Notiziario Scientifico
Settimana dal 16 al 22 settembre 2013
Martedì 17 settembre 2013
Martedì 17 settembre 2013
Martedì 17 settembre 2013
Martedì 17 settembre 2013
Martedì 17 settembre 2013
Mercoledì 18 settembre 2013
Mercoledì 18 settembre 2013
Giovedì 19 settembre 2013
Giovedì 19 settembre 2013
Giovedì 19 settembre 2013
Giovedì 19 settembre 2013
Giovedì 19 settembre 2013
Venerdì 20 settembre 2013
Tutte le informazioni relative a questo notiziario devono pervenire
all'indirizzo di posta elettronica
seminari@mat.uniroma1.it,
o nella casella della posta di Luigi Orsina, entro le ore 9 del venerdì
precedente la settimana di pubblicazione.
Ore 9:00, Aula Picone
9:00 Takashi Suzuki (Osaka University), Elliptic and parabolic equations on planar domains, I
11:15 Pavol Quittner (Comenius University), Long-time behavior of solutions of semilinear parabolic
problems, I
Ore 11:00, Aula Dal Passo, Università di Roma II
Let G be an reductive algebraic group (for example a special linear group) and let B be a Borel
subgroup (i.e., a maximal closed connected solvable subgroup). The representation theory of G is
closely related to the algebraic geometry of the quotient space G/B. In characteristic 0 this
connection is succinctly summarized by the Borel-Bott-Weil Theorem. This shows in particular that
the cohomology of a line bundle is non-zero in at most one degree and its character is either a Weyl
character or 0. In characteristic p the connection between the representation theory and geometry
still exists and has been extremely useful (in work by Haboush, Andersen, Jantzen and others).
Nevertheless there is no known analogue of the Borel-Bott-Weil Theorem. Earlier work (e.g. that of
Andersen and Humphreys) has focused on the module structure of the cohomology spaces. However,
concentrating only on the character one can get complete information in some low rank cases using
infinitesimal methods. So far the cases worked out completely are G = SL(2) (classical), G = SL(3)
(Donkin), and G = Sp(4) in characteristic2 (Donkin and Geranios). We describe an approach to this
problem using infinitesimal methods and how they may be used to give recursive formulas for the
characters of the cohomology of line bundles in favorable circumstances.
Ore 11:00, Aula 311, Università di Roma III
Seminario di Probabilità
Answering a question of Benjamini and Schramm, we show that the Poisson boundary of any planar,
uniquely absorbing (e.g. one-ended and transient) graph with bounded degrees can be realised
geometrically as a circle, namely as the boundary of a tiling of a cylinder by squares. For this, we
introduce a general criterion for identifying the Poisson boundary of a stochastic process that
might have further applications. The talk will be self-contained, assuming no prior knowledge of the
mentioned terminology, and will contain many pictures.
Ore 14:30, Aula 211, Università di Roma III
Seminario di Fisica Matematica
Although at first glance a stochastic perturbation destroys the stability of energy minimizers, the
probabilistic theory of large deviations reveals that the 'most likely' pathways actually solve
their own minimization problem. The well-established theory of large deviations for diffusion
processes treats stochastically driven rare events in ordinary differential equations. The theory is
particularly attractive because it generalizes naturally to stochastic partial differential
equations. Recently, there has been progress in pushing large deviation theory to the limit and
probing new regimes. In this talk, we are interested in the competition between energy and entropy
that emerges in the case of small noise and large system size. We present some recent results in the
context of the 1-d Allen-Cahn equation and explain the proofs, which combine probabilistic and
deterministic methods.
Ore 15:00, Aula 311, Università di Roma III
Seminario di Analisi e Sistemi Dinamici
In this talk we consider a non-local isoperimetric problem arising as the sharp interface limit of
the Ohta-Kawasaki free energy introduced to model microphase separation of diblock copolymers. We
can perform a second order variational analysis that allows us to provide a quantitative second
order minimality condition. We will show that critical configurations with positive second variation
are indeed strict local minimizers of the nonlocal perimeter. Moreover we provide, via a suitable
quantitative inequality of isoperimetric type, an estimate of the deviation from minimality for
configurations close to the minimum in the L^1 topology. Aim of the presentation will be to explain
how to perform variations for non-local variational functionals and to sketch how to combine the
regularity theory for quasi minimizers of the area functional and a suitable penalization argument
to prove the quantitative minimality estimate. The presentation is based on a recent joint work with
Vesa Julin.
