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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/712/'>Velichkov</a>, <a href='/seminar/714/'>Mazzeo</a>, <a href='/seminar/715/'>Mazzeo</a></p>
<p><b>New papers by:</b> <a >Giachetti</a>, <a >Ambrosio</a>, <a href='/person/2883/' >Antonelli</a>, <a href='/person/228/' >Magnani</a>, <a >Tiberio</a>, <a href='/person/234/' >Le Donne</a>, <a href='/person/139/' >Freddi</a>, <a href='/person/2260/' >Stefani</a>, <a >Musina</a>, <a >Oliva</a>, <a href='/person/1212/' >Petitta</a>, <a href='/person/1949/' >Comi</a>, <a >Bellettini</a></p>
<p><b>Modified papers by:</b> <a href='/person/3/'>Ambrosio</a>, <a href='/person/133/'>Ansini</a>, <a href='/person/263/'>Mantegazza</a>, <a href='/person/136/'>Petrache</a>, <a href='/person/141/'>Pinamonti</a>, <a >Ranetbauer</a>, <a >Scarpa</a>, <a >Trussardi</a>, <a href='/person/1304/'>Mészáros</a>, <a >Fathi</a>, <a href='/person/1949/'>Comi</a>, <a href='/person/1957/'>Fanzon</a>, <a >Bétermin</a>, <a href='/person/1326/'>Speight</a>, <a >Kwon</a>, <a href='/person/184/'>Davoli</a>, <a >Palombaro</a>, <a href='/person/199/'>Ponsiglione</a>, <a href='/person/1099/'>De Luca</a>, <a href='/person/2260/'>Stefani</a>, <a >Baldi</a>, <a href='/person/1753/'>De Rosa</a>, <a >Kolasiński</a>, <a href='/person/2063/'>Haus</a>, <a href='/person/59/'>Colombo</a>, <a href='/person/228/'>Magnani</a>, <a >Fagioli</a></p>
<h2>Seminars next week</h2>
<h3>Wed 6 November 2019</h3><ul>
<li><p>
Bozhidar Velichkov (Università degli Studi di Napoli Federico II): <b><a href='/seminar/712/'>Regularity of the two-phase free boundaries.</a></b><br />
Sala Seminari (Dipartimento di Matematica di Pisa), 17:00<br /> </p>
<div style="font-size: smaller;"><p>We consider the two-phase functional $J_{TP}$ defined, for every function $u:D\to\mathbb{R}$ on an open set $D\subset\mathbb{R}^d$, as
</p>
<p>$\displaystyle \qquad\qquad\qquad
J_{TP}(u,D):=\int_{D} \vert\nabla u\vert^2\,dx+\lambda^2_+\vert\Omega_u^+\cap D\vert+\lambda^2_-\vert\Omega_u^-\cap D\vert,$
</p>
<p> where $\lambda_+>0$ and $\lambda_->0$ are fixed constants, $\Omega_u^+=\{u>0\}$ and $\Omega_u^-=\{u<0\}$.
</p>
<p>In this talk, we will present some recent results on the regularity of the free boundary $\partial\Omega_u^+\cup \partial\Omega_u^-\cap D$ of
local minimizers $u$ of the two-phase functional $J_{TP}$ in a fixed open domain $D\subset\mathbb{R}^d$. Precisely, we will show that:
</p>
<p> $-$ In dimension $d=2$, the free boundaries $\partial\Omega_u^+\cap D$ and $\partial\Omega_u^-\cap D$ are $C^{1,\alpha}$-regular curves (this result was proved in recent works of Spolaor-V. and Spolaor-Trey-V.);
</p>
<p> $-$ In dimension $d>2$, the free boundaries $\partial\Omega_u^+\cap D$ and $\partial\Omega_u^-\cap D$ are $C^{1,\alpha}$-regular, up to a (possibly empty) one-phase singular set of lower dimension (De\,Philippis-Spolaor-V.).
</p>
<p>In particular, these results complete (in any dimension) the analysis of the two-phase free boundaries started by Alt, Caffarelli and Friedman in <a href='TAMS, 1984'>TAMS, 1984</a></p>
</div> </li>
</ul>
<h3>Thu 7 November 2019</h3><ul>
<li><p>
Rafe Mazzeo: <b><a href='/seminar/714/'>Spherical cone metrics</a></b><br />
Aula Magna, Dipartimento di Matematica, Università di Pisa, 16:00<br /> </p>
<div style="font-size: smaller;"><p>The study of solutions of Liouville's equation with prescribed logarithmic singularities is the same as the study of constant curvature metrics on a Riemann surface with prescribed conic points.
Understanding such metrics is a classic problem that remains a very active area.
