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Jean Van Schaftingen

Curriculum vitæ

Positions held

Starting Oct 2021
Professeur ordinaire (Full professor), Université catholique de Louvain, Faculté des Sciences (SC) and Institut de Recherche en Mathématique et Physique (IRMP), Louvain-la-Neuve, Belgium
Oct 2015–Sept 2021
Professeur (Professor), Université catholique de Louvain, Faculté des Sciences (SC) and Institut de Recherche en Mathématique et Physique (IRMP), Louvain-la-Neuve, Belgium.
Oct 2007–Sept 2015
Chargé de cours (Associate professor), tenured since Oct 2010, Université catholique de Louvain, Faculté des Sciences (SC) and Institut de Recherche en Mathématique et Physique (IRMP), Louvain-la-Neuve, Belgium.
Oct 2006–Sep 2007
Chargé de recherches du Fonds National de la Recherche Scientifique (F.N.R.S. Postdoctoral Researcher), Université catholique de Louvain (UCLouvain), Département de Mathématique, Unité d’analyse mathématique et de mécaniqueLouvain-la-Neuve, Belgium.
Oct 2002–Sep 2006
Aspirant du Fonds National de la Recherche Scientifique (F.N.R.S. Research Fellow), Université catholique de Louvain, Département de Mathématique, Unité d’analyse mathématique et de mécanique, Louvain-la-Neuve, Belgium.

Education

May 19, 2005
Docteur en sciences mathématiques (PhD in Mathematics), Université catholique de Louvain.
Title of the dissertation: Symmetrizations, Symmetry of Critical Points and \(L^1\) Estimates.
Members of the comittee. Michel Willem (advisor, UCLouvain), Jean Mawhin (chair), Thomas Bartsch (Universität Giessen), Haïm Brezis (Université de Paris VI), Thierry De Pauw (UCLouvain), Jean-Pierre Gossez (Université Libre de Bruxelles) and Patrick Habets (UCLouvain).
Jun 2003
Diplôme d’études approfondies interuniversitaire en mathématiques (Master Degree in Mathematics), Université catholique de Louvain.
Thesis: Symétrisations: mesure, géométrie et approximation, advisor: Michel Willem.
Jun 2002
Ingénieur civil en mathématiques appliquées (Master in Mathematical Engineering), Université catholique de Louvain, summa cum laude. Master’s thesis: Symétrisations et problèmes elliptiques non linéaires, advisor: Michel Willem.

Teaching experience

2001–2002
Undergraduate student instructor, Mécanique des milieux continus (Continuum mechanics), Faculté des Sciences appliquées (Engineering school)
2002–2005
Instructor for exercises in Functional Analysis for student in mathematics and Analysis complements for students in engineering in applied mathematics.

Scientific awards

2006
Concours annuel de la Classe des Sciences de l’Académie royale des Sciences, des Lettres et des Beaux-Arts de Belgique, Groupe I – Mathématiques pour une “contribution originale à l’étude du rôle de la symétrie dans les problèmes non linéaires” (for an «original contribution to the study of the role of symmetry in nonlinear problems»).
2011
Prix Adolphe Wetrems, sciences mathématiques et physiques.
2020
Prix Jacques Deruyts, récompensant l’auteur de travaux originaux dans le domaine de l’analyse mathématique, Académie royale des Sciences, des Lettres et des Beaux-Arts de Belgique.

Grants

2009–2012
Crédit aux chercheurs FC 64984 - 1.5.058.09.F F.R.S.-FNRS, «Propriétes d’espaces de Sobolev et équations aux dérivées partielles elliptiques semilinéaires»
2010–2014
Projet 2.4.550.10.F du Fonds de la Recherche Fondamentale Collective, «Étude qualitative des solutions d’équations aux dérivées partielles elliptiques variationnelles. Symétries, bifurcations, singularités, multiplicité et méthodes numériques.» Promoteurs : D. Bonheure (ULB, promoteur principal), C. Troestler (UMons) et J. Van Schaftingen (UCLouvain).
2013–2014
Crédit aux chercheurs J.044.13.F F.R.S.-FNRS «Problèmes vectoriels en EDP : Équation de Choquard et inégalités pour des champs de vecteurs».
2014–2018
Projet T.1110.14 du Fonds de la Recherche Fondamentale Collective intitulé «Existence et popriétés asymptotiques de solutions de systèmes d’équations aux dérivées partielles elliptiques semilinéaires», promoteurs: D. Bonheure (ULB), C. Troestler (UMons, promoteur principal) et J. Van Schaftingen (UCLouvain).
2017–2018
Mandat d’Impulsion Scientifique (MIS) F.452317 du Fonds de la Recherche Scientifique–FNRS «Topological singularities of Sobolev maps between manifolds for the weak-bounded approximation and lifting problems».
2021–2024
Projet de Recherche (PDR) T.0229.21 du Fonds de la Recherche Scientifique–FNRS “Singular Harmonic Maps and Asymptotics of Ginzburg-Landau Relaxations”.

Research visits

Jan 18, 2004–Mar 12, 2004
Laboratoire J.-L. Lions, Université de Paris 6, France.
Dec 1–9, 2004
Rutgers University, New Brunswick, New Jersey, United States of America.
Feb 14–28, 2005
Courant Institute for the Mathematical Sciences, New York University, United States of America.
Apr 2005
Laboratoire J.-L. Lions, Université de Paris 6.
Nov 2005–Jun 2006
Laboratoire J.-L. Lions, Université de Paris 6.
Nov 27–Dec 5, 2006
Rutgers University, New Brunswick, New Jersey, United States of America.
Jan 8–17, 2008
Rutgers University, New Brunswick, New Jersey, United States of America.
Feb 2–12, 2009
Rutgers University, New Brunswick, New Jersey, United States of America.
Jan 18–27, 2011
Rutgers University, New Brunswick, New Jersey, United States of America.
Jan 14–Mar 20, 2019
University of Oxford, Mathematical Institute, United Kingdom, Academic visitor.

