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<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/618/'>Vezzoni</a>, <a href='/seminar/620/'>Floreani</a>, <a href='/seminar/617/'>Velichkov</a></p>
<p><b>New papers by:</b> <a href='/person/32/' >Garroni</a>, <a >Zeman</a>, <a href='/person/1820/' >Jevnikar</a>, <a href='/person/263/' >Mantegazza</a>, <a href='/person/1836/' >Radici</a>, <a href='/person/231/' >Vitali</a>, <a >Fagioli</a>, <a href='/person/2701/' >Glaudo</a>, <a >Engelstein</a>, <a href='/person/1517/' >Spolaor</a>, <a href='/person/336/' >Velichkov</a>, <a >Ao</a>, <a >Melching</a>, <a href='/person/563/' >Di Francesco</a>, <a href='/person/204/' >Dal Maso</a>, <a href='/person/1400/' >Scala</a>, <a href='/person/985/' >van den Berg</a>, <a >Yang</a>, <a href='/person/60/' >Defranceschi</a>, <a href='/person/44/' >Braides</a></p>
<p><b>Modified papers by:</b> <a href='/person/1152/'>Di Marino</a>, <a href='/person/6/'>Carriero</a>, <a href='/person/263/'>Mantegazza</a>, <a href='/person/44/'>Braides</a>, <a >Recupero</a>, <a href='/person/148/'>Iurlano</a>, <a href='/person/151/'>Pratelli</a>, <a href='/person/26/'>Stepanov</a>, <a href='/person/29/'>Tomarelli</a>, <a href='/person/1826/'>Pluda</a>, <a href='/person/550/'>Conti</a>, <a href='/person/1836/'>Radici</a>, <a href='/person/201/'>Santambrogio</a>, <a href='/person/59/'>Colombo</a>, <a href='/person/61/'>Louet</a>, <a href='/person/192/'>Masnou</a>, <a href='/person/1863/'>Dayrens</a>, <a href='/person/76/'>Marchese</a>, <a >Julin</a>, <a href='/person/1753/'>De Rosa</a>, <a href='/person/104/'>Leaci</a>, <a href='/person/106/'>Brancolini</a>, <a href='/person/1259/'>Trevisan</a>, <a href='/person/116/'>Barchiesi</a>, <a href='/person/245/'>Focardi</a>, <a href='/person/119/'>Novaga</a>, <a href='/person/123/'>Chiadò Piat</a></p>
<h2>Seminars next week</h2>
<h3>Fri 2 February 2018</h3><ul>
<li><p>
Luigi Vezzoni: <b><a href='/seminar/618/'>A quantitative version of the Soap Bubble Theorem</a></b><br />
Scuola Normale Superiore, Aula Mancini, 10:00<br /> </p>
<div style="font-size: smaller;"><p>The celebrated Soap Bubble Theorem of Alexandrov asserts that round spheres are the only closed
constant mean curvature hypersurfaces embedded in the Euclidean space. The talk mainly focuses on
the following quantitive version of the theorem.
</p>
<p>The proof of the theorem, joint work with G.Ciraolo, makes use of a quantitive study of the method of the moving planes and the result implies a new pinching theorem for hypersurfaces in the Euclidean space. Furthermore, the
theorem is optimal in a sense that it will be specified in the talk.
The last part of the talk will be about an on-going study on the generalization of the result in space
forms or, more generally, in warped product spaces.</p>
</div> </li>
</ul>
<h3>Tue 6 February 2018</h3><ul>
<li><p>
Simone Floreani: <b><a href='/seminar/620/'>Applicazione del trasporto ottimo ad un modello di traffico congestionato</a></b><br />
Aula Riunioni, Dip. di Matematica, Univ. di Pisa, 17:00<br /> </p>
<div style="font-size: smaller;"><p>The presentation starts with a review of the general theory of optimal transport, in which the most important results and their consequences are recalled. Then, this theory is applied to the study of some traffic models.
</p>
<p>The starting point is a model introduced by Beckmann in the ’50s, called continuous model of transportation, which takes the form of a divergence constraint optimization problem. The Beckmann’s problem is studied in relation to a proper Monge-Kantorovich one, and it is shown that, under some hypothesis, they admit the same solution.
