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--- Summary ---
* Events: Fall Semester 2015 in Analysis, Lyon
, 19th Internet Seminar: Infinite Dimensional Analysis
* Seminars by: Cremaschi, Louet, Mandel
* New papers by: Battaglia, Knees, Negri, Malchiodi, Ruiz, Jevnikar* Modified papers by: Mosconi, De Philippis, Mazzieri, Brasco, Goldman, Catino, Pratelli, Squassina, Ruffini, Kallel, Bonicatto, Gusev, Paolini, Franzina, Novaga, Mongodi, Stepanov, Jevnikar, Bianchini, Malchiodi
--- 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 11 nov 2015

time: 14:30
sala seminari, dipartimento di matematica di Pisa
Un'introduzione al flusso di Ricci
Laura Cremaschi (SNS, Pisa)
Abstract. Vorrei parlare in maniera piuttosto informale del flusso di Ricci e del primo lavoro di Hamilton sulle 3-varietà con curvatura di Ricci positiva. In base al tempo e al pubblico, potrei accennare al piano di Hamilton per la risoluzione della congettura di Poincaré e al lavoro di Perelman in questa direzione.

time: 17:00
Aula Seminari Dipartimento di Matematica di Pisa 
Optimal transport with relativistic cost: continuity and  Kantorovich potentials for generic cost functions
Jean Louet (Université Paris-Dauphine)
Abstract. The optimal transport problem consists in minimizing the total energy of the displacement among all the (vector-valued) functions having prescribed image measure. In this talk we are interested in a particular case of cost functions: $c$ is given by $h(y-x)$ where h is convex, has a bounded domain and is bounded on this domain. The fact that it takes infinite value makes, in particular, complicated the existence of solutions for the dual problem.
The strategy consists in introducing a "time-parameter" $t>0$ and in studying the re-scaled problem, with cost $h((y-x)/t)$. We show the continuity of the total cost with respect to $t$, and the existence of Kantorovich potentials for "supercritical" time.
This is a joint work with A.Pratelli and F.Zeisler (Erlangen).

* Thursday 12 nov 2015

time: 14:00
Scuola Normale Superiore,  Aula Bianchi Scienze
Minimal energy solutions and bifurcation results for a weakly couled nonlinear Schroedinger system
Rainer Mandel 
Abstract. In this talk I intend to give a panoramic view on existence results for fully nontrivial solutions of the weakly coupled cubic nonlinear Schr\"odinger system

\begin{align*}

-\Delta u + ~~\; u &= u^3 + buv^2 \qquad\text{in }\R^n, \\

-\Delta v + \omega^2 v &= v^3 + bvu^2 \qquad\,\text{in }\R^n, \\

u,v \in H^1(\R^n),&\quad n\in\{1,2,3\}, \quad \omega>0,b\in\R

\end{align*}

which have been obtained during the past ten years.

The focus will be set on a comparison of the methods coming from bifurcation

theory and constrained minimization techniques respectively critical point theory. Amongst other things

I will show that in case $n\in\{2,3\}$ positive solutions exist and converge to a solution of some optimal

partition problem as the coupling parameter $b$ tends to $-\infty$ whereas this phenomenon does not occur

when~$n=1$. 

--- New Papers ---
* Knees, Negri: Convergence of alternate minimization schemes for phase field fracture and damage
* Jevnikar: An existence result for the mean-field equation on compact surfaces in a doubly supercritical regime
* Battaglia, Jevnikar, Malchiodi, Ruiz: A general existence result for the Toda system on compact surfaces
--- Modified Papers ---
* Catino, Mazzieri, Mongodi: Rigidity of gradient Einstein shrinkers
* Goldman, Novaga, Ruffini: Existence and stability for a non-local isoperimetric model of charged liquid drops
* Paolini, Stepanov: Flows of measures generated by vector fields
* Brasco, Franzina: Convexity properties of Dirichlet integrals and Picone-type inequalities
* De Philippis, Franzina, Pratelli: Existence of isoperimetric sets with densities ''converging from below'' on $\mathbb R^N$
* Bianchini, Bonicatto, Gusev: Renormalization for autonomous nearly incompressible BV vector fields in 2D
* Jevnikar, Kallel, Malchiodi: A topological join construction and the Toda system on compact surfaces of arbitrary genus
* Jevnikar: Multiplicity results for the mean field equation on compact surfaces
* Brasco, Mosconi, Squassina: Optimal decay of extremals for the fractional Sobolev inequality
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