Publications

Submitted
, The extension of traces for Sobolev mappings between manifolds.
, and , Limiting behavior of minimizing \(p\)–harmonic maps in 3d as \(p\) goes to \(2\) with finite fundamental group.
and , Singular extension of critical Sobolev mappings under an exponential weak-type estimate.
, Injective ellipticity, cancelling operators, and endpoint Gagliardo-Nirenberg-Sobolev inequalities for vector fields.
Accepted
, Lifting of fractional Sobolev mappings to noncompact covering spaces, to appear in Ann. Inst. H. Poincaré Anal. Non Linéaire
, , and , Families of functionals representing Sobolev norms, to appear in Anal. PDE
2024
, Endpoint Sobolev inequalities for vector fields and cancelling operators, in Duván Cardona, Joel Restrepo and Michael Ruzhansky (eds.), Extended Abstracts 2021/2022. Methusalem Lectures, Birkhäuser, Cham, Trends in Mathematics, No. 3, 2024, 47–56.
, and , Boundary ellipticity and limiting \(L^1\)-estimates on halfspaces, Adv. Math. 439 (2024), 109490 (25 pages).
and , Asymptotic behavior of minimizing \(p\)-harmonic maps when \(p \nearrow 2\) in dimension \(2\), Calc. Var. Partial Differential Equations 62, 229 (45 pages).
2023
, Fractional Gagliardo-Nirenberg interpolation inequality and bounded mean oscillation, C. R. Math. Acad. Sci. Paris 361 (2023), 1041–1049.
, Limiting Sobolev estimates for vector fields and cancelling differential operators, in Jaroslav Lukeš, Zdeněk Mihula, Luboš Pick and Hana Turčinová (eds.), Function spaces and applications XII (Pazeky nad Jizerou, 2023), MatfyzPress, Charles University, Prague, 2023, 135–152.
and , Quantitative characterization of traces of Sobolev maps, Commun. Contemp. Math. 25 (2023), no. 02, 2250003 (31 pages).
, , , and , Spaces of Besov–Sobolev type and a problem on nonlinear approximation, J. Funct. Anal. 284 (2023), no. 4, 109775.
2022
, , and , Sobolev spaces revisited, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 33 (2022), no. 2, 413–437.
and , Limiting Sobolev and Hardy inequalities on stratified homogeneous groups, Annal. Acad. Sc. Fennic. 47 (2022), no. 2, 1065–1098.
, and , Renormalised energies and renormalisable singular harmonic maps into a compact manifold on planar domains, Math. Annal. 383 (2022), 1061–1125.
, Reverse superposition estimates in Sobolev spaces, Pure Appl. Funct. Anal. 7 (2022), no. 2, 805–811.
2021
, and , On limiting trace inequalities for vectorial differential operators, Indiana Univ. Math. J. 70 (2021), no. 5, 2133–2176.
, and , Ginzburg-Landau relaxation for harmonic maps on planar domains into a general compact vacuum manifold, Arch. Rat. Mech. Anal. 242 (2021), no. 2, 875–935.
and , Lifting in compact covering spaces for fractional Sobolev mappings, Anal. PDE 14 (2021), no. 6, 1851–1871.
and , Trace theory for Sobolev mappings into a manifold, Ann. Fac. Sci. Toulouse Math. (6) 30 (2021), no. 2, 281–299.
, and , Going to Lorentz when fractional Sobolev, Gagliardo and Nirenberg estimates fail, Calc. Var. Partial Differential Equations 60 (2021), no. 129
, and , A surprising formula for Sobolev norms, Proc. Natl. Acad. Sci. USA 118 (2021), no. 8, e2025254118.
and , Metric characterization of the sum of fractional Sobolev spaces, Stud. Math. 258 (2021), 27–51.
2020
and , Estimates of the amplitude of holonomies by the curvature of a connection on a bundle, Pure Appl. Funct. Anal. 5 (2020), no. 4, 891–897.
and , Characterization of the traces on the boundary of functions in magnetic Sobolev spaces, Adv. Math. 371 (2020), 107246.
, and , Groundstates for Choquard type equations with Hardy–Littlewood–Sobolev lower critical exponent, Proc. Roy. Soc. Edinb. A 150 (2020), no. 3, 1377–1400.
and , Range convergence monotonicity for vector measures and range monotonicity of the mass, Ric. Mat. 69 (2020), no. 1, 293-326.
and , An estimate of the Hopf degree of fractional Sobolev mappings, Proc. Amer. Math. Soc. 148 (2020), no. 7, 2877–2891.
and , Vortex motion for the lake equations, Comm. Math. Phys. 375 (2020), no. 2, 1459–1501.
2019
, Estimates by gap potentials of free homotopy decompositions of critical Sobolev maps, Adv. Nonlinear Anal. 9 (2019), no. 1, 1214–1250.
and , Optimal embeddings into Lorentz spaces for some vector differential operators via Gagliardo’s lemma, Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), no. 3, 413–436.
, , and , Representing three-dimensional cross fields using fourth order tensors, in Roca X. and Loseille A. (eds.), 27th International Meshing Roundtable. IMR 2018, Springer, Cham, Lecture Notes in Computational Science and Engineering, No. 127, 2019, 89–108.
and , Higher order intrinsic weak differentiability and Sobolev spaces between manifolds, Adv. Calc. Var. 12 (2019), no. 3, 303–332.
, and , Properties of groundstates of nonlinear Schrödinger equations under a weak constant magnetic field, J. Math. Pures Appl. (9) 124 (2019), 123–168.
and , Uniform boundedness principles for Sobolev maps into manifolds, Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, 417–449.
2018
, , , and , Sharp Gagliardo-Nirenberg inequalities in fractional Coulomb–Sobolev spaces, Trans. Amer. Math. Soc. 370 (2018), no. 11, 8285–8310.
and , Groundstates of the Choquard equations with a sign-changing self-interaction potential, Z. Angew. Math. Phys. 69 (2018), no. 3, 69:86.
and , Groundstates for a local nonlinear perturbation of the Choquard equations with lower critical exponent, J. Math. Anal. Appl. 464 (2018), no. 2, 1184–1202.
