## Prossimi Seminari

Martedì 19 Giu ore 14:30
presso Seminario II
seminario di algebra e geometria
tra circa 2 ore
On the Morin problem
Grzegorz Kapustka
We will study the Morin problem and present a method of classification of finite complete families of incident planes in ℙ5 as a result we prove that there is exactly one, up to Aut(P^5), configuration of maximal cardinality 20 and a unique one parameter family containing all the configurations of 19 planes. The method is to study projective models of appropriated moduli spaces of twisted sheaves on K3 surfaces. This is a joint work with A. Verra.
Martedì 19 Giu ore 16:00
presso Seminario I
seminario di fisica matematica
tra circa 4 ore
Singularities of the leading Lyapunov exponents of a random matrix product and a related continuous process
Rafael Greenblatt
** IL SEMINARIO SI TERRA' ALLE ORE 16 ** I will discuss a certain infinite product of random, positive 2×2 matrices appearing in the exact solution of some 1 and 1+1 dimensional disordered models in statistical mechanics, which depends on a deterministic real parameter ε and a random real parameter with distribution μ. For a large class of μ, we prove a prediction by B. Derrida and H. J. Hillhorst (1983) that the leading Lyapunov exponent behaves like C ε^2α in the limit ε→0, where α ∈ (0,1) is determined by μ. The proof is made possible by a contractivity argument which makes it possible to control the error involved in using an approximate stationary distribution similar to the original proposal, along with some refinements in the estimates obtained using that distribution. A limiting procedure gives a continuum process whose leading Lyapunov estimate admits an exact formula, which also allows us to reformulate part of the argument by McCoy and Wu for the presence of an essential singularity in the free energy of the two-dimensional Ising model with columnar disorder in a form which is closely related to the results obtained for the random matrix product, but which does not yet provide a proof.
Martedì 19 Giu ore 16:00
presso Seminario II
seminario di algebra e geometria
tra circa 4 ore
Derived and L-equivalence of manifolds in examples.
Michal Kapustka
I will present several examples of derived and L-equivalent pairs of non-birational Calabi-Yau type manifolds aiming at understanding the relation between these two notions of equivalence. We will try to find a common geometric framework governing these examples. The talk will include joint work with Marco Rampazzo and with Grzegorz Kapustka and Riccardo Moschetti.
Mercoledì 20 Giu ore 14:30
presso Aula Tonelli
seminario di analisi numerica
Scattering by fractal screens: functional analysis and computation
Andrea Moiola
The mathematical analysis and numerical simulation of acoustic and electromagnetic wave scattering by planar screens is a classical topic. The standard technique involves reformulating the problem as a boundary integral equation on the screen, which can be solved numerically using a boundary element method. Theory and computation are both well-developed for the case where the screen is an open subset of the plane with smooth (e.g. Lipschitz or smoother) boundary. In this talk I will explore the case where the screen is an arbitrary subset of the plane; in particular, the screen could have fractal boundary, or itself be a fractal. Such problems are of interest in the study of fractal antennas in electrical engineering, light scattering by snowflakes/ice crystals in atmospheric physics, and in certain diffraction problems in laser optics. The roughness of the screen presents challenging questions concerning how boundary conditions should be enforced, and the appropriate function space setting. But progress is possible and there is interesting behaviour to be discovered: for example, a sound-soft screen with zero area (planar measure zero) can scatter waves provided the fractal dimension of the set is large enough. This research has also motivated investigations into the properties of fractional Sobolev spaces (the classical Bessel potential spaces) on non-Lipschitz domains. Accurate computations are also challenging because of the need to adapt the mesh to the fine structure of the fractal. As well as presenting numerical results, I will outline some outstanding open questions. This is joint work with Simon Chandler-Wilde (Reading) and David Hewett (UCL).
Giovedì 21 Giu ore 10:15
presso - Aula Da Stabilire -
seminario di analisi matematica
Caloric Harnack Inequality, Mean Value Theorem and Capacity: the Bruno Pini Work Towards Modern Parabolic Potential Theory
Ermanno Lanconelli
We describe the pioneering work of Bruno Pini towards the modern Potential Analysis of linear second order parabolic Partial Differential Equations. We mainly focus on the caloric Harnack Inequality discovered by Bruno Pini in 1954, jointly, and independently, with Jacques Hadamard. Pini made of this inequality the crucial tools in his construction of a Wiener-type solution to the ''Dirichlet problem'' for the Heat equation. To this end he also introduced an average operator on the level set of the Heat kernel, characterizing caloric and sub-caloric functions, in analogy with the classical Gauss-Koebe, Blaschke-Privaloff and Saks Theorems for harmonic and sub-harmonic functions. Pini also established, and used, the notion of caloric capacity to study the boundary behavior of his Wiener-type solution to the first boundary value problem for the Heat equation.