I will survey some of the substantial literature on this and then describe a series of papers with Xuwen Zhu which attempts to understand this problem via deformation theory when the cone angles are large. This involves finding a new geometric framework in which the methods of global analysis can be applied.</p>
</div> </li>
</ul>
<h3>Fri 8 November 2019</h3><ul>
<li><p>
Rafe Mazzeo: <b><a href='/seminar/715/'>The large-scale geometry of the Higgs bundle moduli space</a></b><br />
Scuola Normale Superiore, Aula Bianchi, 11:00<br /> </p>
<div style="font-size: smaller;"><p>This talk will survey a number of recent results concerning
the asymptotic structure of the natural hyperkaehler metric on the moduli
space of solutions to the Hitchin equations on a Riemann surface. The
main results are obtained using some new PDE methods that give
a new construction of large solutions. Joint work with Fredrickson,
Swoboda and Weiss.</p>
</div> </li>
</ul>
<h2>New Papers</h2>
<p><b> Magnani, Tiberio:</b> <a href='/paper/4503/'>A remark on vanishing geodesic distances in infinite dimensions</a></p>
<p><b> Ambrosio, Freddi, Musina:</b> <a href='/paper/4504/'>Asymptotic analysis of the Dirichlet fractional Laplacian in domains becoming unbounded</a></p>
<p><b> Antonelli, Le Donne:</b> <a href='/paper/4505/'>Pauls rectifiable and purely Pauls unrectifiable smooth hypersurfaces</a></p>
<p><b> Bellettini, Le Donne:</b> <a href='/paper/4506/'>Sets with constant normal in Carnot groups: properties and examples</a></p>
<p><b> Comi, Stefani:</b> <a href='/paper/4507/'>A distributional approach to fractional Sobolev spaces and fractional variation: asymptotics I</a></p>
<p><b> Giachetti, Oliva, Petitta:</b> <a href='/paper/4508/'>1-Laplacian type problems with strongly singular nonlinearities and
gradient terms</a></p>
<h2>Modified Papers</h2>
<p><b> Magnani, Pinamonti, Speight:</b> <a href='/paper/3474/'>Porosity and differentiability of Lipschitz maps from stratified groups to Banach homogeneous groups</a></p>
<p><b> Ambrosio, Stefani:</b> <a href='/paper/3726/'>Heat and entropy flows in Carnot groups</a></p>
<p><b> Fanzon, Palombaro, Ponsiglione:</b> <a href='/paper/3872/'>Derivation of Linearised Polycrystals from a Two-Dimensional System of Edge Dislocations</a></p>
<p><b> Comi, Stefani:</b> <a href='/paper/4054/'>A distributional approach to fractional Sobolev spaces and fractional variation: existence of blow-up</a></p>
<p><b> De Rosa, Kolasiński:</b> <a href='/paper/4077/'>Equivalence of the ellipticity conditions for geometric variational problems</a></p>
<p><b> Baldi, Haus, Mantegazza:</b> <a href='/paper/4115/'>Existence of a Lens–Shaped Cluster of Surfaces Self–Shrinking by Mean Curvature</a></p>
<p><b> Davoli, Ranetbauer, Scarpa, Trussardi:</b> <a href='/paper/4220/'>Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics</a></p>
<p><b> Ansini, Fagioli:</b> <a href='/paper/4225/'>Nonlinear diffusion equations with degenerate fast-decay mobility by coordinate transformation</a></p>
<p><b> Kwon, Mészáros:</b> <a href='/paper/4417/'>Degenerate nonlinear parabolic equations with discontinuous diffusion coefficients</a></p>
<p><b> Colombo, Fathi:</b> <a href='/paper/4500/'>Bounds on optimal transport maps onto log-concave measures</a></p>
<p><b> Bétermin, De Luca, Petrache:</b> <a href='/paper/4502/'>Crystallization to the square lattice for a two body potential</a></p>
<h2>Open Positions</h2>
<p><a href="/position/427/">Two-year postdoctoral position in analysis at EPFL Lausanne</a> (deadline: Fri 1 November 2019)</p>
<p><a href="/position/428/">Tenure-Track Assistant Professor of Mathematics at EPFL Lausanne</a> (deadline: Fri 1 November 2019)</p>
<p><a href="/position/440/">Post-doc position (assegno di ricerca) at University of Naples "Federico II" (12 months)</a> (deadline: Thu 28 November 2019)</p>
<p><a href="/position/437/">Assistant Professor or higher, Department of Applied Mathematics, University of Waterloo, Canada</a> (deadline: Sun 1 December 2019)</p>
<p><a href="/position/435/">Postdoctoral Researcher at Okinawa Institute of Science and Technology under Prof. Daniel Spector</a> (deadline: Sun 15 December 2019)</p>
<p><a href="/position/439/">4-year PhD student in Probability and Analysis in Eindhoven</a> (deadline: Sun 15 December 2019)</p>
<p><a href="/position/438/">Two-year postdoctoral position in geometric analysis at University of Paris</a> (deadline: Sat 18 January 2020)</p>
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