, and , Weak approximation by bounded Sobolev maps with values into complete manifolds, C. R. Math. Acad. Sci. Paris 356 (2018), no. 3, 264–271.
, Sobolev mappings: from liquid crystals to irrigation via degree theory, Lecture notes of the Godeaux Lecture delivered at the 9th Brussels Summer School of Mathematics (2018)
and , Odd symmetry of least energy nodal solutions for the Choquard equation, J. Differential Equations 264 (2018), no. 2, 1231–1262.
2017
and , Gauge-measurable functions, Rend. Istit. Mat. Univ. Trieste 49 (2017), 113–135.
, , and , Semiclassical Sobolev constants for the electro-magnetic Robin Laplacian, J. Math. Soc. Japan 69 (2017), no. 4, 1667–1714.
, and , Density of bounded maps in Sobolev spaces into complete manifolds, Ann. Mat. Pura Appl. (4) 196 (2017), no. 6, 2261–2301.
and , Approximation of symmetrizations by Markov processes, Indiana Univ. Math. J. 66 (2017), no. 4, 1145–1172.
and , Standing waves with a critical frequency for nonlinear Choquard equations, Nonlinear Anal. 161 (2017), 87–107.
, and , The logarithmic Choquard equation: sharp asymptotics and nondegeneracy of the groundstate, J. Funct. Anal. 272 (2017), no. 12, 5255–5281.
, and , Bourgain–Brezis estimates on symmetric spaces of non-compact type, J. Funct. Anal. 273 (2017), no. 4, 1504-1547.
and , Existence of groundstates for a class of nonlinear Choquard equations in the plane, Adv. Nonlinear Stud. 17 (2017), no. 3, 581–594.
, and , The incompressible Navier Stokes flow in two dimensions with prescribed vorticity, in Sagun Chanillo, Bruno Franchi, Guozhen Lu, Carlos Perez and Eric T. Sawyer (eds.), Harmonic Analysis, Partial Differential Equations and Applications, Birkhäuser, Applied and Numerical Harmonic Analysis, 2017, 19–25.
and , Controlled singular extension of critical trace Sobolev maps from spheres to compact manifolds, Int. Math. Res. Not. IMRN 2017 (2017), no. 12, 3467–3683.
and , A guide to the Choquard equation, J. Fixed Point Theory Appl. 19 (2017), no. 1, 773–813.
, and , An \(L^1\)–type estimate for Riesz potentials, Rev. Mat. Iberoam. 33 (2017), no. 1, 291–304.
, and , Variations on a proof of a borderline Bourgain–Brezis Sobolev embedding theorem, Chinese Ann. Math. Ser. B 38 (2017), no. 1, 235–252.
and , Choquard equations under confining external potentials, NoDEA Nonlinear Differential Equations Appl. 24 (2017), no. 1, 1–24.
, and , Least action nodal solutions for the quadratic Choquard equation, Proc. Amer. Math. Soc. 145 (2017), no. 2, 737–747.
2016
, and , Groundstates and radial solutions to nonlinear Schrödinger–Poisson–Slater equations at the critical frequency, Calc. Var. Partial Differential Equations 55 (2016), no. 146, 58.
and , Nodal solutions for the Choquard equation, J. Funct. Anal. 271 (2016), no. 1, 107–135.
and , Intrinsic colocal weak derivatives and Sobolev spaces between manifolds, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 16 (2016), no. 1, 97–128.
, and , Applications of Bourgain–Brezis inequalities to fluid mechanics and magnetism, C. R. Math. Acad. Sci. Paris 354 (2016), no. 1, 51–55.
and , Geometric partial differentiability on manifolds: the tangential derivative and the chain rule, J. Math. Anal. Appl. 435 (2016), no. 2, 1672–1681.
2015
and , Groundstates of nonlinear Choquard equations: Hardy–Littlewood–Sobolev critical exponent, Commun. Contemp. Math. 17 (2015), no. 5, 1550005 (12 pages).
and , Existence of groundstates for a class of nonlinear Choquard equations, Trans. Amer. Math. Soc. 367 (2015), no. 9, 6557–6579.
and , Semiclassical stationary states for nonlinear Schrödinger equations under a strong external magnetic field, J. Differential Equations 259 (2015), no. 2, 596–627.
, and , Strong density for higher order Sobolev spaces into compact manifolds, J. Eur. Math. Soc. (JEMS) 17 (2015), no. 4, 763–817.
and , Semi-classical states for the Choquard equations, Calc. Var. Partial Differential Equations 52 (2015), no. 1, 199–235.
and , Existence, stability and oscillation properties of slow decay positive solutions of supercritical elliptic equations with Hardy potential, Proc. Roy. Soc. Edinburgh Sect. A 58 (2015), no. 1, 255–271.
2014
, Limiting Bourgain–Brezis estimates for systems of linear differential equations: Theme and variations, J. Fixed Point Theory Appl. 15 (2014), no. 2, 273–297.
, and , Strong approximation of fractional Sobolev maps, J. Fixed Point Theory Appl. 15 (2014), no. 1, 133–153.
and , Hardy–Sobolev inequalities for vector fields and canceling linear differential operators, Indiana Univ. Math. J. 63 (2014), no. 5, 1419–1445.
, Equivalence between Pólya–Szegő and relative capacity inequalities under rearrangement, Arch. Math. (Basel) 103 (2014), no. 4, 367–379.
, Interpolation inequalities between Sobolev and Morrey–Campanato spaces: A common gateway to concentration-compactness and Gagliardo–Nirenberg, Port. Math. 71 (2014), no. 3–4, 159–175.
, Approximation in Sobolev spaces by piecewise affine interpolation, J. Math. Anal. Appl. 420 (2014), no. 1, 40–47.
2013
, and , Density of smooth maps for fractional Sobolev spaces \(W^{s, p}\) into \(\ell\)–simply connected manifolds when \(s \ge 1\), Confluentes Math. 5 (2013), no. 2, 3–22.
and , Desingularization of vortex rings and shallow water vortices by a semilinear elliptic problem, Arch. Rat. Mech. Anal. 210 (2013), no. 2, 409–450.
, A direct proof of the existence of eigenvalues and eigenvectors by Weierstrass’s theorem, Amer. Math. Monthly 120 (2013), no. 8, 741–746.
and , Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics, J. Funct. Anal. 265 (2013), no. 2, 153–184.
and , Stationary solutions of the nonlinear Schrödinger equation with fast-decay potentials concentrating around local maxima, Calc. Var. Partial Differential Equations 47 (2013), no. 1–2, 243–271.
, Limiting Sobolev inequalities for vector fields and canceling linear differential operators, J. Eur. Math. Soc. (JEMS) 15 (2013), no. 3, 877–921.
and , Nonexistence and optimal decay of supersolutions to Choquard equations in exterior domains, J. Differential Equations 254 (2013), no. 8, 3089–3145.
2012
and , Nonlocal Hardy type inequalities with optimal constants and remainder terms, Ann. Univ. Buchar. Math. Ser. 3 (LXI) (2012), no. 2, 187–200.
and , Finding critical points whose polarization is also a critical point, Topol. Methods Nonlinear Anal. 40 (2012), no. 2, 371–379.
, and , Nonlinear Schrödinger equation with unbounded or vanishing potentials: solutions concentrating on lower dimensional spheres, J. Differential Equations 252 (2012), no. 1, 941–968.
2011
and , Extremal functions in Poincaré–Sobolev inequalities for functions of bounded variation, in Denis Bonheure, Mabel Cuesta, Enrique J. and Peter Takáč Lami Dozo, Jean Van Schaftingen and Michel Willem (eds.), Nonlinear Elliptic Partial Differential Equations, Amer. Math. Soc., Contemporary Mathematics, No. 540, 2011, 47–58.
2010
and , Desingularization of vortices for the Euler equation, Arch. Rat. Mech. Anal. 198 (2010), no. 3, 869–925.
and , Groundstates for the nonlinear Schrödinger equation with potential vanishing at infinity, Ann. Mat. Pura Appl. (4) 189 (2010), 273–301.
and , Semiclassical stationary states for nonlinear Schrödinger equations with fast decaying potentials, Calc. Var. Partial Differential Equations 37 (2010), no. 1, 1—27.
, Limiting fractional and Lorentz spaces estimates of differential forms, Proc. Amer. Math. Soc. 138 (2010), no. 1, 235–240.
2009
and , Closure of Smooth Maps in \(W^{1,p}(B^3;S^2)\), Differential Integral Equations 22 (2009), no. 9–10, 881–900.
, Explicit approximation of the symmetric rearrangement by polarizations, Arch. Math. (Basel) 93 (2009), no. 2, 181–190.
and , Existence and concentration for nonlinear Schrödinger equations with fast decaying potentials, C. R. Math. Acad. Sci. Paris 347 (2009), no. 15–16, 921–926.
, and , Pathological solutions to elliptic problems in divergence form with continuous coefficients, C. R. Math. Acad. Sci. Paris 347 (2009), no. 13–14, 773–778.
and , Subelliptic Bourgain–Brezis estimates on groups, Math. Res. Lett. 16 (2009), no. 3, 487–501.
2008
and , Circulation integrals and critical Sobolev spaces: problems of optimal constants, in Dorina Mitrea and Marius Mitrea (eds.), Perspectives in Partial Differential Equations, Harmonic Analysis and Applications, Amer. Math. Soc., Proc. Sympos. Pure Math., No. 79, 2008, 33–47.
, and , Periodic homogenization for convex functionals using Mosco convergence, Ricerche Mat. 57 (2008), no. 2, 209–249.
, Estimates for \(\mathrm{L}^1\) vector fields under higher-order differential conditions, J. Eur. Math. Soc. (JEMS) 10 (2008), no. 4, 867–882.
, , and , Asymptotics and symmetries of least energy nodal solutions of Lane–Emden problems with slow growth, Commun. Contemp. Math. 10 (2008), no. 4, 609–631.
, and , A case of density in \(W^{2,p}(M;N)\), C. R. Math. Acad. Sci. Paris 346 (2008), no. 13–14, 735–740.
and , Bound state solutions for a class of nonlinear Schrödinger equations, Rev. Mat. Iberoam. 24 (2008), no. 1, 297–351.
and , Symmetry of solutions of semilinear elliptic problems, J. Eur. Math. Soc. (JEMS) 10 (2008), no. 2, 439–456.
2007
, and , Periodic homogenization of monotone multivalued operators, Nonlinear Anal. 67 (2007), no. 12, 3217–3239.
and , Boundary estimates for elliptic systems with \(L^1\)–data, Calc. Var. Partial Differential Equations 30 (2007), no. 3, 369–388.
and , The continuity of functions with \(N\)–th derivative measure, Houston J. Math. 33 (2007), no. 3, 927–939.
2006
, Approximation of symmetrizations and symmetry of critical points, Topol. Methods Nonlinear Anal. 28 (2006), no. 1, 61–85.
, Anisotropic symmetrization, Ann. Inst. H. Poincaré Anal. Non Linéaire 23 (2006), no. 4, 539–565.
, Function spaces between BMO and critical Sobolev spaces, J. Funct. Anal. 236 (2006), no. 2, 490–516.
and , Nonlinear Schrödinger equations with potentials vanishing at infinity, C. R. Math. Acad. Sci. Paris 342 (2006), no. 12, 903–908.
, Universal approximation of symmetrizations by polarizations, Proc. Amer. Math. Soc. 134 (2006), no. 1, 177–186.
2005
and , Periodic reiterated homogenization for elliptic functions, J. Math. Pures Appl. (9) 84 (2005), no. 12, 1716–1743.
, Symmetrization and minimax principles, Commun. Contemp. Math. 7 (2005), no. 4, 463–481.
and , Reiterated homogenization for elliptic operators, C. R. Math. Acad. Sci. Paris 340 (2005), no. 3, 209–214.
2004
, Estimates for \(L^1\) vector fields with a second order condition, Acad. Roy. Belg. Bull. Cl. Sci. (6) 15 (2004), no. 1–6, 103–112.
and , Set transformations, symmetrizations and isoperimetric inequalities, in V. Benci and A. Masiello (eds.), Nonlinear analysis and applications to physical sciences, Springer Italia, Milan, 2004, 135–152.
, Estimates for \(L^1\)–vector fields, C. R. Math. Acad. Sci. Paris 339 (2004), no. 3, 181–186.
, A simple proof of an inequality of Bourgain, Brezis and Mironescu, C. R. Math. Acad. Sci. Paris 338 (2004), no. 1, 23–26.

