<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/html4/strict.dtd">
<html>
<head>
<meta http-equiv="Content-type" content="text/html;charset=UTF-8">
<title>cvgmt: Weekly Bulletin</title>
<base href='http://cvgmt.sns.it/'>
<link rel='stylesheet' type='text/css' href='/static/style/fm.css'>
<script src="http://ajax.googleapis.com/ajax/libs/jquery/1.6.1/jquery.min.js" type="text/javascript"></script>
<script type="text/javascript">
var _gaq = _gaq || [];
_gaq.push(['_setAccount', 'UA-19705267-4']);
_gaq.push(['_trackPageview']);
(function() {
var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true;
ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js';
var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s);
})();
</script>
<!-- mathjax -->
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
tex2jax: {inlineMath: [['$','$'], ['\\(','\\)']]}
});
</script>
<script type="text/javascript"
src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML"></script>
</head>
<body>
<h1>cvgmt weekly bulletin</h1>
<p><i>Weekly bulletin for <a href="http://cvgmt.sns.it">http://cvgmt.sns.it</a></i></p>
<h2>Summary</h2>
<p><b>Seminars by:</b> <a href='/seminar/606/'>Pagliari</a>, <a href='/seminar/607/'>Byeon</a>, <a href='/seminar/603/'>Del Nin</a>, <a href='/seminar/608/'>Bellettini</a></p>
<p><b>New papers by:</b> <a href='/person/256/' >Vittone</a>, <a href='/person/1099/' >De Luca</a>, <a href='/person/199/' >Ponsiglione</a>, <a href='/person/201/' >Santambrogio</a>, <a href='/person/1227/' >Rizzi</a>, <a >Fagioli</a>, <a >Schmidtchen</a>, <a >Carrillo</a>, <a >Ottazzi</a></p>
<p><b>Modified papers by:</b> <a >Kim</a>, <a href='/person/162/'>Dragoni</a>, <a href='/person/1099/'>De Luca</a>, <a href='/person/1732/'>Franceschi</a>, <a href='/person/166/'>Morini</a>, <a href='/person/199/'>Ponsiglione</a>, <a >Chambolle</a>, <a >Silva</a>, <a href='/person/106/'>Brancolini</a>, <a >Badal</a>, <a href='/person/77/'>Malusa</a>, <a >Scheven</a>, <a >Prandi</a>, <a >Wirth</a>, <a >Feleqi</a>, <a href='/person/1227/'>Rizzi</a>, <a href='/person/183/'>Cicalese</a>, <a >Rossmanith</a>, <a href='/person/1304/'>Mészáros</a>, <a href='/person/119/'>Novaga</a>, <a href='/person/638/'>Schmidt</a></p>
<h2>Seminars next week</h2>
<h3>Mon 20 November 2017</h3><ul>
<li><p>
Valerio Pagliari (Dipartimento di matematica, Universita' di Pisa): <b><a href='/seminar/606/'> A $\Gamma$-convergence result for nonlocal perimeters</a></b><br />
Sala Riunioni, VII Piano, Dipartimento di Matematica, Università di Padova, 12:30<br /> </p>
<div style="font-size: smaller;"><p>We focus on a class of integral functionals known as nonlocal perimeters. Intuitively, these functionals express a weighted interaction between a set and its complement, possibly localised to some reference set; the weight is provided by a positive kernel $K$ which might be singular.
Firstly, we describe some general properties of these functionals and we show that they are indeed perimeters in a generalised sense. Then, we establish existence of minimisers for the corresponding Plateau's problem and, when $K$ is radial and strictly decreasing, we prove that halfspaces are minimisers if we prescribe “flat” boundary conditions. Finally, in the second part of the talk, the asymptotic behaviour of the functionals is discussed: we show that suitable rescalings of the nonlocal perimeters associated with certain kernels $\Gamma$-converge to the classical perimeter, up to a multiplicative constant that we exhibit explicitly.
This is a joint work with J. Berendsen.</p>
</div> </li>
<li><p>
Jaeyoung Byeon: <b><a href='/seminar/607/'>Single peak solutions to nonlinear Neumann problems with a degeneracy</a></b><br />
Scuola Normale Superiore, Aula Bianchi, 14:00<br /> </p>
<div style="font-size: smaller;"><p>There have been enormous studies on singularly perturbed nonlinear elliptic problems
with the Neumann boundary condition. As for a single peak solution which concentrates near a point on the boundary of a given domain, its existence for a critical point of the mean curvature and its nonexistence for the regular point of the mean curvature were known only when a certain nondegeneracy holds.
