PROGRAM

12 June    13 June    14 June    15 June    16 June    17 June    printable version

Monday 12 June
10.00    Opening of the Meeting
10.15 - 11.00    Marco PELOSO (Politecnico di Torino)
“Analysis of the Hodge-Laplacian on forms on the Heisenberg group” 
11.00    Coffee Break
11.30 - 12.15    Andrea MALCHIODI (SISSA/ISAS, Trieste)
“Minimal surfaces in CR manifolds” 
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We consider surfaces immersed in three-dimensional CR manifolds. We define the notion of mean curvature and of the associated (p-)minimal surfaces, extending some concepts previously given for the (flat) Heisenberg group. As a differential equation, the p-minimal surface equation is degenerate (hyperbolic and elliptic). To analyze the singular set of solutions (where the tangent plane of the graph coincides with the contact plane) we prove some extension theorems, which describe how the characteristic curves meet the singular set. This allows us to classify the entire solutions to this equation and to solve a Bernstein-type problem (for graphs over the xy-plane) in the Heisenberg group H1.
In H1, the p-minimal surfaces are classical ruled surfaces with the rulings generated by Legendrian lines. We also discuss some related issues.
12.15 - 13.00    Luca CAPOGNA (University of Arkansas)
“Generalized mean curvature flow in Carnot group” 
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The sub-Riemannian mean curvature flow consists in flowing hypersurfaces in the direction of the "horizontal normal" with velocity depending on the horizontal mean curvature. The presence of so-called characteristic points makes this study much harder than its Riemannian counterpart. The level set formulation of the flow, coupled with the notion of viscosity (or generalized) solution extends well to the sub-Riemannian setting and allows to prove analogues of the results by Evans-Spruck, Chen-Giga-Goto. I will describe ongoing joint work with Giovanna Citti (U. Bologna) where we study viscosity solutions of the mean curvature flow of level sets in Carnot groups.
13.00    Lunch
14.45 - 15.30    Ugo BOSCAIN (SISSA/ISAS, Trieste)
“Singular Riemannian Geometry from a Control Theory Point of View” 
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In this talk I will consider problems of Singular Riemannian Geometry that naturally arise in Control Theory.
More precisely consider n smooth vector fields on a n-dimensional manifold. If these vector fields are always linearly independent, then they define a classical Riemannian metric on the manifold (the metric for which they are orthonormal).
On the other side, relaxing the hypothesis that they are always linearly indipendent, then the corresponding Riemannian metric has singularities and interesting phenomena appears.
A famous example in R2 is provided by the vector fields F1(x1,x2)=(1,0), F2(x1,x2)=(0,x1), originally introduced by Grushin, Lanconelli and Franchi for the study of hypoelliptic operators in PDEs
I will discuss the relation between curvature and conjugate points, and, for the two dimensional compact case, I will present a Gauss-Bonnet like theorem, on the relation between the integral of the curvature and the topology of the manifold.
15.30 - 16.15    Andrea PASCUCCI (Università di Bologna)
“Equations of Kolmogorov type and applications to stochastic volatility modeling” 
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The talk will present a survey of the theory of partial differential equations of Kolmogorov type arising in physics and in mathematical finance. These evolutionary equations, which are generally non-uniformly parabolic, are naturally associated to stochastic models with memory. Financial derivatives with dependence on the past provide some typical examples: in particular, some applications to the modeling of stochastic volatility for the evaluation of derivative securities will be discussed.
16.15    Coffee Break
16.45 - 17.30    Laurent DENIS (Université d'Evry Val d'Essonne)
“Maximum principle for solutions of quasilinear SPDE's” 
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17.30 - 18.00    Anis MATOUSSI (Université du Maine)
“Stochastic PDE, Stochastic flow and Backward Stochastic Differential Equations” 
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I will present results on existence and uniqueness of solution of semilinear SPDE's and reflected SPDE's, using stochastic flow and Backward SDE method.