Invited talks

Feb 25, 2004
Groupe de travail – analyse non linéaire, Laboratoire J.-L. Lions, Université de Paris 6, Symétries de points critiques obtenus par des méthodes de minimax.
Mar 11, 2004
Groupe de travail – équations elliptiques et paraboliques non linéaires, Université de Paris 11, Symétrisations et symétries de solutions de problèmes variationnels.
Dec 2, 2004
Joint Princeton, Institute for Advanced Study and Rutgers analysis seminar, Princeton University, \(L^1\) estimates for vector fields.
Dec 7, 2004
Rutgers analysis seminar, Rutgers University, New Brunswick, New Jersey, United States of America, Approximation of symmetrizations, random symmetrizations and symmetry of critical points.
Feb 17, 2005
Analysis Seminar, Courant Institute for the Mathematical Sciences, New York University, \(L^1\) Estimates for vector fields.
Apr 5, 2005
Groupe de travail – analyse non linéaire, Laboratoire J.-L. Lions, Université de Paris 6, Estimations \(L^1\) pour des champs de vecteurs.
May 20–22, 2005
Joint BeNeLuxFra conference in Mathematics, Gand, Belgique, \(L^1\) Estimates for vector fields.
May 24, 2005
Oberseminar Analysis, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany, \(L^1\) Estimates for vector fields.
Jun 26, 2005
Topological and Variational Methods for Differential Equations, Mathematisches Forschungsinstitut Oberwolfach, Germany, Symmetrization and symmetry of critical points.
Aug 1–5, 2005
Fixed Point Theory and its Applications, Będlewo, Poland, Symmetry properties of solutions of semilinear elliptic problems.
Sep 12, 2005
PhD Day, Belgian Mathematical Society, Brussels, Belgium, Approximation of symmetrizations and symmetry of critical points.
Dec 15, 2005
Séminaire d’analyse, Tours, France, Réarrangement symétrique: approximation et symétrie de points critiques.
Feb 15, 2006
Groupe de travail –analyse non linéaire, Laboratoire J.-L. Lions, Université de Paris 6, États stationnaires pour l’équation de Schrödinger non linéaire dans le cas semi-classique.
May 5, 2006
Séminaire “Équations aux dérivées partielles et applications”, Collège de France, Paris, France, Estimations pour des systèmes elliptiques à données \(L^1\).
May 22, 2006
Séminaire “Équations aux Dérivées Partielles”, Institut Camille Jordan, Université de Lyon I, France, Estimations pour des systèmes elliptiques à données \(L^1\).
Nov 6, 2006
Oberseminar Analysis Mathematisches Institut, Universität zu Köln, Cologne, Germany, Approximation of symmetrizations by polarizations and symmetry of solutions of elliptic problems .
Nov 14, 2006
Analysis and Partial Differential Equations Seminar, Department of Mathematics, University of Bristol, United Kingdom, \(L^1\) estimates for vector fields.
Nov 29, 2006
Rutgers analysis seminar, Rutgers University, New Brunswick, New Jersey, United States of America, \(L^1\) estimates for vector fields.
Jun 3–10, 2007
Geometric Analysis and Nonlinear Partial Differential Equations, Będlewo, Poland, Estimates for \(L^1\) vector fields.
Jan 15, 2008
Rutgers analysis seminar, Rutgers University, New Brunswick, New Jersey, United States of America, Desingularization of vortices for the Euler equation by a semilinear elliptic problem.
Feb 11–12, 2008
Seminar on Analysis, Institut für Mathematik, RWTH Aachen, Germany, Desingularization of vortices for the Euler equation by a semilinear elliptic problem.
Apr 10, 2008
Mathematisches Institut, Justus Liebig Universität Gießen, Germany, Desingularization of vortices for the Euler equation by a semilinear elliptic problem.
May 15, 2008
Seminarium Zakładu Równań Fizyki Matematycznej, Wydział Matematiky, Informatyki i Mechaniki, Uniwersytet Warszawski, Warsaw, Poland, Estimates for \(L^1\) vector-fields.
Jun 4, 2008
Colloquium, Centre for Analysis, Scientific computing and Applications, Technische Universiteit Eindhoven, Pays-Bas, Semilinear elliptic problems and vortices for the Euler equation.
Jun 17, 2008
SFB Seminar, Institut für Angewandte Mathematik, Universität Bonn, Estimates for \(L^1\) vector-fields.
Jul 3–4, 2008
Four Generations under One Roof, A workshop in nonlinear analysis, Université de Paris 6, Semilinear elliptic problems and vortices for the Euler equation.
Jan 15, 2009
Analysis and PDEs Seminar, Swansea University, Wales, United Kingdom, Desingularisation of vortices for the Euler equation by a semilinear elliptic problem.
Feb 11, 2009
Nonlinear Analysis and PDEs Seminar, Rutgers University, Semiclassical stationary states for the nonlinear Schrödinger equations with fast decaying potentials.
April 2, 2009
Seminario di Analisi, Dipartimento di Matematica “Ulisse Dini” Universitá degli Studi di Firenze, Estimates for \(L^1\) vector fields.
July 16, 2009
CASA Minimsymposium on Special limits in PDEs Technische Universiteit Eindhoven, Netherlands, Periodic homogenization, convergence of monotone operators and Mosco convergence.
Jan 15-16, 2009
Second South West Regional PDE Winter School, Swansea University, Wales, United Kingdom, Limiting estimates for \(L^1\) vector fields.
Feb 22, 2010
Oberseminar Geometrische Analysis, Goethe Universität Frankfurt, Germany, Existence of optimal functions for Poincaré-Sobolev inequalities.
Jun 3, 2010
ERC Nonlinear Problems in PDEs, Università degli Studi di Parma, What can be estimated by \(L^1\) norms of some derivatives of a vector field?
Jun 17, 2010
Analysis and PDEs Seminar, Swansea University, Wales, United Kingdom, Semiclassical stationary states for nonlinear Schroedinger equations with fast decaying potentials.
Sep 14-17, 2010
4th Group Actions in Topology and Analysis Conference, Milan 2010, Approximation of symmetrizations.
Jan 26, 2011
Nonlinear analysis seminar, Rutgers University, New Brunswick, New Jersey, United States of America, Nonexistence of positive supersolutions for semilinear elliptic problems with a nonlocal nonlinearity.
Feb 23, 2011
Seminario di Analisi Matematica, Sapienza Università di Roma, What can be estimated by the \(L^1\) norm of some components of the derivatives of a vector field?
