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<h2>cvgmt weekly bulletin</h2>
<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/885/'>Weiss</a></p>
<p><b>New papers by:</b> <a >Burchard</a>, <a href='/person/33/' >Prinari</a>, <a >Bazzana</a>, <a href='/person/2247/' >Tamanini</a>, <a >Carbonaro</a>, <a >Savona</a>, <a href='/person/198/' >Brasco</a>, <a href='/person/1259/' >Trevisan</a>, <a href='/person/3720/' >Carazzato</a>, <a href='/person/4045/' >Sk</a>, <a href='/person/3371/' >Topaloglu</a>, <a href='/person/44/' >Braides</a>, <a >Solci</a>, <a >Truskinovsky</a>, <a href='/person/1881/' >Colturato</a>, <a >Causin</a></p>
<p><b>Modified papers by:</b> <a >Erbar</a>, <a href='/person/263/'>Mantegazza</a>, <a href='/person/2184/'>Saracco</a>, <a href='/person/3464/'>Wu</a>, <a >Conforti</a>, <a href='/person/3978/'>Diana</a>, <a href='/person/2575/'>Pozzetta</a>, <a >Bartolucci</a>, <a href='/person/25/'>Eleuteri</a>, <a href='/person/1820/'>Jevnikar</a>, <a >Chiarini</a>, <a href='/person/2462/'>Rigoni</a>, <a >Greco</a>, <a href='/person/2207/'>Pasqualetto</a>, <a href='/person/33/'>Prinari</a>, <a href='/person/3875/'>Magnabosco</a>, <a href='/person/3628/'>Rossi</a>, <a href='/person/1196/'>Pegon</a>, <a >Sturm</a>, <a href='/person/65/'>Savaré</a>, <a >Léonard</a>, <a href='/person/2883/'>Antonelli</a>, <a >Ripani</a>, <a >Parini</a>, <a href='/person/2247/'>Tamanini</a>, <a >Gentil</a>, <a href='/person/4047/'>Sodini</a>, <a href='/person/217/'>Fusco</a>, <a href='/person/226/'>Gigli</a>, <a href='/person/230/'>Zappale</a>, <a >Monsaingeon</a>, <a >Carlier</a>, <a href='/person/3823/'>Violo</a>, <a href='/person/759/'>Fornasier</a>, <a >Vorotnikov</a></p>
<h2>Events next week</h2>
<ul>
<li><p>
<b><a href='/event/780/'>Enjoying Probability and Fluids in Lausanne</a></b><br />
Mon 18 September 2023 - Fri 22 September 2023<br />
EPFL, Lausanne (Switzerland)<br />
</p></li>
<li><p>
<b><a href='/event/786/'>11th Workshop of the GAMM Activity Group "Analysis of Partial Differential Equations"</a></b><br />
Mon 18 September 2023 - Wed 20 September 2023<br />
Eichstätt, Germany<br />
</p></li>
<li><p>
<b><a href='/event/791/'>Shape Optimization and Isoperimetric and Functional Inequalities</a></b><br />
Mon 18 September 2023 - Fri 22 September 2023<br />
Levico Terme (Italy)<br />
</p></li>
<li><p>
<b><a href='/event/793/'>Guess what? A Pisan workshop in Geometric Analysis</a></b><br />
Wed 20 September 2023 - Fri 22 September 2023<br />
Centro De Giorgi (Pisa)<br />
</p></li>
<li><p>
<b><a href='/event/805/'>Differential Geometry @L'AQuila 2023</a></b><br />
Wed 20 September 2023 - Fri 22 September 2023<br />
L'Aquila<br />
</p></li>
<li><p>
<b><a href='/event/728/'>Variational models for material failure</a></b><br />
Wed 20 September 2023 - Fri 22 September 2023<br />
FAU Erlangen-Nürnberg<br />
</p></li>
</ul>
<h2>Seminars next week</h2>
<h3>Wed 20 September 2023</h3><ul>
<li><p>
Agenda: Get-together (30 min), presentation Georg Weiss (60 min), questions and discussions (30 min).<br />
Georg Weiss: <b><a href='/seminar/885/'>Rectifiability, finite Hausdorff measure, and compactness for non-minimizing Bernoulli free boundaries</a></b><br />
, 10:00<br />
</p>
<div style="font-size: smaller;"><p>While there are numerous results on minimizers or stable solutions of the Bernoulli problem proving regularity of the free boundary and analyzing singularities, much less is known about critical points of the corresponding energy. Saddle points of the energy (or of closely related energies) and solutions of the corresponding time-dependent problem occur naturally in applied problems such as water waves and combustion theory.
</p>
<p>For such critical points $u$−which can be obtained as limits of classical solutions or limits of a singular perturbation problem−it has been open since <a href='Weiss03'>Weiss03</a> whether the singular set can be large and what equation the measure $\Delta u$ satisfies, except for the case of two dimensions. In the present result we use recent techniques such as a frequency formula for the Bernoulli problem as well as the celebrated Naber-Valtorta procedure to answer this more than 20 year old question in an affirmative way:
</p>
<p>For a closed class we call variational solutions of the Bernoulli problem, we show that the topological free boundary $\partial \{u > 0\}$ (including degenerate singular points $x$, at which $u(x + r)/r \to 0$ as $r \to 0$) is countably $\mathcal H^{n-1}$-rectifiable and has locally finite $\mathcal H^{n−1}$-measure, and we identify the measure $\Delta u$ completely. This gives a more precise characterization of the free boundary of $u$ in arbitrary dimension than was previously available even in dimension two.
