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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/788/'>Young</a>, <a href='/seminar/787/'>Lucardesi</a></p>
<p><b>New papers by:</b> <a href='/person/1394/' >Cristoferi</a>, <a href='/person/3371/' >Topaloglu</a>, <a href='/person/58/' >De Lellis</a>, <a href='/person/235/' >Bonacini</a>, <a href='/person/3845/' >De Masi</a></p>
<p><b>Modified papers by:</b> <a >Giri</a>, <a href='/person/1810/'>Nardini</a>, <a >Cirant</a>, <a >Kohli</a>, <a >Cannarsa</a>, <a >Habermann</a>, <a href='/person/44/'>Braides</a>, <a href='/person/2229/'>Vallocchia</a>, <a href='/person/3128/'>Goffi</a>, <a href='/person/58/'>De Lellis</a>, <a >Vecchi</a>, <a >Boscain</a>, <a href='/person/204/'>Dal Maso</a>, <a >Salort</a>, <a href='/person/3405/'>Capolli </a>, <a href='/person/973/'>Ruffini</a>, <a href='/person/977/'>Mazzoleni</a>, <a href='/person/3321/'>Ghinassi</a>, <a href='/person/96/'>Lazzaroni</a>, <a >Carlone</a>, <a href='/person/1084/'>Barilari</a>, <a href='/person/3261/'>Maione</a>, <a href='/person/245/'>Focardi</a>, <a href='/person/2553/'>Borrelli</a>, <a >De Falco</a></p>
<h2>Seminars next week</h2>
<h3>Tue 16 March 2021</h3><ul>
<li><p>
Please write to Andrea.pinamonti@unitn.it or to Andrea.marchese@unitn.it if you want to attend the seminar.<br /> Robert Young (Courant Institute, New York): <b><a href='/seminar/788/'>Metric differentiation and embeddings of the Heisenberg group</a></b><br />
Zoom seminar, 16:00<br /> </p>
<div style="font-size: smaller;"><p>Pansu and Semmes used a version of Rademacher's differentiation theorem to show that there is no bilipschitz embedding from the Heisenberg groups into Euclidean space. More generally, the non-commutativity of the Heisenberg group makes it impossible to embed into any $L_p$ space for $p\in (1,\infty)$. Recently, with Assaf Naor, we proved sharp quantitative bounds on embeddings of the Heisenberg groups into $L_1$ and constructed a metric space based on the Heisenberg group which embeds into $L_1$ and $L_4$ but not in $L_2$; our construction is based on constructing a surface in $\mathbb{H}$ which is as bumpy as possible. In this talk, we will describe what are the best ways to embed the Heisenberg group into Banach spaces, why good embeddings of the Heisenberg group must be "bumpy" at many scales, and how to study embeddings into $L_1$ by studying surfaces in $\mathbb{H}$.</p>
</div> </li>
</ul>
<h3>Thu 18 March 2021</h3><ul>
<li><p>
Ilaria Lucardesi (Institut Elie Cartan de Lorraine): <b><a href='/seminar/787/'>Shape optimization in the class of bodies of constant width.</a></b><br />
Dipartimento di Matematica e Informatica di Ferrara (on-line), 15:00<br /> </p>
<div style="font-size: smaller;"><p>A body of constant width $d$ is a convex set with the following property: every pair of parallel (distinct) planes tangent to it have distance $d$ from each other, independently of their direction. This property is of course enjoyed by the ball, but it is shared by many other sets.
One of the first shape optimization results in this class dates back to the late 1800s: Barbier, in 1860, showed that all plane convex sets of constant width $d$ have the same perimeter, equal to $\pi d$. An immediate consequence, by the classical isoperimetric inequality, is that the disk maximizes the area in the class. Some years after Barbier, at the beginning of the 1900s, Blaschke and Lebesgue proved that the set which minimizes the area is the so-called Reuleaux triangle, whose boundary is made of three arcs of circle of radius $d$ with same length (equal to $\pi d/3$). Since then, many alternative proofs of this result, with very different flavors, appeared (e.g., Eggleston '52, Besicovitch '63, Campi-Colesanti-Gronchi '96, Ghandehari '96, Harrell '02), and several other shape functionals have been considered, of geometric and spectral type.
