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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/899/'>Marx-Kuo</a>, <a href='/seminar/898/'>Nardulli</a></p>
<p><b>New papers by:</b> <a href='/person/4323/' >Brusca</a>, <a >Mora-Corral</a>, <a href='/person/965/' >Mondino</a>, <a href='/person/1830/' >Friedrich</a>, <a href='/person/230/' >Zappale</a>, <a href='/person/3688/' >Bresciani</a>, <a >Solci</a>, <a href='/person/42/' >Morandotti</a>, <a >Krömer</a>, <a href='/person/5073/' >Cucinotta</a>, <a href='/person/1714/' >Caroccia</a>, <a href='/person/2100/' >Kruzik</a>, <a href='/person/1400/' >Scala</a>, <a href='/person/4538/' >Donati</a>, <a href='/person/3132/' >Tyulenev</a>, <a href='/person/3935/' >Verzellesi</a></p>
<p><b>Modified papers by:</b> <a href='/person/135/'>Catino</a>, <a >Izydorek</a>, <a >Janczewska</a>, <a href='/person/2184/'>Saracco</a>, <a >Zarnescu</a>, <a href='/person/1813/'>Monteil</a>, <a href='/person/151/'>Pratelli</a>, <a href='/person/26/'>Stepanov</a>, <a href='/person/3611/'>Marziani</a>, <a href='/person/157/'>Pallara</a>, <a >Kohli</a>, <a href='/person/2340/'>La Manna</a>, <a >Cannarsa</a>, <a >Grosjean</a>, <a href='/person/1196/'>Pegon</a>, <a >Mougenot</a>, <a href='/person/2808/'>Carbotti</a>, <a href='/person/2998/'>Cito</a>, <a href='/person/3128/'>Goffi</a>, <a >Slastikov</a>, <a href='/person/4538/'>Donati</a>, <a href='/person/1084/'>Barilari</a>, <a >Boscain</a>, <a >Biswas</a>, <a href='/person/3136/'>Di Fratta</a>, <a href='/person/3270/'>Roncoroni</a>, <a href='/person/4167/'>Carano</a>, <a href='/person/204/'>Dal Maso</a>, <a href='/person/3406/'>ASHOK KUMAR</a>, <a href='/person/4313/'>Freguglia</a>, <a href='/person/4192/'>Durastanti</a>, <a href='/person/1644/'>Almi</a>, <a >Kryzhevich</a>, <a href='/person/373/'>Malchiodi</a>, <a href='/person/120/'>Solombrino</a>, <a >Mastrolia</a>, <a href='/person/250/'>Lemenant</a></p>
<h2>Events next week</h2>
<ul>
<li><p>
<b><a href='/event/854/'>Recent Advances in Comparison Geometry</a></b><br />
Mon 26 February 2024 - Fri 1 March 2024<br />
Hangzhou, Academic Island in the Xianghu Lake Tourist Resort<br />
</p></li>
<li><p>
<b><a href='/event/832/'>Bio-PDE Days Vienna</a></b><br />
Wed 28 February 2024 - Fri 1 March 2024<br />
TU Wien - Vienna<br />
</p></li>
</ul>
<h2>Seminars next week</h2>
<h3>Mon 26 February 2024</h3><ul>
<li><p>
Join from PC, Mac, Linux, iOS or Android: https://stanford.zoom.us/j/93331169510?pwd=azRkNTJOVXMzREdiQUttdm55QTJ0dz09
Password: 512274
Or iPhone one-tap (US Toll): +18333021536,,93331169510# or +16507249799,,93331169510#
Or Telephone:
Dial: +1 650 724 9799 (US, Canada, Caribbean Toll) or +1 833 302 1536 (US, Canada, Caribbean Toll Free)
Meeting ID: 933 3116 9510
Password: 512274
International numbers available: https://stanford.zoom.us/u/aenXWaDkeo
Meeting ID: 933 3116 9510
Password: 512274
SIP: 93331169510@zoomcrc.com
Password: 512274<br />
Jared Marx-Kuo: <b><a href='/seminar/899/'>An Allen--Cahn Energy on Hypersurfaces and Index of Minimizers</a></b><br />
ONLINE: details below, 17:00<br />
</p>
<div style="font-size: smaller;"><p>The Allen--Cahn equation is a well known model for minimal surfaces. We will briefly review the history between the two objects and then define an Allen--Cahn based energy functional on hypersurfaces of a closed manifold. For critical points of this energy, the morse index and nullity agrees with the original Allen--Cahn index and nullity. We use this to compute the index and nullity of all Allen--Cahn solutions on the unit circle. We also discuss the non-locality of the first and second variations of our Allen—Cahn energy, and its connections to the Dirichlet-to-Neumann map for the Allen—Cahn equation.</p>
