[1]   S. Xambó-Descamps, “Alessio Figalli: Mágia, Método, Misión,” Boletín electrónico de la SEMA, vol. 24, no. abril, pp. 12–29, 2020. https://web.mat.upc.edu/sebastia.xambo/Bios/AF/2020-Xambo--AlessioFigalli.pdf.

[2]   A. Figalli and J. Serra, “On stable solutions for boundary reactions: a De Giorgi-type result in dimension 4 + 1,” Inventiones mathematicae, vol. 219, no. 1, pp. 153–177, 2020. https://arxiv.org/pdf/1705.02781.pdf.

[3]   S. Dipierro, J. Serra, and E. Valdinoci, “Improvement of flatness for nonlocal phase transitions,” American Journal of Mathematics, vol. 142, no. 4, pp. 1083–1160, 2020. https://arxiv.org/pdf/1611.10105.pdf.

[4]   X. Cabré, A. Figalli, X. Ros-Oton, and J. Serra, “Stable solutions to semilinear elliptic equations are smooth up to dimension 9,” Acta Mathematica, vol. 224, pp. 187–252, 2020. https://arxiv.org/pdf/1907.09403.pdf.

[5]   A. Figalli, X. Ros-Oton, and J. Serra, “Generic regularity of free boundaries for the obstacle problem,” Publications mathématiques de l’IHÉS, pp. 1–112, 2020. https://arxiv.org/pdf/1912.00714.pdf.

[6]   X. Cabré, E. Cinti, and J. Serra, “Stable s-minimal cones in ℝ³ are flat for s ∼ 1,” Journal für die reine und angewandte Mathematik, vol. 2020, no. 764, pp. 157–180, 2020. https://upcommons.upc.edu/bitstream/handle/2117/165885/cones-CRELLE.pdf.

[7]   X. Fernández-Real and J. Serra, “Regularity of minimal surfaces with lower-dimensional obstacles,” Journal für die reine und angewandte Mathematik, vol. 2020, no. 767, pp. 37–75, 2020. https://arxiv.org/pdf/1802.07607.pdf.

[8]   E. Cinti, J. Serra, and E. Valdinoci, “Quantitative flatness results and BV estimates for nonlocal anisotropic minimal surfaces,” Journal of Differential Geometry, vol. 112, no. 3, pp. 447–504, 2019. https://arxiv.org/pdf/1602.00540v2.pdf.

[9]   A. Figalli and J. Serra, “On the fine structure of the free boundary for the classical obstacle problem,” Inventiones mathematicae, vol. 215, no. 1, pp. 311–366, 2019. https://arxiv.org/pdf/1709.04002.pdf.

[10]   L. Caffarelli, X. Ros-Oton, and J. Serra, “Obstacle problems for integro-differential operators: regularity of solutions and free boundaries,” Inventiones mathematicae, vol. 208, no. 3, pp. 1155–1211, 2017. https://arxiv.org/pdf/1601.05843.pdf.

[11]   X. Ros-Oton and J. Serra, “Boundary regularity for fully nonlinear integro-differential equations,” Duke Mathematical Journal, vol. 165, no. 11, pp. 2079–2154, 2016. https://arxiv.org/pdf/1404.1197.pdf.

[12]   X. Ros-Oton and J. Serra, “Regularity theory for general stable operators,” J. Differential Equations, vol. 260, no. 12, pp. 8675–8715, 2016.

[13]   RSME, Olimpiada Matemática Española (1963-2004). Real Sociedad Matemática Española, 2004. «Por ello quiero felicitar y agradecer a la Comisión de Olimpiadas de la RSME su esfuerzo y generosidad, y especialmente al profesor Josep Grané sin cuyo trabajo este material no se habría realizado» (de la presentación de Carlos Andradas, Presidente de la RSME).

[14]   RSME, “OME: Problemas propuestos y resultados (1993-2019),” 2019. https://www.rsme.es/olimpiada-matematica-espanola/problemas-propuestos-y-resultados/.

[15]   J. Serra, “Two symmetry problems in reaction-diffusion equations,” 2010. Master Thesis. FME/UPC. 59 p.

[16]   J. Serra, “Radial symmetry of solutions to diffusion equations with discontinuous nonlinearities,” J. Differential Equations, vol. 254, no. 4, pp. 1893–1902, 2013.

[17]   X. Ros-Oton, “Minimizers to reaction-diffusion PDEs, Sobolev inequalities, and monomial weights,” 2010. Master Thesis. FME/UPC. 55 p.

[18]   J. Serra, Elliptic and parabolic PDEs: regularity for nonlocal diffusion equations and two isoperimetric problems. PhD thesis, FME/UPC, 2014. 329 p.