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Tuesday 13 June
09.30 - 10.15    Guozhen LU (Wayne State University)
“Potential and Capacitary estimates on stratified groups” 
10.15 - 11.00    Abbas BAHRI (Rutgers University)
“Compactness” 
11.00    Coffee Break
11.30 - 12.00    Giuseppe DI FAZIO (Università di Catania)
“Strong A∞ weights and quasilinear degenerate elliptic equations” 
12.00 - 12.30    Luisa MOSCHINI (Università di Roma "La Sapienza")
“Sharp two-sided heat kernel estimates for critical Schrodinger operators on bounded domains” 
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12.30 - 13.00    Maria Alessandra RAGUSA (Università di Catania)
“On a class of hypoelliptic differential operators” 
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13.00    Lunch
14.45 - 15.30    Marco BIROLI (Politecnico di Milano)
“Γ-convergence for strongly local Dirichlet forms in open sets with holes with homogeneous Neumann boundary conditions” 
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15.30 - 16.00    Raffaela CAPITANELLI (Università di Roma "La Sapienza")
“p-Lagrangians on fractals” 
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We present some functional inequalities for measure-valued p-Lagrangians on homogeneous spaces. This approach is very useful for the study of the dynamics of intrinsically irregular structures as the most common fractals.
16.00 - 16.30    Francesco UGUZZONI (Università di Bologna)
“A boundary point regularity criterion for a class of degenerate parabolic equations” 
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Wednesday 14 June
09.30 - 10.15    Ugo GIANAZZA (Università di Pavia)
“Harnack Estimates for Quasi-Linear Degenerate Parabolic Differential Equations” 
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We establish the intrinsic Harnack inequality for non-negative solutions of a class of degenerate, quasilinear, parabolic equations, including equations of the p-Laplacian and porous medium type. It is shown that the classical Harnack estimate, while failing for degenerate parabolic equations, it continues to hold in a space-time geometry intrinsic to the degeneracy.
The proof uses only measure-theoretical arguments, it reproduces the classical Moser theory, for non-degenerate equations, and it is novel even in that context. Hölder estimates are derived as a consequence of the Harnack inequality. The results solve a long stading issue in the theory of degenerate parabolic equations.
10.15 - 11.00    Yves ACHDOU (Université Pierre et Marie Curie)
“Approximation of solutions of Hamilton-Jacobi equations on the Heisenberg group” 
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11.00    Coffee Break
11.30 - 12.15    Isabeau BIRINDELLI (Università di Roma "La Sapienza")
“Geometric properties of minimizers in phase transition models in the Heisenberg group” 
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We consider a functional related with phase transition models in the Heisenberg group framework. We prove that level sets of local minimizers satisfy some density estimates, that is, they behave as codimension one sets. We thus deduce a uniform convergence property of these level sets to interfaces with minimal area. These results are then applied in the construction of (quasi)periodic, plane-like minimizers, i.e., minimizers of our functional whose level sets are contained in a spacial slab of universal size in a prescribed direction. As a limiting case, we obtain the existence of hypersurfaces contained in such a slab which minimize the surface area with respect to a given periodic metric.
This is a joint work with Enrico Valdinoci.
12.15 - 13.00    Bianca STROFFOLINI (Università di Napoli)
“Semiconcavity of the distance in the Heisenberg group” 
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13.00    Lunch
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Thursday 15 June
09.30 - 10.15    Jorge HOUNIE (Universidade Federal de São Carlos)
“Some extensions of the F. and M. Riesz theorem” 
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10.15 - 11.00    Antonio BOVE (Università di Bologna)
“Analytic hypo-ellipticity for sums of squares of vector fields” 
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We make a short survey of the most recent results on a.h.e. for sums of squares and its connection with Treves conjecture
11.00    Coffee Break
11.30 - 12.15    Cristian GUTIERREZ (Temple University)
“Second derivatives estimates for solutions to the Monge-Ampere equation” 
12.15 - 13.00    Giovanna CITTI (Università di Bologna)
“Estimates of the fundamental solution for a family of hypoelliptic operators” 
13.00    Lunch
14.45 - 15.30    Abdelaziz RHANDI (Université Cadi Ayyad)
“Global Properties of Transition Densities associated to Parabolic Problems with Unbounded Coefficients” 
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15.30 - 16.00    Enrico PRIOLA (Università di Torino)
“Liouville theorems for Kolmogorov equations” 
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Let L be a second order elliptic operator on Rn (with first and second order terms); a regular and bounded function u: Rn → R is called a bounded harmonic function for L if Lu=0 on Rn.
We study existence and non-existence of non-constant bounded harmonic functions for L. This problem has also a probabilistic interpretation.