</div>
</li>
</ul>
<h3>Tue 27 February 2024</h3><ul>
<li><p>
Stefano Nardulli (CMCC-UFABC, Santo André, São Paulo, SP (Brasil)): <b><a href='/seminar/898/'>Multiplicity of solutions to the multiphasic Allen–Cahn–Hilliard system with a small volume constraint on closed parallelizable manifolds</a></b><br />
SNS, Aula Mancini, 14:00<br />
</p>
<div style="font-size: smaller;"><p>We prove the existence of multiple solutions to the Allen–Cahn–Hilliard (ACH) vectorial equation (with two equations) involving a triple-well (triphasic) potential with a small volume constraint on a closed parallelizable Riemannian manifold. More precisely, we find a lower bound for the number of solutions depending on some topological invariants of the underlying manifold. The phase transition potential is considered to have a finite set of global minima, where it also vanishes, and a subcritical growth at infinity. Our strategy is to employ the Lusternik–Schnirelmann and infinite-dimensional Morse theories for the vectorial energy functional. To this end, we exploit that the associated ACH energy Γ-converges to the weighted multi-perimeter for clusters, which combined with some deep theorems from isoperimetric theory yields the suitable setup to apply the photography method. Along the way, the lack of a closed analytic expression for the multi-isoperimetric function for clusters imposes a delicate issue. Furthermore, using a transversality theorem, we also show the genericity of the set of metrics for which solutions to the ACH system are nondegenerate. This a joint work with J.H. Andrade, J. Conrado, P. Piccione, and Reinaldo Resend Oliveira.</p>
</div>
</li>
</ul>
<h2>New Papers</h2>
<p><b> Verzellesi:</b> <a href='/paper/6418/'>Variational properties of local functionals driven by arbitrary anisotropies</a></p>
<p><b> Cucinotta, Mondino:</b> <a href='/paper/6419/'>Half Space Property in RCD(0,N) spaces</a></p>
<p><b> Bresciani, Friedrich, Mora-Corral:</b> <a href='/paper/6420/'>Variational models with Eulerian-Lagrangian formulation allowing for material failure</a></p>
<p><b> Caroccia, Scala:</b> <a href='/paper/6421/'>On the singular planar Plateau problem</a></p>
<p><b> Cucinotta:</b> <a href='/paper/6422/'>On the properties of the set where a generalized function of bounded variation takes an infinite value</a></p>
<p><b> Brusca, Donati, Solci:</b> <a href='/paper/6423/'>Higher-order singular perturbation models for phase transitions</a></p>
<p><b> Tyulenev:</b> <a href='/paper/6424/'>Tracaes of Sobolev spaces to irregular subsets of metric measure spaces</a></p>
<p><b> Krömer, Kruzik, Morandotti, Zappale:</b> <a href='/paper/6425/'>Measure structured deformations</a></p>
<h2>Modified Papers</h2>
<p><b> Barilari, Kohli:</b> <a href='/paper/4501/'>On sub-Riemannian geodesic curvature in dimension three</a></p>
<p><b> Barilari, Boscain, Cannarsa:</b> <a href='/paper/4827/'>On the induced geometry on surfaces in 3D contact sub-Riemannian manifolds</a></p>
<p><b> Monteil, Pegon:</b> <a href='/paper/5121/'>Mass concentration in rescaled first order integral functionals</a></p>
<p><b> Catino, Mastrolia, Roncoroni:</b> <a href='/paper/5721/'>Two rigidity results for stable minimal hypersurfaces</a></p>
<p><b> Marziani, Solombrino:</b> <a href='/paper/5848/'>Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation</a></p>
<p><b> Dal Maso, Donati:</b> <a href='/paper/5871/'>Gamma-convergence of quadratic functionals perturbed by bounded linear functionals</a></p>
