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6/1/26, 11:10 AM
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Jean Mawhin6/1/26, 11:15 AM
Petru Mironescu, in a series of works alone or in collaboration, especially with the late Haïm Brezis, has shown the important role played by a formula of Jacobi in the definition and study of the distributional Jacobian.
In this lecture, we recall some aspects of the tortuous history of this formula described in [1], and comment on some new historical facts and some new links to classical...
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Antoine Detaille6/1/26, 12:00 PM
In a striking contrast with the classical situation of real-valued Sobolev functions, a Sobolev mapping taking its values into a manifold N need not be a limit of smooth N-valued maps with respect to the strong convergence.
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A natural idea to try restoring the approximation property by smooth maps is to work with a weaker notion of convergence.
Unlike the strong approximation problem, which... -
Oscar Dominguez6/1/26, 2:15 PM
In this talk, we introduce, via the Gagliardo completion, an extrapolation framework within De Giorgi’s Γ-convergence theory and develop its applications to variational problems arising in image processing, in particular, the Rudin-Osher-Fatemi (ROF) model. Special emphasis is given to new tools connecting extrapolation theory and variational analysis, specifically the extrapolation of...
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Adriano Pisante6/1/26, 3:00 PM
In this talk we will focus for $N\geq 2$ on fractional $W^{1-1/N,N}$ maps from an $(N−1)$-dimensional sphere into itself as traces of maps with finite energies modelled on the $N$-Dirichlet integral. We consider energy minimization among maps with trace of prescribed topological degree. Our goal is to prove existence and quantitative stability for minimizers in homotopy classes. Due to the...
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Giacomo Canevari6/1/26, 4:15 PM
Manifold-valued Sobolev maps naturally arise in variational problems and models of partially ordered media, where the topology of the target can enforce the formation of singularities. These singularities may act as obstructions to familiar constructions, such as approximation by smooth maps. In this talk, given a positive integer $p$, we consider $W^{1,p}$-maps from a Euclidean domain of...
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Gabriella Tarantello6/2/26, 9:15 AM
Constant Mean Curvature (CMC) c-immersions of a closed orientable surface S (with genus g ≥ 2) into hyperbolic 3-manifolds emerged by the work of Uhlenbeck in connection with irreducible representations of the fundamental group of S into the Mobious group.
In view of Bryant surfaces, the value c =1 of the mean curvature enters as a “critical” (yet significant) parameter in this context....
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Mike Novack6/2/26, 10:00 AM
The classical double bubble theorem characterizes in every dimension surface-area minimizing partitions of R^n into three chambers, two of which have prescribed finite volume. In this talk we will discuss a variant of the double bubble problem in which two of the chambers have infinite volume. Unlike the standard double bubble problem, the characterization of minimizers depends on the...
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Anna Skorobogatova6/2/26, 11:15 AM
One possible framework in which to study the Plateau problem is by using currents with multiplicities modulo q, for a fixed integer q. This setting allows for minimizing surfaces to exhibit codimension 1 singularities like triple junctions, which are seen in physical soap films, and has close connections to the known regularity theory for stable minimal submanifolds, while at the same time...
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Dominik Stantejsky6/2/26, 12:00 PM
Motivated by experiments with nematic liquid crystal droplets, we study harmonic maps on the three-dimensional unit ball that arise as minimizers of the one-constant approximation of the Oseen-Frank energy subject to strong anchoring planar boundary condition. Through a reflection method, we are able to study regularity of minimizers close to the boundary. We also obtain results on the type...
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Peter Sternberg6/2/26, 2:30 PM
We consider the vector Allen-Cahn (Modica-Mortola) energy with a 4-well potential. The goal is to produce a stable, diffuse version of a stable, tetrahedral cone in the absence of any symmetry assumptions. This is accomplished via standard Gamma-convergence theory once we can exhibit a bounded 3D domain which is partitioned by such a cone into a locally minimizing 4 chamber configuration with...
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Lucia Scardia6/2/26, 3:15 PM
Nonlocal energies are continuum models for large systems of particles with long-range interactions. Under the assumption that the interaction potential is radially symmetric, several authors have investigated qualitative properties of energy minimisers. But what can be said in the case of anisotropic kernels?
I will present some results and partial answers in this direction obtained in...
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Piotr Hajłasz6/2/26, 4:30 PM
The main theme of this talk is the study of mappings—primarily continuously differentiable and Lipschitz—that are critical everywhere, in the sense that the rank of their derivative is small at every point. Such mappings arise naturally in a variety of contexts across analysis, geometry, and topology. I will show how ideas from different areas combine to address fundamental questions about...
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Etienne Sandier6/3/26, 10:00 AM
We show a symmetry result in an exterior domain in dimension 2 for minimizing harmonic maps to the sphere perturbed by a jacobian term. We hope this could be useful in the study of various Skyrmion models.
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Antoine Lemenant6/3/26, 11:15 AM
The Griffith functional, arising in variational models of crack propagation and linearized elasticity, shares many features with the classical Mumford–Shah functional. A major difficulty in this vectorial setting is that the energy only controls the symmetric part of the gradient, rather than the full gradient itself. In this talk, I will present a strategy to obtain the L^2-integrability of...
