Notiziario Scientifico

Settimana dal 17 al 23 giugno 2013

Lunedì 17 giugno 2013
Ore 14:30, Aula 311, Università di Roma III
Seminario di Analisi e Sistemi Dinamici
Juan Davila (Universidad de Chile)
Finite Morse index solutions to a 4th order equation with power nonlinearity
We obtain a Liouville type theorem for finite Morse index solutions of a fourth order equation with power nonlinearity. This result is sharp with respect to the exponent and dimension. The main tool is a monotonicity formula adapted to this problem. This is joint work with Louis Dupaigne, Kelei Wang and Juncheng Wei.

Lunedì 17 giugno 2013
Ore 15:00, Aula Picone
Seventh school in "Analysis and Applied Mathematics"
15:00 Lev Truskinovsky: From maximal stability to minimal stability: a paradigm change, I
17:00 Giuseppe Savarè: Gradient flows and rate independent evolutions: a variational approach, I

Martedì 18 giugno 2013
Ore 9:30, Aula Picone
Seventh school in "Analysis and Applied Mathematics"
9:30 Felix Otto: Quantitative results in stochastic homogenization, I
11:30 Lev Truskinovsky: From maximal stability to minimal stability: a paradigm change, II
14:30 Giuseppe Savarè: Gradient flows and rate independent evolutions: a variational approach, II

Martedì 18 giugno 2013
Ore 14:00, Aula di Consiglio
Colloquium di Geometria
John Lott (Università di Berkeley)
What's new with the Ricci flow?
I'll talk about old and new developments. No prior knowledge is assumed.

Mercoledì 19 giugno 2013
Ore 9:30, Aula Picone
Seventh school in "Analysis and Applied Mathematics"
9:30 Felix Otto: Quantitative results in stochastic homogenization, II
11:30 Giuseppe Savarè: Gradient flows and rate independent evolutions: a variational approach, III

Mercoledì 19 giugno 2013
Ore 14:30, Aula di Consiglio
Seminario di Algebra e Geometria
Bernd Sturmfels (Università di Berkeley)
Non-negative polynomials and sums of squares
We discuss the geometry underlying the difference between non-negative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary quartics are shown to be Noether-Lefschetz loci of K3 surfaces. The projective duals of these hypersurfaces are defined by rank constraints on Hankel matrices. We compute their degrees using numerical algebraic geometry, thereby verifying results due to Maulik and Pandharipande. The non-SOS extreme rays of the two cones of non-negative forms are parametrized respectively by the Severi variety of plane rational sextics and by the variety of quartic symmetroids. This lecture is based on work of Greg Blekherman, and on our joint paper with Jonathan Hauenstein, John Christian Ottem and Kristian Ranestad.

Mercoledì 19 giugno 2013
Ore 15:00, Aula 311, Università di Roma III
Seminario di Analisi e Sistemi Dinamici
David Sauzin (CNRS)
On the resurgent approach to Ecalle-Voronin's invariants
Given a holomorphic germ at the origin of C with a simple parabolic fixed point (i.e. F(w) = w + c w^2 + O(w^3) with non-zero c), the local dynamics is described by means of an attracting and a repelling Fatou coordinates, which also allow one to define a pair of "horn maps", of crucial importance for the problem of analytic classification and the definition of the parabolic renormalization operator (subject of many recent studies). We show how Ecalle's theory of resurgence yield a construction of a pair of Fatou coordinates from their common asymptotic expansion, which is a generically divergent Borel-summable formal series, and a description of the horn maps from the singular structure of the Borel transform of this formal series. Joint work with Artem Dudko (Stony Brook).

Giovedì 20 giugno 2013
Ore 12:00, Aula Picone
Seventh school in "Analysis and Applied Mathematics"
12:00 Felix Otto: Quantitative results in stochastic homogenization, III
14:30 Giuseppe Savarè: Gradient flows and rate independent evolutions: a variational approach, IV
16:15 Lev Truskinovsky: From maximal stability to minimal stability: a paradigm change, III

Giovedì 20 giugno 2013
Ore 15:00, Aula 1B1, Dipartimento SBAI
Seminario di Geometria
Tommaso Traetta (Università di Roma III)
Cycle decompositions with a nice automorphism group
A cycle decomposition of a graph Gamma is a set of cycles whose edges partition the edge-set of Gamma. The Oberwolfach problem OP(F) (with F denoting any graph on v vertices that is the vertex-disjoint union of cycles) asks for a decomposition of K_v or K_v - I (i.e., the complete graph minus a 1-factor) whose cycles can be partitioned into classes each isomorphic to F. A successful approach to tackle this problem is to require that our solution has an automorphism group G fixing one vertex and acting sharply transitively on the others, namely, it is 1-rotational under G. In the case where F consists of a single cycle, a solution to OP(F) is more commonly called a Hamiltonian cycle system of order v (briefly, HCS(v)). Although the literature on this topic is quite extensive, very little is known on the existence of an HCS(v) with a nice automorphism group. In this talk, I will present some recent results concerning these problems.

Venerdì 21 giugno 2013
Ore 9:30, Aula Picone
Seventh school in "Analysis and Applied Mathematics"
9:30 Felix Otto: Quantitative results in stochastic homogenization, IV
11:30 Lev Truskinovsky: From maximal stability to minimal stability: a paradigm change, IV

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