Jul 7-8, 2011
Seminar on Analysis, Institut für Mathematik, RWTH Aachen, Germany, What can be estimated by the \(L^1\) norm of some components of the derivatives of a vector field?
Dec 13-15, 2011
Initial Training Network FRonts and Interfaces in Science and Technology (FIRST), Bath, United Kingdom, Nonexistence of positive super solutions for semilinear elliptic problems with a nonlocal nonlinearity.
Dec 15, 2011
Analysis and PDEs Seminar, Swansea University, Nonexistence of positive super solutions for semilinear elliptic problems with a nonlocal nonlinearity.
Sep 4–7, 2012
Meeting on Applied Mathematics and Calculus of Variations, Rome, Strong density for higher order Sobolev spaces into compact manifolds.
Nov 22, 2012
Analysis and PDEs Seminar, Swansea University, Wales, United Kingdom, Density of smooth maps in higher order Sobolev spaces with values in manifolds.
Dec 12–14, 2012
Workshop on Nonlocal Problems, Initial Training Network FRonts and Interfaces in Science and Technology (FIRST) Zürich, Switzerland, Existence of groundstates for a class of nonlinear Choquard equations.
Mar 6–7, 2013
Nonlinear PDE Days (Frankfurt–Gießen–Karlsruhe–Köln), Universität Frankfurt, Germany, Desingularization of stationary shallow water vortices
Apr 19, 2013
Séminaire - Analyse non linéaire et EDP, Université libre de Bruxelles, Existence et nonexistence de solutions pour des équations de Choquard
May 30, 2013
Analysis and PDEs Seminar, Swansea University, Wales, United Kingdom, Which differential operators on vector fields can appear in \(L^1\) Hardy and Sobolev inequalities?
Jan 7–10, 2014
Variational Methods in Elliptic Equations and Systems, Workshop in the memory of Miguel Ramos, Universidade de Lisboa, Lisbon, Portugal, Semi-classical states for the Choquard equation.
May 12, 2014
Partial Differential Equations Seminar, University of Oxford, Desingularization of stationary shallow water vortices.
May 15, 2014
Analysis and PDEs Seminar, Swansea University, Wales, United Kingdom, Semi-classical states for the Choquard equation.
Jun 30–Jul 4, 2014
Partial differential equations and nonlinearities, A conference in honor of Haïm Brezis, Paris, Lifting in Sobolev spaces revisited.
Dec 2, 2014
Seminario di Matematica, Dipartimento di Matematica, Politecnico di Bari, Semi-classical states for the Choquard equation.
Mar 9, 2015
Séminaire de Physique Mathématique, Université de Grenoble, Désingularisation de tourbillons pour l’équation des lacs.
Sep 9-11, 2015
Workshop in Nonlinear PDEs, Université Libre de Bruxelles, Nonlinear Schrödinger equation under a magnetic field kept in the foreground.
Nov 3, 2015
Seminario de Ecuaciones Diferenciales, Universidad di Granada, Nodal solutions for the Choquard equation.
Nov 16, 2015
Groupe de Travail Calcul des Variations, Laboratoire de Mathématiques, Université Paris-Sud (Orsay), Approximation d’applications Sobolev à valeur dans des variétés riemanniennes complètes.
Nov 16, 2015
Séminaire de l’équipe équations aux dérivées partielles, Institut de recherche mathématique de Rennes, Université de Rennes 1, L'équation de Schrödinger non linéaire quand le champ magnétique est à l’avant-plan.
May 30–Jun 3, 2016
Workshop on Nonlinear PDEs and Calculus of Variations, Chern Institute of Mathematics, Nankai University (香港中文大學), Tianjin, China, Symmetry of groundstates of some magnetic nonlinear Schrödinger equation and of least action nodal solutions to some Choquard equations.
Jun 4, 2016
Tianjin University (天津大学), China, Nodal solutions for the Choquard equation.
Aug 3, 2016
Godeaux Lecture (Belgian Mathematical Society) and Brussels Summer School of Mathematics, Brussels, Belgium, Sobolev mappings: from liquid crystals to irrigation via degree theory.
Sep 12–16, 2016
Partial Differential Equations and Related Topics, Alghero, Italy, Symmetry of groundstates of some magnetic nonlinear Schrödinger equation and of least action nodal solutions to some Choquard equations.
Oct 29, 2016
Nonlinear PDE, Inequalities and Applications, Riemann International School of Mathematics Varese, Italy, Nodal solutions for the Choquard equation and their odd symmetry.
Nov 28, 2016
Department of Mathematics, The Chinese University of Hong Kong (香港中文大學), Approximation by bounded mappings of Sobolev mappings into complete manifolds.
March 21, 2017
Séminaire d’analyse harmonique, Département de Mathématiques d’Orsay, Paris, France, Extension singulière contrôlée d’applications Sobolev.
June 1, 2017
Kandidatenseminar Analysis, Justus Liebig Universität Gießen, Mathematisches Institut, Nodal solutions for the Choquard equation and their odd symmetry.
June 12–16, 2017
23rd Rolf Nevanlinna Colloquium, ETH Zürich, Forschungsinstitut für Mathematik, Uniform boundedness principle for Sobolev maps between manifolds.
Oct 4–7, 2017
Workshop on Analysis and PDE, Leibniz Universität Hannover, The Choquard equation under a logarithmic potential.
Nov 20, 2017
Universitatea din Bucuresti, Facultatea de Matematica si Informatica, Seminar de analiză și EDP,\(L^1\) estimates and canceling conditions.
Nov 22, 2017
Institutul de Matematică “Simion Stoilow” al Academiei Române, IMAR Monthly lecture, Is symmetry better? Symmetry and symmetry breaking arising in calculus of variations and partial differential equations.
Dec 4, 2017
Università di Roma “La Sapienza”, Seminario di Analisi Matematica, Uniform boundedness principle for Sobolev maps between manifolds.
Mar 13, 2018
Department of Mathematics, The Chinese University of Hong Kong, Uniform boundedness principle for Sobolev maps between manifolds.
Mar 15, 2018
Hong Kong University of Science and Technology, Seminar on PDE, Limiting Sobolev estimates for vector fields and canceling differential operators.
Jun 15, 2018
Journée d’analyse et équations aux dérivées partielles, Bruxelles, Lifting fractional Sobolev maps over a compact covering.
Jun 18–22, 2018
Analysis of singular patterns in variational models, Toulouse, Lifting fractional Sobolev maps over a compact covering.
Jul 2–4, 2018