<p><b> Goffi:</b> <a href='/paper/6055/'>Interior a priori estimates for supersolutions of fully nonlinear subelliptic equations under geometric conditions</a></p>
<p><b> Goffi:</b> <a href='/paper/6056/'>High-order estimates for fully nonlinear equations under weak concavity assumptions</a></p>
<p><b> Carano:</b> <a href='/paper/6087/'>Relaxed area of $0$-homogeneous maps in the strict $BV$-convergence</a></p>
<p><b> ASHOK KUMAR, Biswas:</b> <a href='/paper/6088/'>Strict monotonicity of the first $q$-eigenvalue of the fractional $p$-Laplace operator over annuli</a></p>
<p><b> Grosjean, Lemenant, Mougenot:</b> <a href='/paper/6147/'>Stable domains for higher order elliptic operators</a></p>
<p><b> Di Fratta, Slastikov, Zarnescu:</b> <a href='/paper/6158/'>Sufficient conditions for the existence of minimizing harmonic maps with axial symmetry in the small-average regime</a></p>
<p><b> Izydorek, Janczewska, Kryzhevich, Stepanov:</b> <a href='/paper/6242/'>Nonholonomic controllability of control affine systems on compact manifolds</a></p>
<p><b> Goffi:</b> <a href='/paper/6324/'>Interior Hölder and Calderón-Zygmund estimates for fully nonlinear equations with natural gradient growth</a></p>
<p><b> Carbotti, Cito, La Manna, Pallara:</b> <a href='/paper/6325/'>Stability of the Gaussian Faber-Krahn inequality</a></p>
<p><b> Freguglia, Malchiodi:</b> <a href='/paper/6395/'>Yamabe metrics on conical manifolds</a></p>
<p><b> Almi, Durastanti, Solombrino:</b> <a href='/paper/6416/'>A Pontryagin Maximum Principle for agent-based models with convex state space</a></p>
<p><b> Pratelli, Saracco:</b> <a href='/paper/6417/'>Cylindrical estimates for the Cheeger constant and applications</a></p>
<h2>Open Positions</h2>
<p><a href="/position/869/">Postdoc position (2 years) at the University of Rome "Tor Vergata" on "Geometric flows and applications"</a> (deadline: Sun 25 February 2024)</p>
<p><a href="/position/852/">postdoctoral position in Prague Calculus of Variations and Continuum Mechanics</a> (deadline: Thu 29 February 2024)</p>
<p><a href="/position/879/">PhD position in polynomial optimization for calculus of variations in Prague</a> (deadline: Thu 29 February 2024)</p>
<p><a href="/position/880/">Postdoctoral position in polynomial optimization for calculus of variations in Prague</a> (deadline: Thu 29 February 2024)</p>
<p><b>(new)</b> <a href="/position/883/">Postdoc position an the University of Duisburg-Essen, Germany</a> (deadline: Thu 7 March 2024)</p>
<p><a href="/position/881/">Associate Professor MAT/07</a> (deadline: Mon 11 March 2024)</p>
<p><a href="/position/877/">PhD or Postdoc position (3 years) in Applied Analysis, TU Dresden</a> (deadline: Tue 12 March 2024)</p>
<p><a href="/position/860/">3 Maitre de Conférence (permanent) positions in Université de Lorraine, France</a> (deadline: Mon 18 March 2024)</p>
<p><a href="/position/862/">Research contract at Scuola Normale Superiore on "Variational and Analytical aspects of Geometric PDEs"</a> (deadline: Mon 18 March 2024)</p>
<p><a href="/position/878/">Maitre de Conference Position at IMATH-University of Toulon</a> (deadline: Fri 29 March 2024)</p>
<p><b>(new)</b> <a href="/position/882/">5-10 Postdoctoral positions at Jyväskylä</a> (deadline: Sun 31 March 2024)</p>
<p><a href="/position/876/">Ph.D. position in modular-topology optimization of compliant structures, mechanisms, and materials, Czech Technical University in Prague</a> (deadline: Tue 30 April 2024)</p>
<p><a href="/position/843/">LMS Distinguished Visiting Fellowships programme at ICMU Kyiv</a> (deadline: Fri 31 May 2024)</p>
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