placidi Gendanken experiments for the identification of
microstructured continua
Lunedì 12 ottobre 2015
Ore 14.30, aula di Consiglio
Colloquium di Analisi Matematica
Camillo De Lellis (Universität Zürich)
The regularity of 2-dimensional area-minimizing integral currents
Building upon the Almgren's big regularity paper, Chang proved in the eighties
that the singularities of area-minimizing integral 2-dimensional currents are
isolated. His proof relies on a suitable improvement of Almgren's center manifold
and its construction is only sketched. In recent joint works with Emanuele Spadaro
and Luca Spolaor we give a complete proof of the existence of the center manifold
needed by Chang and extend his theorem to two classes of currents which are
'almost area minimizing' in a suitable sense.
Martedì 13 ottobre 2015
Ore 15.00, aula di Consiglio
Seminario di Modellistica Differenziale Numerica
M. Briani (IAC-CNR)
Numerical methods for pricing options under jump-diffusion processes
and stochastic volatility models
Partial integro-differential equation (PIDE) formulations are often preferable
for pricing options under models with stochastic volatility and jumps. In this
talk, we consider the numerical approximation of such models.
On one hand, due to the non-local nature of the integral term, we propose to use
Implicit-Explicit (IMEX) Runge-Kutta methods for the time integration to solve
the integral term explicitly, giving higher order accuracy schemes under weak
stability time-step restrictions. On the other hand, we propose a hybrid tree-finite
difference method to approximate the Heston model, possibly in the presence of jumps.
Numerical tests are presented to show the computational efficiency of the approximation.
Martedì 13 ottobre 2015
Ore 15.00, aula B, Università di Roma Tre,
via della Vasca Navale 84
Colloqui di Fisica
Vincenzo Artale (ENEA)
The Thermohaline Circulation: New Problems and Prospects
on its Study and Numerical Simulation Focusing in Particular
on the Mediterranean Ocean Circulation
Since of the '50s Stommel's pioneeristic works, the dominant paradigm
of the ocean conveyor belt is based on the concept that the horizontal
pressure forces resulting from the hydrostatically balanced horizontal
density differences drive the ocean flow. More recently, many studies
have revitalized the role of the ocean's eddy and wind field in
establishing the characteristic and variability of the global
thermohaline circulation. These recent finding reconcile Stommel
theory with the modeling results of '70 regarding the effect of eddies
on the deep flow, still an important component of the THC. Moreover
the THC, due to the intrinsic heterogeneity and nonlinearity of the
ocean circulation, describable by many variables that vary
significantly over space and time scale covering many order of
magnitude, if only due to the dominance of advective fluxes within the
ocean water 3-D domains, but also to the many complex feedback between
the domains. As consequence positive (negative) feedback can lead to
instability that drives the system to new modes of behaviour that bear
little resemblance to the external forcing, if such destabilising
processes are not properly represented, the ocean circulation, for
example simulated in the OGCM, may not able to display important
observed modes of ocean internal variability. In this talk we review
those studies, which collectively, are changing the classical view of
the global conveyor belt; in particular we discuss how these results
have had an influence on some recent theoretical and numerical results
on the Mediterranean thermohaline circulation and on its future
development.
Mercoledì 14 ottobre 2015
Ore 14.30, aula di Consiglio
Seminario di Algebra e Geometria
Michael Rapoport (Bonn)
The combinatorics and geometry of the (arithmetic) fundamental lemma
The fundamental lemma is a conjectural identity between two orbital integrals.
I will explain that it comes down to an explicit combinatorial statement that
compares numbers of certain lattices in related p-adic vector spaces. The arithmetic
fundamental lemma gives a conjectural interpretation of the derivative of an orbital
integral. I will explain that also this conjecture comes down to a very concrete
statement, this time in geometry.
Mercoledì 14 ottobre 2015
Ore 16.00, aula F, Università di Roma Tre,
largo san L. Murialdo 1
Colloquium di Matematica
Thomas Ehrhard (CNRS, Paris VII)
On the mathematical interpretation of programs and proofs
We shall see how the notions of monoidal categories, adjunctions and
monads/comonads are deeply connected to the mathematical interpretation
of functional computer programs and of mathematical proofs. We shall
illustrate how this interpretation can suggest improvements of the syntax
of programs. For instance, it allows to accommodate the call-by-name and
the call-by-value evaluation strategies in a common functional setting, or
provides a simple algebraic understanding of the 'call with current continuation'
primitive of the language scheme, both using the category of coalgebras of a comonad.
Giovedì 15 ottobre 2015
Ore 14.00, aula 211, Università di Roma Tre,
largo san L. Murialdo 1
Seminario di Geometria
Margherita Lelli Chiesa (Università di Roma Tre)
Brill-Noether theory of curves on abelian surfaces and applications
Brill-Noether theory of curves on K3 surfaces is well understood. Quite little is
known for curves lying on abelian surfaces. Given a general abelian surface S with
polarization L of type (1,n), we will first show that a general curve in |L| is
Brill-Noether general. We will then study the locus |L|^r_d of smooth curves in |L|
possessing a g^r_d and prove that this is nonempty in some unexpected cases (with
negative Brill-Noether number). As an application, we obtain the existence of a
component of the Brill-Noether locus M^r_{g,d} having the expected codimension in
the moduli space of curves M_g. Time permitting, we will mention applications to
enumerative geometry and hyperkähler manifolds. Most of this work is joint with
A. L. Knutsen and G. Mongardi.
Venerdì 16 ottobre 2015
Ore 11.00, aula 311, Università di Roma Tre,
largo san L. Murialdo 1
Seminario di Logica e Informatica
Thomas Ehrhard (Paris VII)
Linear logic, polarization and evalutaion strategies
There are two well known translations of the lambda-calculus into the
multiplicative-exponential fragment of linear logic: the call-by-name
and the call-by-value translations. The former is the standard
'Girard's translation' and the latter was called 'boring' by Girard in
his seminal LL paper. We shall see how one can extend the
lambda-calculus with simple constructions inspired by linear logic in
order to factorize these translation through a single functional
language admittedly much simpler than proof nets, and where weakening
and contraction remain implicit. This calculus bears some similarities
with Paul Levy's 'call-by-push-value' and, just as the LL translation
of classical systems, gives an essential role to the category of
coalgebras of the exponential '!'. It corresponds to a kind of
half-polarized version of linear logic.
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