[CvGmt News] [CVGMT] weekly bulletin

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Fri Nov 27 12:00:01 CET 2015


Weekly bulletin of http://cvgmt.sns.it

--- Summary ---
* Events: Fall Semester 2015 in Analysis, Lyon
, 19th Internet Seminar: Infinite Dimensional Analysis
* Seminars by: Musso, Del Pino , Lucardesi
* New papers by: Marchese, Spolaor, Mennucci, Muratov, Bardelli, Novaga, Mucci, Acerbi* Modified papers by: Giacomelli, Santambrogio, Speight, De Pascale, Paolini, Stepanov, Louet, Di Castro
--- Events ---
Fall Semester 2015 in Analysis, Lyon
Tuesday 1 sep 2015 -- Thursday 31 dec 2015
Lyon, France
From September 1 to December 31, 2015 a semester in Analysis will take place in Lyon, France, with the following main events:

- Workshop Analysis in Lyon (October 26-30, 2015); on Thursday October 29, Luigi Ambrosio will be awarded a "doctorat honoris causa" from the École normale supérieure de Lyon.

- Winter school on nonlinear function spaces in mathematics and physical sciences (December 14-18, 2015)

During the semester, the École normale supérieure de Lyon and the Université Claude Bernard Lyon 1 will host short and long term visitors. 

The scientific committee of the semester is the following:

- Stefano Bianchini (SISSA Trieste)

- Albert Fathi (École normale supérieure de Lyon)

- Alessio Figalli (University of Texas at Austin)

- Petru Mironescu (Université Lyon 1)

19th Internet Seminar: Infinite Dimensional Analysis
Tuesday 13 oct 2015 -- Saturday 4 jun 2016
Final Worshop in Casalmaggiore, Cremona (Italy), May 30th to June 4th 2016
The I-Sem is a well-established series of courses in the field of Mathematical Analysis.
It introduces master, Ph.D. students and postdocs to subjects related to functional analysis and evolution equations.
 
As usual, the course consists of three phases.

Phase 1 (October-February) The organisers provide a weekly lecture via the ISem website. The participants are expected to study the lecture notes, to solve the proposed problems, to post their remarks and questions in the website, and to post the solutions of the problems, in turn. Participants belonging to the same institution are encouraged to collaborate, possibly under the supervision of a senior local coordinator.

Phase 2 (February-May) The participants form small international groups to work on various projects which supplement the theory of Phase 1 and provide some applications. Each group is coordinated by a senior mathematician who provides bibliographical material and help.

Phase 3 (30 May-4 June, 2016) A final one-week workshop will be held at Istituto Santa Chiara,  Casalmaggiore, Cremona (Italy). There the teams will present their projects and some additional lectures  will be delivered by leading experts.

The virtual lecturers are Alessandra Lunardi, Michele Miranda and Diego Pallara and the topic is "Infinite dimensional analysis". For more details we refer to the page http:////dmi.unife.it//isem19.

--- Seminars next week ---
* Wednesday 2 dec 2015

time: 15:00
Scuola Normale Superiore,  Aula Mancini
A non-compactness result on the fractional Yamabe problem in large dimensions
Monica Musso 
Abstract. Let $(X^{n+1}, g^+)$ be an $(n+1)$-dimensional asymptotically hyperbolic manifold with a conformal infinity $(M^n, [h])$.
The fractional Yamabe problem addresses to solve
\[P^{\gamma}[g^+,h] (u) = cu^{n+2\gamma \over n-2\gamma}, \quad u > 0 \quad \text{on } M\]
where $c \in {\mathbb{R}} $ and $P^{\gamma}[g^+,h]$ is the fractional conformal Laplacian whose principal symbol is $(-\Delta)^{\gamma}$.
We construct a metric on the half space $X = {\mathbb{R}}^{n+1}_+$, which is conformally equivalent to the unit ball,
for which the solution set of the fractional Yamabe equation is non-compact
provided that $n \ge 24$ for $\gamma \in (0, \gamma^*)$ and $n \ge 25$ for $\gamma \in [\gamma^*,1)$ where $\gamma^* \in (0, 1)$ is a certain transition exponent.
The value of $\gamma^*$ turns out to be approximately 0.940197. This is a joint work with Seunghyeok Kim and Juncheng Wei.

time: 16:30
Scuola Normale Superiore,  Aula Mancini
 Bubbling blow-up in critical parabolic problems
Manuel Del Pino  
Abstract. We construct solutions with finite and infinite type-II blow-up (and analyze their stability) in two related parabolic problems: 
the standard semilinear heat equation with a power nonlinearity at the critical exponent in a bounded domain in RN, and the harmonic map flow from a two-dimensional
domain  into the sphere S2.  Both problems have stationary states with energy scaling-invariance  in entire space  which are the building blocks of the bubbling patterns.

* Thursday 3 dec 2015

time: 15:00
sala seminari, dipartimento di matematica di Pisa
The wave equation on domains with cracks growing on a prescribed path.
Ilaria Lucardesi (SISSA Trieste)
Abstract.  In this talk I analyze a scalar wave equation in a time  
varying domain of the form "set minus a growing crack", when the crack  
develops along a given path. Under suitable regularity assumptions, I  
show existence, uniqueness and continuous dependence on the cracks of  
the weak solution of the wave equation under study. This is a joint  
work with Gianni Dal Maso.

--- New Papers ---
* Bardelli, Mennucci: Probability measures on infinite dimensional Stiefel manifolds
* Marchese: Lusin type theorems for Radon measures
* Acerbi, Mucci: Curvature-dependent energies: a geometric and analytical approach
* Spolaor: Almgren's type regularity for Semicalibrated Currents
* Muratov, Novaga: On well-posedness of variational models of charged drops
--- Modified Papers ---
* Paolini, Stepanov: Flows of measures generated by vector fields
* De Pascale, Louet, Santambrogio: The Monge problem with vanishing gradient penalization: vortices and asymptotic profile
* Speight: Lusin Approximation and Horizontal Curves in Carnot Groups
* Di Castro, Giacomelli: The 1-harmonic flow with values into a smooth planar curve
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