International Workshop on Critical Phenomena, National Chiao Tung University, Hsinchu, Taiwan, Limiting Sobolev estimates for vector fields and canceling differential operators.
Jul 5–9, 2018
The 12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Taipei, Taiwan, The Choquard Equation Under a Logarithmic Potential.
Jul 16–19, 2018
Variational Problems arising from Physics and Geometry, On the occasion of the 60th birthday of Thomas Bartsch, Rauischholzhausen (Germany), Vortex dynamics for the lake equation.
Jul 23–27, 2018
Geometric PDEs in Freiburg 2018, Freiburg im Breisgau (Germany), Uniform boundedness principle for Sobolev maps between manifolds.
Sep 21, 2018
Séminaire d’analyse, École Polytechnique Fédérale de Lausanne (EPFL), Lausanne, Switzerland, Critical estimates on the homotopy of maps between manifolds.
Oct 30, 2018
Nonlinear Analysis and PDE Seminar, Rutgers University, N.J., United States of America, Endpoint estimates in Lorentz spaces for vector fields.
Nov 9, 2018
Colloquium, Department of Mathematics, University of Pittsburgh, Pa., United States of America, Endpoint Sobolev inequalities for vector fields.
Dec 5, 2018
Recent breakthroughs in Mathematics, Belgian Mathematical Society, Brussels, Belgium, about optimal transport, PDEs and Alessio Figalli's Fields medal in 2018.
Feb 11, 2019
Partial Differential Equations Seminar, University of Oxford, United Kingdom, Ginzburg–Landau functionals with a general compact vacuum manifold on planar domains.
Feb 18, 2019
Analysis and PDEs seminar, Swansea University, United Kingdom, Vortex dynamics for the lake equations.
Feb 20, 2019
Partial Differential Equations and their Applications Seminar, University of Warwick, Coventry, United Kingdom, Endpoint estimates in Lorentz spaces for vector fields.
May 13–17, 2019
Analytic-Geometric Inequalities and Related Topics, Institut Mittag-Leffler, The Royal Sweedish Academy of SciencesStockholm, Sweden, “Limiting Sobolev estimates for vector fields and canceling differential operators”.
May 20–24, 2019
Workshop on variational problems in physics, Centre international de Mathématiques et d’Informatique de Toulouse, Toulouse, France, “Ginzburg–Landau functionals for a general compact vacuum manifold on planar domains”.
Jun 2–6, 2019
New Perspectives in nonlinear PDE: A research workshop in honor of Prof. Haim Brezis, Department of Mathematics, Technion, Haifa, Israel, “Estimates for the Hopf invariant in critical fractional Sobolev spaces”.
Sep 9–11 , 2019
Regularity aspects of linear growth functionals, Institute for Mathematics, University of Augsburg, Augsburg, Germany, “Endpoint estimates in Lorentz spaces for vector fields”.
Oct 31, 2019
Bourgain Day, Paleis der Academiën, Brussels Belgium, Germany, “Sobolev topology, Ginzburg-Landau energy and elliptic systems regularity”.
Jan 28, 2020
Rutgers analysis seminar, Rutgers University, New Brunswick, New Jersey, “Ginzburg-Landau functionals for a general compact vacuum manifold on planar domains”.
June 11, 2020
Corona seminar: Inequalities on Function Spaces of Smooth Functionsonline, “Marcinkiewicz meets Gagliardo and Sobolev: weak-type formulas for norms of the gradient”.
Nov 2–6, 2020
Workshop on Vortex Filaments, Fields Institute, Toronto, Canada (online), “Vortex dynamics for the lake equations”.
Feb 1–3, 2021
ICMC Summer Meeting on Differential Equations – 2021 Chapter, Universidade de São Paulo, Instituto de Ciências Matemáticas e de Computação, São Carlos, Brazil (online), “Ginzburg–Landau functionals for a general compact vacuum manifold on planar domains”.
Feb 9, 2021
Learning Seminar on PDE and Applications, Rutgers University, New Brunswick, United States of America (online), “Marcinkiewicz–Gagliardo weak-type formulas for Sobolev norms”.
Apr 22, 2021
Nonlinear Analysis Seminar Series, Okinawa Institute of Science and Technology (沖縄科学技術大学院大学), Okinawa, Japan (online), “Vortex dynamics for the lake equations”.
Jun 7–11, 2021
Canadian Mathematical Society 75+1 Anniversary meeting, Harmonic Analysis and Partial Differential Equations session, Toronto (Canada), (online), “Marcinkiewicz meets Gagliardo and Sobolev: weak-type formulas for norms of the gradient”.
Jun 20–26, 2021
8th European Congress of Mathematics, Geometric-functional inequalities and related topics session, Portorož, Slovenia (online), “Reverse superposition estimates, lifting over a compact covering and extensions of traces for fractional Sobolev mappings”.
Sep 5–10, 2021
Nonlinear Potential Theoretic Methods in Partial Differential Equations, Banff International Research station, Alberta, Canada (online), “Ginzburg–Landau functionals on planar domains for a general compact vacuum manifold”.
Oct 17–23, 2021
Rajchman, Zygmund, Marcinkiewicz conference, Warsaw, Poland (online), “Marcinkiewicz meets Gagliardo and Sobolev: getting weak differentiability from weak-type estimates”.
Apr 20, 2022
Webinar in Analysis and Differential Equations (CAMGSD, CMAFcIO & GFM), Lisbon, Portugal (online), “Ginzburg-Landau functionals on planar domains for a general compact vacuum manifold”.
Jun 3, 2022
Zhejiang UniversityHangzhou, China (online), “Ginzburg-Landau functionals on planar domains for a general compact vacuum manifold”.
Jun 9, 2022
Energy, Entropy, and Dissipative Dynamics (EDDY) seminar, RWTH, Aachen, Germany), “Ginzburg-Landau functionals on planar domains for a general compact vacuum manifold”.
Jul 4, 2022
Università di Roma “La Sapienza”, Seminario di Analisi Matematica, Ginzburg--Landau functionals on planar domains for a general compact vacuum manifold.
Oct 26, 2022
Universiteit Gent (UGent), Ghent Methusalem Colloquium, Endpoint Sobolev inequalities for vector fields and cancelling operators.
Nov 17, 2022
Analysis seminar, Universität Duisburg–Essen, Essen, Limiting Sobolev estimates for vector fields and cancelling differential operators.
Oct 4–6, 2023
Conference on Trends in Analysis 2023, Universität Duisburg–Essen, Duisburg, \(p \nearrow 2\)–harmonic maps on three-dimensional domains.