In this talk I would like to explain a purely variational approach to prove the same results without the nondegeneracy.</p>
</div> </li>
</ul>
<h3>Wed 22 November 2017</h3><ul>
<li><p>
Giacomo Del Nin: <b><a href='/seminar/603/'>Asymptotic planar N-bubble</a></b><br />
Sala Seminari (Dipartimento di Matematica), 17:00<br /> </p>
<div style="font-size: smaller;"><p>We consider in the plane a fixed finite number N of "bubbles", that is
disjoint finite perimeter sets which possibly share portions of their
boundaries, and look for configurations that minimize, under a volume
constraint, the total weighted length of their boundaries: the interface
between each bubble and the exterior is given weight 1 while the interface
between any two bubbles is given weight $2-\varepsilon$. We are interested in
the case when $\varepsilon$ converges to 0: we prove that minimizing
configurations approach in the limit a configuration of disjoint disks
which maximize the number of tangencies among them. Moreover we obtain
some information about the structure of minimizers for small $\varepsilon$.</p>
</div> </li>
</ul>
<h3>Fri 24 November 2017</h3><ul>
<li><p>
Costante Bellettini: <b><a href='/seminar/608/'>Stable constant-mean-curvature hypersurfaces: regularity and compactness.</a></b><br />
Scuola Normale Superiore, Aula Tonelli, 14:00<br /> </p>
<div style="font-size: smaller;"><p>This talk describes a recent joint work of the speaker with Neshan Wickramasekera (Cambridge). The work develops a regularity theory, with an associated compactness theorem, for weakly defined hypersurfaces (codimension 1 integral varifolds) of a smooth Riemannian manifold that are stationary and stable on their regular parts for volume preserving ambient deformations. The main regularity theorem gives two structural conditions on such a hypersurface that imply that, away from a set of codimension 7 or higher, the hypersurface is locally either a single smoothly embedded disk or precisely two smoothly embedded disks intersecting tangentially. Easy examples show that neither structural hypothesis can be relaxed. An important special case is when the varifold corresponds to the boundary of a Caccioppoli set, in which case the structural conditions can be considerably weakened.</p>
</div> </li>
</ul>
<h2>New Papers</h2>
<p><b> Ottazzi, Vittone:</b> <a href='/paper/3658/'>On the codimension of the abnormal set in step two Carnot groups</a></p>
<p><b> De Luca, Ponsiglione:</b> <a href='/paper/3659/'>Low energy configurations of topological singularities in two dimensions: A $\Gamma$-convergence analysis of dipoles</a></p>
<p><b> Rizzi:</b> <a href='/paper/3660/'>A counterexample to gluing theorems for MCP metric measure spaces</a></p>
<p><b> Carrillo, Fagioli, Santambrogio, Schmidtchen:</b> <a href='/paper/3661/'>Splitting schemes & segregation in reaction-(cross-)diffusion systems</a></p>
<h2>Modified Papers</h2>
<p><b> Brancolini, Rossmanith, Wirth:</b> <a href='/paper/2916/'>Optimal micropatterns in 2D transport networks and their relation to image inpainting</a></p>
<p><b> Badal, Cicalese, De Luca, Ponsiglione:</b> <a href='/paper/3262/'>$\Gamma$-convergence analysis of a generalized $XY$ model: fractional vortices and string defects</a></p>
<p><b> Scheven, Schmidt:</b> <a href='/paper/3320/'>On the dual formulation of obstacle problems for the total variation and the area functional</a></p>
<p><b> Mészáros, Silva:</b> <a href='/paper/3398/'>On the variational formulation of some stationary second order mean field games systems</a></p>
<p><b> Kim, Mészáros:</b> <a href='/paper/3429/'>On nonlinear cross-diffusion systems: an optimal transport approach</a></p>
<p><b> Dragoni, Feleqi:</b> <a href='/paper/3519/'>Ergodic Mean Field Games with Hoermander diffusions</a></p>
<p><b> Franceschi, Prandi, Rizzi:</b> <a href='/paper/3558/'>On the essential self-adjointness of sub-Laplacians</a></p>
<p><b> Malusa, Novaga:</b> <a href='/paper/3630/'>Crystalline evolutions in chessboard-like microstructures</a></p>
<p><b> Chambolle, Morini, Novaga, Ponsiglione:</b> <a href='/paper/3657/'>Generalized crystalline evolutions as limits of flows with smooth anisotropies</a></p>
<h2>Open Positions</h2>
<p><a href="/position/276/">Lecturer/Senior Lecturer/Reader in Mathematics School of Mathematics, University of Bristol UK</a> (deadline: Mon 27 November 2017)</p>
<p><a href="/position/282/">Tenure-track position (RTD-B) at the University of Verona</a> (deadline: Thu 30 November 2017)</p>
<p><a href="/position/277/">Postdoctoral Positions in the Max Planck Research Group "Rigidity and Flexibility in PDEs"</a> (deadline: Fri 1 December 2017)</p>
<p><a href="/position/278/">PhD Position in the Max Planck Research Group "Rigidity and Flexibility in PDEs"</a> (deadline: Fri 1 December 2017)</p>
<p><a href="/position/283/">Research Scientist P3</a> (deadline: Fri 1 December 2017)</p>
<p><a href="/position/280/">Chairs in Mathematics and Statistical Science School of Mathematics, University of Bristol UK</a> (deadline: Mon 4 December 2017)</p>
</body>
</html>