</p>
<p>We also show that limits of (not necessarily minimizing) classical solutions as well as limits of critical points of a singularly perturbed energy are variational solutions, so that the result above applies directly to all of them.
This is a joint work with Dennis Kriventsov (Rutgers).</p>
</div>
</li>
</ul>
<h2>New Papers</h2>
<p><b> Bazzana, Colturato, Savona:</b> <a href='/paper/6198/'>Learning about unprecedented events: Agent-based modelling and the stock market impact of COVID-19</a></p>
<p><b> Carbonaro, Tamanini, Trevisan:</b> <a href='/paper/6199/'>Boundedness of Riesz transforms on $RCD(K,\infty)$ spaces</a></p>
<p><b> Brasco, Prinari, Sk:</b> <a href='/paper/6200/'>On Morrey's inequality in Sobolev-Slobodeckij spaces</a></p>
<p><b> Burchard, Carazzato, Topaloglu:</b> <a href='/paper/6201/'>Maximizers of nonlocal interactions of Wasserstein type</a></p>
<p><b> Braides, Causin, Solci, Truskinovsky:</b> <a href='/paper/6202/'>Beyond the classical Cauchy-Born rule</a></p>
<h2>Modified Papers</h2>
<p><b> Gigli, Tamanini:</b> <a href='/paper/3687/'>Second order differentiation formula on $RCD(K,N)$ spaces</a></p>
<p><b> Gigli, Tamanini:</b> <a href='/paper/3764/'>Second order differentiation formula on $RCD^*(K,N)$ spaces</a></p>
<p><b> Gigli, Tamanini:</b> <a href='/paper/3875/'>Benamou-Brenier and duality formulas for the entropic cost on $RCD^*(K,N)$ spaces</a></p>
<p><b> Gentil, Léonard, Ripani, Tamanini:</b> <a href='/paper/3889/'>An entropic interpolation proof of the HWI inequality</a></p>
<p><b> Conforti, Tamanini:</b> <a href='/paper/4549/'>A formula for the time derivative of the entropic cost and applications</a></p>
<p><b> Erbar, Rigoni, Sturm, Tamanini:</b> <a href='/paper/4946/'>Tamed spaces -- Dirichlet spaces with distribution-valued Ricci bounds</a></p>
<p><b> Tamanini:</b> <a href='/paper/4967/'>A generalization of Costa's Entropy Power Inequality</a></p>
<p><b> Monsaingeon, Tamanini, Vorotnikov:</b> <a href='/paper/4968/'>The dynamical Schrödinger problem in abstract metric spaces</a></p>
<p><b> Magnabosco, Rossi:</b> <a href='/paper/5451/'>Almost-Riemannian manifolds do not satisfy the $\mathsf{CD}$ condition</a></p>
<p><b> Carlier, Pegon, Tamanini:</b> <a href='/paper/5579/'>Convergence rate of general entropic optimal transport costs</a></p>
<p><b> Parini, Saracco:</b> <a href='/paper/5612/'>Optimization of the anisotropic Cheeger constant with respect to the anisotropy</a></p>
<p><b> Chiarini, Conforti, Greco, Tamanini:</b> <a href='/paper/5675/'>Gradient estimates for the Schrödinger potentials: convergence to the Brenier map and quantitative stability</a></p>
<p><b> Fornasier, Savaré, Sodini:</b> <a href='/paper/5710/'>Density of subalgebras of Lipschitz functions in metric Sobolev spaces
and applications to Wasserstein Sobolev spaces</a></p>
<p><b> Sodini:</b> <a href='/paper/5841/'>The general class of Wasserstein Sobolev spaces: density of cylinder
functions, reflexivity, uniform convexity and Clarkson's inequalities</a></p>
<p><b> Antonelli, Pasqualetto, Pozzetta, Violo:</b> <a href='/paper/5929/'>Topological regularity of isoperimetric sets in PI spaces having a deformation property</a></p>
<p><b> Diana, Fusco, Mantegazza:</b> <a href='/paper/5970/'>Stability for the Surface Diffusion Flow</a></p>
<p><b> Eleuteri, Prinari, Zappale:</b> <a href='/paper/6061/'>Asymptotic analysis of thin structures with point dependent energy growth</a></p>
<p><b> Bartolucci, Jevnikar, Wu:</b> <a href='/paper/6106/'>On the global bifurcation diagram of the equation $-\Delta u=\mu|x|^{2\alpha}e^u$ in dimension two</a></p>
<h2>Open Positions</h2>
<p><a href="/position/801/">Postdoc position: Regularity and geometrical properties of solutions to PDEs</a> (deadline: Fri 22 September 2023)</p>
<p><a href="/position/797/">Full Professor for Geometry/Optimization at University of Salzburg</a> (deadline: Sun 24 September 2023)</p>
<p><a href="/position/799/">Postdoc position in Mathematics of Machine Learning, University of Würzburg</a> (deadline: Sat 30 September 2023)</p>
<p><b>(new)</b> <a href="/position/802/">Ph.D. Student or Postdoc Positions at University of Freiburg</a> (deadline: Mon 16 October 2023)</p>
<p><a href="/position/800/">Postdoc position in Analysis/Geometry at SISSA (Trieste, Italy)</a> (deadline: Tue 31 October 2023)</p>
<p><a href="/position/699/">Chapman Fellow at Imperial College London</a> (deadline: Mon 6 November 2023)</p>
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