Ore 9:00, Aula Picone
9:00 Camillo De Lellis (Universitat Zurich), From Nash to Onsager: funny coincidences across
differential geometry, PDEs and the theory of turbulence, I
11:15 Takashi Suzuki (Osaka University), Elliptic and parabolic equations on planar domains, II
15:00 Pavol Quittner (Comenius University), Long-time behavior of solutions of semilinear parabolic
problems, II
Ore 15:00, Aula 311, Università di Roma III
Seminario di Analisi e Sistemi Dinamici
Given a smooth domain Omega, s in (0,1), p in (1,frac[n+2s][n-2s]) and a small epsilon > 0, we
consider the nonlocal equation epsilon^[2s] (-Delta)^s u + u = u^p with Dirichlet datum. We
construct solutions that concentrate at interior points of the domain. The proof, as it often
happens in these type of problems, uses a scaling blow up of the space variable by a factor
epsilon^[-1] and an appropriate LyapunovSchmidt bifurcation argument. Nevertheless, several
important differences arise here. In particular, the leading of the reduced energy functional in
this case is not exponential, but polynomial with respect to the distance from the boundary. The
exponent of such asymptotics is also quite unexpected, namely it is n+4s, which is different from
the decay of the fundamental solution of (-Delta)^s (that is n-2s), from the one of 1+(-Delta)^s
(that is n+2s), from the one of the ground state of the associated Schroedinger equation (that is
again n+2s) and also from the order in epsilon of the corrector for the equatuion (once more, n+2s).
The competition among these different exponents causes of course some technical difficulties, that
can be overcome by a careful analysisof the nonlocal Robin function.
Ore 9:00, Aula Picone
9:00 Camillo De Lellis (Universitat Zurich), From Nash to Onsager: funny coincidences across
differential geometry, PDEs and the theory of turbulence, II
11:15 Matthew J. Gursky (University of Notre Dame), Some fully nonlinear equations in geometry, I
15:00 K Sandeep (TIFR, Bangalore), Semilinear elliptic problems in the hyperbolic space, I
Ore 11:00, Aula Dal Passo, Università di Roma II
Let G be an reductive algebraic group (for example a special linear group) and let B be a Borel
subgroup (i.e., a maximal closed connected solvable subgroup). The representation theory of G is
closely related to the algebraic geometry of the quotient space G/B. In characteristic 0 this
connection is succinctly summarized by the Borel-Bott-Weil Theorem. This shows in particular that
the cohomology of a line bundle is non-zero in at most one degree and its character is either a Weyl
character or 0. In characteristic p the connection between the representation theory and geometry
still exists and has been extremely useful (in work by Haboush, Andersen, Jantzen and others).
Nevertheless there is no known analogue of the Borel-Bott-Weil Theorem. Earlier work (e.g. that of
Andersen and Humphreys) has focused on the module structure of the cohomology spaces. However,
concentrating only on the character one can get complete information in some low rank cases using
infinitesimal methods. So far the cases worked out completely are G = SL(2) (classical), G = SL(3)
(Donkin), and G = Sp(4) in characteristic2 (Donkin and Geranios). We describe an approach to this
problem using infinitesimal methods and how they may be used to give recursive formulas for the
characters of the cohomology of line bundles in favorable circumstances.
Ore 11:00, Aula 211, Università di Roma III
Seminario di Geometria
Ore 14:00, Aula 211, Università di Roma III
Seminario di Geometria
Let X be a nonsingular subvariety in projective space covered by lines. For a point x in X, denote
by C_x the subvariety of the projective tangent space of X at x, corresponding to the set of lines
through x lying on X. When the family C_x is isotrivial as x varies over general points of X, we say
that X has isotrivial VMRT-structure. We will discuss the question "is a Fano manifold of Picard
number 1 with isotrivial VMRT-structure quasi-homogeneous"? We will give an affirmative answer
when C_x satisfies certain conditions, which hold for complete intersections of dimension bigger
than 1 and of multi-degree different from (2,2), (2,3), (2,2,2). This implies that a Fano complete
intersection of index bigger than 3 and multi-degree different from (2), (3), (2,2), (2,2,2) cannot
have isotrivial VMRT-structure.
Ore 15:30, Aula 211, Università di Roma III
Seminario di Geometria
I will show that the Chow form of every polarized K3 surface has a pfaffian structure by relating
this question to the existence of Ulrich bundles on the K3 surfaces.
Ore 9:00, Aula Picone
9:00 K Sandeep (TIFR, Bangalore), Semilinear elliptic problems in the hyperbolic space, II
11:15 Matthew J. Gursky (University of Notre Dame), Some fully nonlinear equations in geometry, II
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invitati a comunicare il proprio indirizzo di posta elettronica a
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