</p>
<p>Consequently, the model is complicated in order to take care of congestion effects, understanding if there are still connections with the optimal transport theory and if a meaningful notion of equilibrium can be found. Avoiding deep technicalities, that are only mentioned, an interesting result is presented: the solution of the congestion traffic model solves a peculiar Monge-Knatorovich one, where the cost function depends on the solution of the problem itself. Moreover, the solution also satisfies a very famous notion of non-cooperative equilibrium.</p>
</div> </li>
</ul>
<h3>Wed 7 February 2018</h3><ul>
<li><p>
Bozhidar Velichkov (Universite Joseph Fourier (Grenoble)): <b><a href='/seminar/617/'>Un approccio variazionale alla regolarità delle frontiere libere singolari</a></b><br />
Sala Seminari Dipartimento di Matematica di Pisa, 17:00<br /> </p>
<div style="font-size: smaller;"><p>In questo seminario affronteremo il problema della regolarità delle frontiere libere dei minimi del funzionale di Bernoulli $u\mapsto\int \vert\nabla u\vert^2+<br>\{u>0\}<br>$. Negli anni ottanta, Alt e Caffarelli dimostrarono che le frontiere libere di Bernoulli si possono decomporre in due insiemi disgiunti: l'insieme dei punti regolari (Reg), localmente dato dal grafico di una funzione liscia, e l'insieme dei punti singolari (Sing), di dimensione di Hausdorff al massimo $d-5$. Recentemente, De Silva e Jerison, ispirandosi del risultato di Bombieri - De Giorgi - Giusti per le superfici minime, hanno costruito esplicitamente un cono minimo in $\mathbb{R}^7$ con singolarità isolata nell'origine, dimostrando che l'insieme Sing non è vuoto.
L'obiettivo principale di questo seminario è di mostrare che le frontiere libere di Bernoulli con una singolarità isolata sono grafici $C^1$ sui corrispondenti coni minimi. Lo strumento principale è una disuguaglianza variazionale, la disuguaglianza epiperimetrica logaritmica, introdotta in una serie di lavori in collaborazione con Maria Colombo e Luca Spolaor. Infine, mostreremo il risultato analogo per le superfici minime che estende il teorema di Leon Simon. I due risultati sopracitati sono stati ottenuti in collaborazione con Luca Spolaor (Princeton) e Max Engelstein (MIT).</p>
</div> </li>
</ul>
<h2>New Papers</h2>
<p><b> Glaudo:</b> <a href='/paper/3750/'>On the c-concavity with Respect to the Quadratic Cost on a Manifold</a></p>
<p><b> Engelstein, Spolaor, Velichkov:</b> <a href='/paper/3751/'>Uniqueness of the blow-up at isolated singularities for the Alt-Caffarelli functional</a></p>
<p><b> Mantegazza:</b> <a href='/paper/3752/'>Some Elementary Questions in the Calculus of Variations</a></p>
<p><b> Di Francesco, Fagioli, Radici:</b> <a href='/paper/3753/'>Deterministic particle approximation for nonlocal transport equations with nonlinear mobility</a></p>
<p><b> Fagioli, Radici:</b> <a href='/paper/3754/'>Solutions to aggregation-diffusion equations with nonlinear mobility constructed via a deterministic particle approximation</a></p>
<p><b> Braides, Dal Maso, Garroni:</b> <a href='/paper/3755/'>Variational formulation of softening phenomena in Fracture Mechanics: the one-dimensional case</a></p>
<p><b> Braides, Defranceschi, Vitali:</b> <a href='/paper/3756/'>A relaxation approach to Hencky's plasticity</a></p>
<p><b> Ao, Jevnikar, Yang:</b> <a href='/paper/3757/'>Wave equations associated to Liouville-type problems: global existence in time and blow up criteria</a></p>
<p><b> van den Berg:</b> <a href='/paper/3758/'>Heat content in non-compact Riemannian manifolds</a></p>