Advanced courses

Jan 22–24, 2013
Universitá di Pisa, Dipartimento di Matematica, 6h minicourse: “Symmetrization and symmetry properties of solutions to variational problems”
Jan 18–Mar 8, 2019
University of Oxford, Mathematical Institute, 16h course: “Sobolev mappings into manifolds”
Mar 28–31, 2019
VIIth Spring School of Analysis in memory of Aleksander Pełczyński: Differentiation and Geometry, Institute of Mathematics of the Polish Academy of Sciences, Banach center, Będlewo, (Poland), 6h minicourse: “Endpoint Sobolev estimates for vector fields and canceling differential operators”.
Jun 27–Jul 1, 2022
Geometric and analytic aspects of functional variational principles, Centro Internazionale Matematico Estivo (CIME), (Cetraro, Cosenza, Italy), 4h minicourse: “Limiting Sobolev estimates for vector fields and canceling dfferential operators”.
May 28–Jun 3, 2023
Function Spaces and Applications XII, Faculty of Mathematics and Physics of Charles University and Faculty of Electrical Engineering of the Czech Technical University in Prague (Paseky nad Jizerou, Czech Republic), 5h minicourse: “Limiting Sobolev estimates for vector fields and cancelling differential operators”.

Conferences attended

Apr 22, 2003
–May 9, 2003
Workshop and Conference on Recent Trends in Nonlinear Variational Problems, Abdus Salam International Centre for Theoretical Physics, Trieste, Italy
Jun 21–25, 2004
Nonlinear Analysis — Conference in Honor of Haïm Brezis, Paris, France.
Jul 2–8, 2006
Global and Geometric Aspects of Nonlinear Partial Differential Equations, European Science Foundation Programme, Évolène, Valais, Switzerland.
Apr 26–30, 2010
Differential and topological problems in modern theoretical physics, SISSA, Trieste, Italy.
Jul 24–30, 2012
Calculus of variations, Oberwolfach, Germany.

Doctoral training

Achieved theses

2007–2011
Jonathan Di Cosmo, Nonlinear Schrödinger equation and Schrödinger–Poisson system in the semiclassical limit, (coadvisor: Denis Bonheure, Université Libre de Bruxelles).
2011–2017
Alexandra Convent, Intrinsinc Sobolev maps between manifolds.
2014–2019
Justin Dekeyser, Equimeasurable functions and their application to vortex dynamics in lakes.

Ongoing theses

2021–
Benoît Van Vaerenbergh, Relaxation \(p\)-harmonique d’applications harmoniques singulières renormalisables.

Informal advising

2015–2016
Xia Jiankang (夏健康), Choquard equation: coercive potentials and critical frequency problem.

Supervision of postdocs

2015–2016
Luca Battaglia.
2016–2019
Antonin Monteil.
2017–2019
Rémy Rodiac.
2018–2021
Katarzyna Mazowiecka.
2021–2023
Bohdan Bulanyi.
2021–2024
Adolfo Arroyo-Rabasa.

Editorial responsibilities

2012–2020
Advances in Nonlinear Analysis, De Gruyter.
2015–
Journal of Fixed Point Theory and its Applications, Birkhäuser, section editor.

Research funding responsibilities

2016–2021
Membre du jury FRIA (président de 2019 à 2021)
2021–
Membre de commission scientifique du Fonds de la Recherche Scientifique–FNRS.

Organization of workshops

26–30 mai 2008
Spring school in nonlinear partial differential equations, Louvain-la-Neuve, partiellement financée par le réseau GLOBAL de l’European Science Foundation (comité d’organisation).
10–12 septembre 2008
Nonlinear Differential Equations, Académie Royale de Belgique, Bruxelles (comité d’organisation).
2–4 septembre 2009
Workshop on Nonlinear Elliptic PDEs, ULB, Bruxelles (comité scientifique).
May 17–21, 2010
Spring School in Nonlinear Partial Differential Equations, Bruxelles.
Jun 27–29, 2011
Workshop on singular reaction-diffusion, Louvain-la-Neuve.
May 30–Jun 6, 2012
Spring School in Nonlinear Partial Differential Equations, Bruxelles.
Jul 11–12, 2013
Workshop on Variational methods and partial differential equations, Louvain-la-Neuve.
Dec 14–18, 2015
Winter school “Nonlinear Function Spaces in Mathematics and Physical Sciences”, Lyon.
Nov 13–17, 2017
First Belgium–Chile–Italy conference in PDEs, Université libre de Bruxelles.