Giovedì 21 Giu ore 11:00
presso - Aula Da Stabilire -
seminario di analisi matematica
RECENT RESULTS ABOUT THE MAXIMUM PRINCIPLE ON UNBOUNDED DOMAINS
Italo Capuzzo Dolcetta
I will give an overview of some results concerning the validity of sign propagation property u ≤ 0 on ∂Ω, F(x,u,Du,D2u) ≥ 0 in Ω implies u ≤ 0 in Ω in an unbounded domain Ω satisfying either measure-type or geometric conditions related to the directions of ellipticity of the (possibly) degenerate fully nonlinear mapping F.
Giovedì 21 Giu ore 12:00
presso - Aula Da Stabilire -
seminario di analisi matematica
Measure-valued and discontinuous solutions of some evolution equations
Michiel Bertsch
Motivated by an application to stratified turbulent flows in oceanography, I shall discuss some singular solutions of nonlinear PDE's of evolutionary type, in particular discontinuous and Radon measure valued solutions. We focus on different regularizations of backward parabolic equations, first order scalar conservation laws, and, if time permits, a toy problem for a Hamilton-Jacobi equation. Most of this lecture is based on collaborations with L. Giacomelli, F. Smarrazzo, A. Terracina and A. Tesei.
Giovedì 21 Giu ore 15:00
presso - Aula Da Stabilire -
seminario di analisi matematica
Sobolev and BV functions in infinite dimension
Alessandra Lunardi
In Hilbert or Banach spaces $X$ endowed with a good probability measure $\mu$ there are a few "natural" definitions of Sobolev spaces and of spaces of bounded variation functions. The available theory deals mainly with Gaussian measures and Sobolev and BV functions defined in the whole $X$, while the study and Sobolev and BV spaces in domains, and/or with respect to non Gaussian measures, is largely to be developed. As in finite dimension, Sobolev and BV functions are tools for the study of different problems, in particular for PDEs with infinitely many variables, arising in mathematical physics in the modeling of systems with an infinite number of degrees of freedom, and in stochastic PDEs through Kolmogorov equations. In this talk I will describe some of the main features and open problems concerning such function spaces.
Giovedì 21 Giu ore 16:00
presso - Aula Da Stabilire -
seminario di analisi matematica
The Agmon-Douglis-Nirenberg Problem for Dynamic Boundary Conditions
Jerome Goldstein
Giovedì 21 Giu ore 17:00
presso - Aula Da Stabilire -
seminario di analisi matematica
Regularity of the optimal sets for spectral functionals and the free boundary for the vectorial Bernoulli problem
Susanna Terracini
Venerdì 22 Giu ore 09:30
presso - Aula Da Stabilire -
seminario di analisi matematica
EVOLUTIONARY POLITICS: LESSONS FROM THE IMMUNE SYSTEM
Miguel Angel Herrero García
Miguel A. Herrero Real Academia de Ciencias and Universidad Complutense, Madrid, Spain. Consider a society consisting of a large number of individuals (about 10 13, several orders of magnitude larger than today´s world population) organized in hundreds of different social groups (current count of UN countries being about 200) and employed in many different jobs. Assume further a huge immigration rate (about 1011 new arrivals per day) coupled to a high mortality rate, so as to balance the previous figure. Such society enjoys full employment, and wealth is shared by all individuals. Order is maintained by an extremely efficient police force that keeps threatening aliens at bay. What kind of government could possibly be up to the task of ruling such society? The answer is simple: none. Anarchy prevails in the society we have summarily described, which is not located at the remote island of Utopia: it is just you (or me) and no central organ of control is in charge of its operation. Its efficient performance is an emergent property, resulting from individual decisions of its cells, and is not centrally regulated from any commanding headquarters. We shall describe in this lecture some features of one of the cornerstones of this complex structure, the immune system, and will shortly remark on other cell regulation properties which show a distinct emergent character as well.
