| 11/03/21 | Seminario | 17:00 | 18:00 | | Alessandro Della Corte | Università di Camerino |
DinAmicI: Another Internet Seminar (DAI Seminar)
The simplest erasing substitution
- in streaming mode -
(see the instructions in the abstract)
The symbolic action of a substitution on the binary expansion generates naturally an interval map. In case of erasing substitutions, the map is typically Baire-1 and not Darboux. As a model case, we consider what is arguably the simplest erasing substitution, mapping 0s to the empty word and 1s to 0 or 1 depending on the parity. The corresponding interval map is shown to have fractal properties (bounds are given on the Hausdorff dimension of the fibers) and to display rich dynamical behavior, including Devaney chaos, uniform distributional chaos of type 1, infinite topological entropy as well as the presence of cycles attracting in a finite time every rational.
Note:
The zoom link to the seminar will be posted on the DinAmicI website and on Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
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| 11/03/21 | Seminario | 14:00 | 15:00 | | Mohameden Ahmedou | Università di Gießen | New blow up phenomena for the Nirenberg's problem on half spheres
( MS Teams Link for the streaming )
In this talk I will report on a refined blow up analysis of finite energy approximated solutions to the Nirenberg's problem on half spheres. The later consists of prescribing under minimal boundary conditions the scalar curvature to be a given function. In particular we give a precise location of blow up points and blow up rates. Such an analysis shows that the blow up picture of the Nirenberg's problem on half spheres is far more complicated that in the case of closed spheres. Indeed besides the combination of interior and boundary blow ups, there are "non simples blow ups" for subcritical solutions having zero or nonzero weak limit. The formation of such non simple blow ups is governed by a vortex problem, unveiling an unexpected connection with Euler equations in fluid dynamic and mean fields type equations in mathematical physics.
This is joint work with Mohamed Ben Ayed (Sfax University).
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |
| 05/03/21 | Seminario | 15:00 | 16:00 | | Olivier SCHIFFMANN | CNRS - Paris Saclay |
Online / Algebra & Representation Theory Seminar (O/ARTS)
"Cohomological Hall algebras associated to ADE surface singularities"
- in streaming mode
(see the instructions in the abstract)
To a (reasonable) CY category C of global dimension two one can attach an associative algebra - its cohomological Hall algebra (COHA) - which is an algebra structure on the Borel-Moore homology of the stack of objects in C. In examples related to quivers (i.e. when C is the category of representations of the preprojective algebra of a quiver Q) this yields (positive halves) of Kac-Moody Yangians. In ongoing joint work with Diaconescu, Sala and Vasserot, we consider the case of the category of coherent sheaves supported on the exceptional locus of a Kleinian surface singularity. This is related to the above quiver case by a '2d-COHA' version of Cramer's theorem relating the (usual) Hall algebras of two hereditary categories which are derived equivalent.
N.B.: please click HERE to attend the talk in streaming |
| 04/03/21 | Seminario | 14:00 | 15:00 | | Weiwei Ao | Wuhan University | Symmetry and symmetry breaking for the fractional Caffarelli-Kohn-Nirenberg inequality
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In this talk, I will discuss about a fractional version of the Caffarelli-Kohn-Nirenberg inequality.
We first study the existence and nonexistence of extremal solutions. We also show some results for the symmetry and symmetry breaking region for the minimizers. In order to get these result we reformulate the fractional Caffarelli-Kohn-Nirenberg inequality in cylindrical variables. We also get the non-degeneracy and uniqueness of minimizers in the radial symmetry class. This is joint work with Azahara DelaTorre and Maria del Mar Gonzalez.
NB:This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |
| 25/02/21 | Seminario | 16:00 | 17:00 | | Paolo Giulietti | Università di Pisa |
DinAmicI: Another Internet Seminar (DAI Seminar)
Infinite mixing for accessible skew products
- in streaming mode -
(see the instructions in the abstract)
I will present some decay of correlations results on skew products which are locally accessible. The results rely on the study of a twisted transfer operator and could be generalized to many other situations. I will also present numerical counterparts to such results.
Note:
The zoom link to the seminar will be posted on the DinAmicI website and on Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
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| 25/02/21 | Seminario | 14:00 | 15:00 | | Jacopo Bellazzini | Universita' di Pisa | Ground state energy threshold and blow-up for NLS with competing nonlinearities
( MS Teams Link for the streaming )
Aim of the talk is to discuss qualitative properties of the nonlinear Schr\"odinger equation with combined nonlinearities, where the leading term is an intracritical focusing power-type nonlinearity, and the perturbation is given by a power-type defocusing one. Fixed the mass of the problem, we completely answer the question wether the ground state energy , which is a threshold between global existence and formation of singularities, is achieved. As a byproduct of the variational characterization of the ground state energy, we show the existence of blowing-up solutions in finite time, for any initial data with energy below the ground state energy threshold in case of cylindrical symmetry.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
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| 18/02/21 | Colloquium | 14:00 | 15:00 | | Toshiyuki Kobayashi | The University of Tokyo | A foundation of group-theoretic analysis on manifolds
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Symmetry of geometry is inherited by symmetry of function spaces, called the regular representation. From this viewpoint, the classical theory of expansions such as Fourier series or spherical harmonics may be interpreted as "analysis and synthesis" of the regular representation.