Moreover, we investigate bounded harmonic functions for more general non-local Kolmogorov operators L which arise in the study of stochastic differential equations driven by Levy processes.
16.00    Coffee Break
16.30 - 17.00    Diego PALLARA (Università di Lecce)
“Analytic Semigroups Generated by Elliptic Operators with Boundary Degeneration of First Order” 
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17.00 - 17.30    Giorgio METAFUNE (Università di Lecce)
“Global Regularity of Invariant Measures” 
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Friday 16 June
09.30 - 10.15    Zoltan BALOGH (Universität Bern)
“Differentiability in Metric Spaces” 
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A Stepanov type differentiability theorem in the context of metric measure spaces implying almost pointwise differentiabilty of Sobolev funtions will be presented. Sufficient liminf type conditions for membership in Sobolev spaces are given in terms of local Lipschitz numbers.
Joint work with Marianna Csörnyei, kevin Rogovin and Thomas Zürcher.
10.15 - 11.00    Bruno FRANCHI (Università di Bologna)
“Compensated compactness in the contact complex of Heisenberg groups” 
11.00    Coffee Break
11.30 - 12.15    Thierry COULHON (Université de Cergy-Pontoise)
“Large time behavior of heat kernels on forms” 
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This is a report on a joint work with Qi S. Zhang. We derive large time upper bounds for heat kernels on vector bundles of differential forms on a class of non-compact Riemannian manifolds under certain curvature conditions.
12.15 - 12.45    Daniele MORBIDELLI (Università di Bologna)
“The Liouville theorem for conformal maps in the Grushin metric” 
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12.45    Lunch
14.30 - 15.15    Sandro SALSA (Politecnico di Milano)
“Thin obstacle problems and fractional Laplacian” 
15.15 - 16.00    Valentino MAGNANI (Università di Pisa)
“On Pansu differentiability” 
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We show uniform estimates on the Pansu difference quotient of mappings between Carnot groups
16.00    Coffee Break
16.30 - 17.00    Annunziata LOIUDICE (Università di Bari)
“Semilinear subelliptic equations on rational Carnot groups” 
17.00 - 17.30    Fausto FERRARI (Università di Bologna)
“A Steiner formula in the Heisenberg group for Carnot-Charathéodory balls” 
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We shall deal with a Steiner formula in the Heisenberg group for balls given by the Carnot-Charathéodory distance. As a byproduct we shall deduce some informations concerning the intrinsic curvatures measures of the ball itself
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Saturday 17 June
09.30 - 10.15    Luca LORENZI (Università di Parma)
“On a class of degenerate elliptic operators with unbounded coefficients” 
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10.15 - 10.45    Giovannni CUPINI (Università di Firenze)
“On a class of elliptic operators with unbounded coefficients” 
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We consider a class of second order, linear elliptic operators with unbounded lower-order coefficients. Assuming suitable growth conditions on the coefficients, such operators generate a strongly continuous semigroup in Lp(RN). An explicit characterization of the domain is given.
10.45    Coffee Break
11.15 - 12.00    Marco BRAMANTI (Politecnico di Milano)
“Schauder estimates for parabolic and elliptic nondivergence operators of Hörmander type” 
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12.00 - 12.45    Vincenzo VESPRI (Università di Firenze)
“Extension of DeGiorgi's theory to a class of non power-like singularities” 
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We consider local bounded solutions of
β(u)t = Σi,j=1n Di(aij(x,t)Dj(u))
where the coefficients aij are uniformly elliptic, bounded and measurable functions and β is a C1-piecewise function with at least a linear growth.
Moreover, if s0 is an irregular point for β, we assume β to be locally concave in a proper right neighborhood of s0 and locally convex in a proper left neighborhood of the same point.
Assume, for the sake of semplicity, s0=0. By using suitable DeGiorgi's techniques, we have the following alternative:
1) either u is continuous and its modulus of continuity can be given in a quantitatively way,
2) or in cylinders of length β(s)/s for any s>0 small enough, we have that
β'(s)s/β(s) ≤ C1 | {(x,t) ∈ Q such that u(x,t) ≤ s} | |Q|-1 ≤- C2 (log s)-1
This latter inequality implies the regularity of the solution for a large class of functions β and therefore we are able to extend DeGiorgi's theory to a class of non power-like singularities.
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