Venerdì 22 Giu ore 10:30
presso - Aula Da Stabilire -
seminario di analisi matematica
New Results on Instantaneous Blowup in HN
Gisèle Ruiz Goldstein
Venerdì 22 Giu ore 11:30
presso - Aula Da Stabilire -
seminario di analisi matematica
On Harnack's contributions to potential theory
Umberto Bottazzini
One of B. Pini's most quoted papers deals with his (and Hadamard's) contemporary derivation of a theorem analogue to a theorem by Harnack on harmonic functions. In the talk I will focus on Harnack's contributions to potential theory and his solution to Dirichlet problem as presented in his 1887 book as well as to Kellog's 1929 book on potential theory to which Pini himself referred in his paper
Venerdì 22 Giu ore 14:30
presso - Aula Da Stabilire -
seminario di analisi matematica
Mild solutions to a second order Hamilton- Jacobi equation arising in mathematical finance
Viorel Barbu
Existence and uniqueness of a mild solution to the dynamic programming equation corresponding to optimal control associated with the Heston stochastic volatility control is studied. The approach is based on nonlinear semigroup theory in the space $L^{1}$.
Venerdì 22 Giu ore 15:30
presso - Aula Da Stabilire -
seminario di analisi matematica
Regularity in free boundary problems with distributed sources
Sandro Salsa
We describe recent results obtained in collaboration with Daniela De Silva and Fausto Ferrari on two-phase free bounday problems in presence of distributed sources. The focus will be mainly on higher regularity and related open problems.
Giovedì 28 Giu ore 16:00
presso Aula Seminario VIII piano
seminario di analisi matematica
The Lane-Emden equation on a planar domain
Angela Pistoia
I will review some old and new results concerning existence, multiplicity and asymptotic behaviour of solutions to the classical Lane-Emden equation on a planar domain when the exponent of the non-linearity is large.
Giovedì 05 Lug ore 14:00
presso Seminario II
seminario di algebra e geometria
CR Structures Of Once-Punctured Torus Bundles
Alex Casella
The Cauchy-Riemann geometry (CR in short) is modelled on the three sphere and the group of its biholomorphic transformations. In 2008 Falbel makes use of ideal triangulations to shows that the figure eight knot complement admits a (branched) CR structure. This three manifold belongs to a larger class of important three manifolds that are fiber bundles over the circle, with fiber space the once-punctured torus. In this talk we introduce the audience to these manifolds and show that almost every once-punctured torus bundle admits a (branched) CR structure.
Venerdì 06 Lug ore 17:30
presso Aula Vitali
seminario di analisi matematica
Regularity properties of the solutions of several hyperbolic equations and systems
Petar Popivanov
This talk deals with the regularity properties (including propagation and interaction of nonlinear waves) of the solutions of the Cauchy problem to 2D semilinear wave equation with the removable singularities of the solutions of fully nonlinear hyperbolic systems arising in the mechanics of compressible fluids with constant entropy, and with the regularizing properties of the multidimensional wave equation with dissipative term. We shall first discuss the machinery of the pseudodifferential, respectively paradifferential operators which is applied. More precisely, "radially smooth" initial data having singularities on a "massive" set of angles in the plane, including the Cantor continuum set, yield singularities propagating as in the linear case. There is a big difference between the 2D case and the multidimensional case (3D) when the interaction of several (for example four) characteristic hyper-planes could produce singularities on a dense subset of the compliment of the light cone of the future located over the origin. A result of Bony for the triple interaction of progressing linear waves in the 2D case is commented too as then new effect appears: new born wave propagating along the cone of the future with vertex at the origin. We assume that the first variation of the nonlinear system under consideration is linear, symmetric and positive one in the sense of Friedrichs. A microlocal version of the Moser's condition on the existence of global solutions on the torus of the same system enables us to prove the nonexistence of isolated singularities at each characteristic point of the main symbol of the first variation. For symmetric quasilinear hyperbolic systems we study the propagation of regularity. As usual, the strength of the singularities is measured both in Sobolev space and microlocalized Sobolev spaces. An example from fluid mechanics will be presented in order to illustrate our results.
Lunedì 09 Lug ore 11:00
presso Dipartimento di Matematica - Sede di Rimini "Angherà 1"
seminario di finanza matematica
Generalizations of Black-Scholes model. Numerical implementations.
Angela Slavova
We propose new modules in programming environment MATHEMATICA for the Black-Scholes model taking into account the sensitivity coefficients and considering discrete dividends taxed at rate tax. Then Black Scholes model with Leland corrections is presented in the case when we have discrete dividends and discrete taxes. The modules presented in this talk are component of web-based application, realized in the program environmental with central mathematical kernel and in some sense realizes the problem proposed above, and the build software instruments can be used for research investigations, as well as for training.