In this talk, we address the following fundamental questions about the regular representation on manifolds X acted algebraically by reductive Lie groups G such as GL(n,R).
A. Does the group G "control well" the space of function on X?
B. What can we say about "spectrum" for L^2(X)?
We highlight "multiplicity" for A and "temperdness" for B, and explain some geometric ideas of the solution.
N.B.: this talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006
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| 11/02/21 | Seminario | 16:00 | 17:00 | | Misha Bialy | Tel Aviv University |
DinAmicI: Another Internet Seminar (DAI Seminar)
Birkhoff-Poritsky conjecture for centrally-symmetric billiards
- in streaming mode -
(see the instructions in the abstract)
In this talk I shall discuss Birkhoff-Poritsky conjecture for centrally-symmetric C^2-smooth convex planar billiards.
We assume that the domain A between the invariant curve of 4-periodic orbits and the boundary of the phase cylinder is foliated by C^0-invariant curves.
Under this assumption we prove that the billiard curve is an ellipse.
Other versions of Birkhoff-Poritsky conjecture follow from this result.
For the original Birkhoff-Poritsky formulation we show that if a neighborhood of the boundary of billiard domain has
a C^1-smooth foliation by convex caustics of rotation numbers in the interval (0, 1/4]
then the boundary curve is an ellipse.
The main ingredients of the proof are :
(1) the non-standard generating function for convex billiards;
(2) the remarkable structure of the invariant curve consisting of 4-periodic orbits; and
(3) the integral-geometry approach initiated in
[B0], [B1] for rigidity results of circular billiards.
Surprisingly, we establish a Hopf-type rigidity for billiards in the ellipse.
Based on a joint work with Andrey E. Mironov (Novosibirsk).
Note:
The zoom link to the seminar will be posted on the DinAmicI website and on Mathseminars.org. Moreover, it will be also streamed live via the youtube DinAmicI channel.
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| 11/02/21 | Seminario | 14:00 | 15:00 | | Luca Martinazzi | Universita' di Padova | Entire solutions to a prescribed curvature equation in R^4 and the Nirenberg problem
Several existence and non-existence results for the Nirenberg problem of prescribing the Gauss curvature on a closed surface are classically known. In higher dimension, analog results hold with the Q-curvature replacing the Gauss curvature. In many cases a non-existence result is associated with a blow-up phenomenon which leads to entire solutions of the Liouville equation $-Delta u = e^{2u}$ in dimension 2 or higher-dimensional analogs. On the other hand, Borer, Galimberti and Struwe studied a blow-up phenomenon which could lead to solutions to the equation
$$-Delta u =(1-|x|^2)e^{2u} in R^2$$ (1)
or
$$Delta^2 u =(1-|x|^2)e^{4u} in R^4$$ (2)
While non-existence results have been shown for (1) by Struwe, the question remained opened for (2). We recently gave a positive answer with A. Hyder, giving sharp conditions under which (2) admits solutions with controlled behaviour at infinity, hence answering an open question by Struwe. More related open questions will be discussed.
MS Teams Link for the streaming
Note: This talk is part of the activity of the MIUR Excellence Department Project CUP E83C18000100006 |
| 04/02/21 | Seminario | 14:00 | 15:00 | | Lorenzo Valvo | Università degli Studi di Roma | Seminario di Equazioni Differenziali
Hamiltonian Control of Magnetic Field Lines: Computer Assisted Results Proving the Existence of KAM Barriers
(MS Teams link for the streaming at the end of the abstract)
A control theory for Hamiltonian systems, based on KAM theory, was introduced in [Ciraolo, 2004] and applied to a model of magnetic field in [Chandre, 2006]. By a combination of Frequency Analysis and of a rigorous (Computer Assisted) KAM algorithm we show that in the phase space of the magnetic field, due to the control term, a set of invariant tori appears, and it acts as a transport barrier. Our analysis, which is common (but often also limited) to celestial mechanics, is very general and can be applied to quasi-integrable Hamiltonian systems satisfying a few additional mild assumptions.
MS Teams Link for the streaming
Note:
This talk is part of the activity of the MIUR Excellence Department Project MATH@TOV CUP E83C18000100006 |