<p><b> Melching, Scala, Zeman:</b> <a href='/paper/3759/'>Damage model for plastic materials at finite strains</a></p>
<h2>Modified Papers</h2>
<p><b> Barchiesi, Brancolini, Julin:</b> <a href='/paper/2516/'>Sharp dimension free quantitative estimates for the Gaussian isoperimetric inequality</a></p>
<p><b> Pratelli, Radici:</b> <a href='/paper/2690/'>On the piecewise approximation of bi-Lipschitz curves</a></p>
<p><b> Radici:</b> <a href='/paper/2743/'>A planar Sobolev extension theorem for piecewise linear homeomorphisms</a></p>
<p><b> Dayrens, Masnou, Novaga:</b> <a href='/paper/2761/'>Existence, regularity and structure of confined elasticae</a></p>
<p><b> Colombo, De Rosa, Marchese:</b> <a href='/paper/3293/'>Improved stability of optimal traffic paths</a></p>
<p><b> Di Marino, Louet:</b> <a href='/paper/3381/'>The entropic regularization of the Monge problem on the real line</a></p>
<p><b> Conti, Focardi, Iurlano:</b> <a href='/paper/3473/'>Approximation of fracture energies with $p$-growth via piecewise affine finite elements</a></p>
<p><b> Pratelli, Radici:</b> <a href='/paper/3520/'>On the planar minimal BV extension problem</a></p>
<p><b> Pratelli, Radici:</b> <a href='/paper/3521/'>Approximation of planar BV homeomorphisms by diffeomorphisms</a></p>
<p><b> Recupero, Santambrogio:</b> <a href='/paper/3533/'>Sweeping processes with prescribed behaviour on jumps</a></p>
<p><b> Carriero, Leaci, Tomarelli:</b> <a href='/paper/3605/'>Segmentation and Inpainting of Color Images</a></p>
<p><b> Braides, Chiadò Piat:</b> <a href='/paper/3641/'>Homogenization of networks in domains with oscillating boundaries</a></p>
<p><b> Stepanov, Trevisan:</b> <a href='/paper/3671/'>Towards geometric integration of rough differential forms</a></p>
<p><b> Mantegazza, Novaga, Pluda:</b> <a href='/paper/3727/'>Lectures on Curvature Flow of Networks</a></p>
<h2>Open Positions</h2>
<p><a href="/position/302/">Associate Professor, Scuola Normale Superiore</a> (deadline: Thu 8 February 2018)</p>
<p><a href="/position/299/">11 PhD Positions, Graduate School IntComSin, Regensburg-Erlangen</a> (deadline: Thu 15 February 2018)</p>
<p><a href="/position/305/">FAU Erlangen - 11 Doctorate Positions - Interfaces, Complex Structures and Singular Limits in Continuum Mechanics</a> (deadline: Thu 15 February 2018)</p>
<p><a href="/position/301/">Postdoctoral position at Durham</a> (deadline: Mon 19 February 2018)</p>
<p><b>(new)</b> <a href="/position/307/">PhD and Postdoctoral Position at EPFL Lausanne</a> (deadline: Tue 20 February 2018)</p>
<p><a href="/position/295/">Bandi PhD SNS 2018/2019</a> (deadline: Wed 28 February 2018)</p>
<p><b>(new)</b> <a href="/position/309/">Postdoctoral Position at Rome, Dept of Mathematics, Sapienza</a> (deadline: Thu 1 March 2018)</p>
<p><a href="/position/306/">5 postdoc positions in math at GSSI</a> (deadline: Fri 2 March 2018)</p>
<p><a href="/position/303/">Full Professorship in Applied Mathematics WWU Münster</a> (deadline: Sat 31 March 2018)</p>
<p><b>(new)</b> <a href="/position/308/">Assistant professor, applied mathematics department, Ecole Polytechnique</a> (deadline: Sat 31 March 2018)</p>
<p><a href="/position/286/">20 PhD fellowships in Paris 2018/19 - Fondation Science Mathémathiques Paris</a> (deadline: Sun 1 April 2018)</p>
<p><a href="/position/298/">11 PhD Positions, Graduate School IntComSin, Regensburg-Erlangen</a> (deadline: Sun 1 July 2018)</p>
<p><a href="/position/304/">FAU Erlangen - 11 Doctorate Positions - Interfaces, Complex Structures and Singular Limits in Continuum Mechanics</a> (deadline: Sun 1 July 2018)</p>
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