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Itai Shafrir6/3/26, 12:00 PM
Several authors (Alama, Bronsard, Golovaty, Mironescu) have recently studied
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the minimizers $\{u_\varepsilon\}$ of the energy $ E_\varepsilon(u) = E^{g,\alpha}_\varepsilon(u)$, given by
\begin{equation}
%\label{eq:1}
E_\varepsilon(u) = \frac{1}{2} \int_\Omega \left( |\nabla
u|^2 + \frac{1}{2\varepsilon^2}(1 - |u|^2)^2 \right) \, dx + \frac{1}{2\varepsilon^s} \int_{\partial\Omega}
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6/3/26, 8:00 PM
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Giovanni Leoni6/4/26, 9:15 AM
This talk explores the trace theory of Sobolev spaces in the critical $p=1$ case. After reviewing the first-order case in which the trace of $W^{1,1}(\Omega)$ is $L^1(\partial\Omega)$, we focus on higher-order Sobolev spaces whose traces are Besov spaces. We will present new and classical results on the trace and lifting problem for these spaces.
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Adriana Garroni6/4/26, 10:00 AM
I will present a recent result obtained in collaboration with S. Conti, V. Crismale and A. Malusa.
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We consider a phase-field model `a la Ambrosio Tortorelli in order to approximate sharp interface energies for grain boundaries accounting for the Read and Shockley law for small angle grain boundaries.
The independent variable takes values in the orthogonal group O(d) modulo a lattice point... -
Maria Angeles Garcia Ferrero6/4/26, 11:15 AM
Let us consider two notions of concentration for homogeneous polynomials in d complex variables on the unit sphere: a local notion measuring the fraction of the L2-norm supported on a measurable subset and a global notion given by the generalized Wehrl entropy. Lieb and Solovej proved that the extremizers in both cases are monomials up to a unitary rotation. Their result generalizes the one by...
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Elise Bonhomme6/4/26, 12:00 PM
In this talk, I will present joint work with Mitia Duerinckx and Antoine Gloria, in which we establish the homogenization of the so-called "double-porosity" model in a random setting where the resonant inclusions are neither uniformly bounded nor uniformly separated. This mesoscopic model (used to describe flows in fractured porous media) arises as the limit of a diffusion process in a highly...
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Augusto Ponce6/4/26, 2:30 PM
Classical works by F. Bethuel and by F. Hang and F.-H. Lin identified the local and global topological obstructions preventing smooth maps from being dense in the Sobolev space $W^{1,p}(M^{m};N^{n})$ between two Riemannian manifolds when $p<m$. These obstructions are related to the extension of continuous maps from certain subsets of $M^{m}$ into $N^{n}$.
Inspired by the notion of modulus...
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Katarzyna Mazowiecka6/4/26, 3:15 PM
We consider maps between spheres $\mathbb S^n$ to $\mathbb S^\ell$ that minimize the Sobolev-space energy $W^{s,n/s}$ for some $s \in (0,1)$ in a given homotopy class. The basic question is: in which homotopy class does a minimizer exist? This is a nontrivial question since the energy under consideration is conformally invariant and bubbles can form. Sacks-Uhlenbeck theory tells us that...
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Rémy Rodiac6/4/26, 4:30 PM
We will discuss the existence of critical points of the $n$-Ginzburg-Landau energy in the unit ball of $\mathbb R^n$ with prescribed degree one on the boundary. We will first prove that there does not exist any minimizer of this energy among maps with prescribed degree $d\neq 0$. Then we will show that we can devise a min-max scheme which allows us to prove the existence of critical points...
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Armin Schikorra6/5/26, 10:00 AM
For maps between -spheres we can estimate their degree in terms of their Hoelder- and fractional Sobolev-spaces norm in a sharp way. We will discuss some approaches about a similar estimate for maps from $\mathbb S^3$ to $\mathbb S^2$ and the Hopf degree.
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Based on joint works with A. Grzela, K. Mazowiecka, J. Van Schaftingen -
Dmitry Golovaty6/5/26, 11:15 AM
I will present a recent result demonstrating that the Oseen-Frank model which explicitly incorporates electrostatics converges to its highly anisotropic counterpart in which the splay contribution dominates. This is a joint work with Peter Sternberg.
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Radu Ignat6/5/26, 12:00 PM
We consider the standard Ginzburg-Landau system for N-dimensional maps defined in the unit ball for some parameter $\epsilon>0$. For a boundary data corresponding to a vortex of topological degree one, the aim is to prove the (radial) symmetry of the ground state of the system. We show this conjecture in any dimension N≥7 and for every $\epsilon>0$, and then, we also prove it in dimension...
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Rémy Rodiac
We will discuss the existence of critical points of the $n$-Ginzburg-Landau energy in the unit ball of $\mathbb R^n$ with prescribed degree one on the boundary. We will first prove that there does not exist any minimizer of this energy among maps with prescribed degree $d\neq 0$. Then we will show that we can devise a min-max scheme which allows us to prove the existence of critical points...
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Jean Van Schaftingen
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