In the first part of the talk, I will introduce some tools to represent planar bodies of constant width, both analytically and numerically. In the second part, I will present a recent result, obtained in collaboration with Antoine Henrot, about the maximization of the Cheeger constant among the planar bodies of prescribed constant width.</p>
</div> </li>
</ul>
<h2>New Papers</h2>
<p><b> De Lellis:</b> <a href='/paper/5056/'>The Nash-Kuiper Theorem and the Onsager conjecture</a></p>
<p><b> De Masi:</b> <a href='/paper/5057/'>Rectifiability of the free boundary for varifolds</a></p>
<p><b> Bonacini, Cristoferi, Topaloglu:</b> <a href='/paper/5058/'>Riesz-type inequalities and overdetermined problems for triangles and quadrilaterals</a></p>
<h2>Modified Papers</h2>
<p><b> Dal Maso, Lazzaroni, Nardini:</b> <a href='/paper/2914/'>Existence and uniqueness of dynamic evolutions for a peeling test in dimension one</a></p>
<p><b> Barilari, Kohli:</b> <a href='/paper/4501/'>On sub-Riemannian geodesic curvature in dimension three</a></p>
<p><b> Capolli , Maione, Salort, Vecchi:</b> <a href='/paper/4546/'>Asymptotic behaviours in Fractional Orlicz-Sobolev spaces on Carnot groups</a></p>
<p><b> Cirant, Goffi:</b> <a href='/paper/4574/'>On the problem of maximal $L^q$-regularity for viscous Hamilton-Jacobi equations</a></p>
<p><b> Barilari, Boscain, Cannarsa, Habermann:</b> <a href='/paper/4655/'>Stochastic processes on surfaces in three-dimensional contact sub-Riemannian manifolds</a></p>
<p><b> Mazzoleni, Ruffini:</b> <a href='/paper/4808/'>A spectral shape optimization problem with a nonlocal competing term</a></p>
<p><b> Borrelli:</b> <a href='/paper/4847/'>Symmetric solutions for a 2D critical Dirac equation</a></p>
<p><b> De Lellis, Focardi, Ghinassi:</b> <a href='/paper/4849/'>Endpoint regularity for 2d Mumford-Shah minimizers: On a theorem of Andersson and Mikayelyan</a></p>
<p><b> Braides, Vallocchia:</b> <a href='/paper/4860/'>Two geometric lemmas for $S^{N-1}$-valued maps and an application to the homogenization of spin systems</a></p>
<p><b> De Lellis, Giri:</b> <a href='/paper/4924/'>Smoothing does not give a selection principle for transport equations with bounded autonomous fields</a></p>
<p><b> Maione, Salort, Vecchi:</b> <a href='/paper/4950/'>Maz'ya-Shaposhnikova formula in Magnetic Fractional Orlicz-Sobolev spaces</a></p>
<p><b> Borrelli, Carlone:</b> <a href='/paper/4989/'>Bifurcating standing waves for effective equations in gapped honeycomb structures</a></p>
<p><b> Borrelli, De Falco:</b> <a href='/paper/5032/'>Detection of chaos in the general relativistic Poynting-Robertson effect: Kerr equatorial plane</a></p>
<h2>Open Positions</h2>
<p><a href="/position/555/">PhD position, Marie Curie Network TraDE-Opt, University of Graz</a> (deadline: Wed 17 March 2021)</p>
<p><a href="/position/552/">Post-doc at the University of Firenze</a> (deadline: Tue 30 March 2021)</p>
<p><a href="/position/554/">5-10 Postdoctoral and 1-2 Ph.D. student positions at Jyväskylä</a> (deadline: Wed 31 March 2021)</p>
<p><a href="/position/556/">2-years postdoc position in Analysis at Bocconi University, Milan</a> (deadline: Wed 31 March 2021)</p>
<p><a href="/position/557/">PhD position in spectral theory of differential operators, Oldenburg</a> (deadline: Fri 7 May 2021)</p>
<p><a href="/position/551/">Recruitment of Shing-Tung Yau Center of Southeast University (SEU-Yau Center) Nanjing, China</a> (deadline: Fri 11 February 2022)</p>
<p><a href="/position/469/">Recruitment of the Nanjing Center for Applied Mathematics（NCAM） Nanjing, China</a> (deadline: Fri 11 February 2022)</p>
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