[19]   X. Ros-Oton, Integro-differential equations: Regularity theory and Pohozaev identities. PhD thesis, FME/UPC, 2014. 309 p.

[20]   X. Ros-Oton and J. Serra, “The Pohozaev identity for the fractional Laplacian,” Archive for Rational Mechanics and Analysis, vol. 213, no. 2, pp. 587–628, 2014. https://arxiv.org/pdf/1207.5986.pdf.

[21]   X. Ros-Oton and J. Serra, “The Dirichlet problem for the fractional Laplacian: regularity up to the boundary,” Journal de Mathématiques Pures et Appliquées, vol. 101, no. 3, pp. 275–302, 2014. https://www.sciencedirect.com/science/article/pii/S0021782413000895.

[22]   X. Ros-Oton and J. Serra, “Nonexistence results for nonlocal equations with critical and supercritical nonlinearities,” Comm. Partial Differential Equations, vol. 40, no. 1, pp. 115–133, 2015.

[23]   X. Ros-Oton and J. Serra, “The extremal solution for the fractional Laplacian,” Calc. Var. Partial Differential Equations, vol. 50, no. 3-4, pp. 723–750, 2014.

[24]   X. Cabré, X. Ros-Oton, and J. Serra, “Sharp isoperimetric inequalities via the ABP method,” J. Eur. Math. Soc. (JEMS), vol. 18, no. 12, pp. 2971–2998, 2016.

[25]   X. Cabré and J. Serra, “An extension problem for sums of fractional Laplacians and 1-D symmetry of phase transitions,” Nonlinear Anal., vol. 137, pp. 246–265, 2016.

[26]   J. Serra, “Regularity for fully nonlinear nonlocal parabolic equations with rough kernels,” Calc. Var. Partial Differential Equations, vol. 54, no. 1, pp. 615–629, 2015.

[27]   X. Cabré and X. Ros-Oton, “Regularity of stable solutions up to dimension 7 in domains of double revolution,” Communications in Partial Differential Equations, vol. 38, no. 1, pp. 135–154, 2013. https://arxiv.org/pdf/1202.1220.pdf.

[28]   X. Cabré and X. Ros-Oton, “Sobolev and isoperimetric inequalities with monomial weights,” Journal of Differential Equations, vol. 255, no. 11, pp. 4312–4336, 2013. https://www.sciencedirect.com/science/article/pii/S0022039613003677.

[29]   X. Ros-Oton, “Regularity for the fractional Gelfand problem up to dimension 7,” Journal of Mathematical Analysis and Applications, vol. 419, no. 1, pp. 10–19, 2014. https://www.sciencedirect.com/science/article/pii/S0022247X14003990.

[30]   S. Dipierro, J. Serra, and E. Valdinoci, “Nonlocal phase transitions: rigidity results and anisotropic geometry,” Rend. Semin. Mat. Univ. Politec. Torino, vol. 74, no. 2, pp. 135–149, 2016.

[31]   X. Ros-Oton, J. Serra, and E. Valdinoci, “Pohozaev identities for anisotropic integrodifferential operators,” Comm. Partial Differential Equations, vol. 42, no. 8, pp. 1290–1321, 2017.

[32]   X. Ros-Oton and J. Serra, “Fractional Laplacian: Pohozaev identity and nonexistence results,” C. R. Math. Acad. Sci. Paris, vol. 350, no. 9-10, pp. 505–508, 2012.

[33]   X. Cabré, X. Ros-Oton, and J. Serra, “Euclidean balls solve some isoperimetric problems with nonradial weights,” C. R. Math. Acad. Sci. Paris, vol. 350, no. 21-22, pp. 945–947, 2012.

[34]   J. Serra, “C^σ+α regularity for concave nonlocal fully nonlinear elliptic equations with rough kernels,” Calc. Var. Partial Differential Equations, vol. 54, no. 4, pp. 3571–3601, 2015.

[35]   X. Ros-Oton and J. Serra, “Local integration by parts and Pohozaev identities for higher order fractional Laplacians,” Discrete Contin. Dyn. Syst., vol. 35, no. 5, pp. 2131–2150, 2015.

[36]   X. Ros-Oton and J. Serra, “Boundary regularity estimates for nonlocal elliptic equations in C¹ and C^1,α domains,” Ann. Mat. Pura Appl. (4), vol. 196, no. 5, pp. 1637–1668, 2017.

[37]   X. Ros-Oton and J. Serra, “The structure of the free boundary in the fully nonlinear thin obstacle problem,” Adv. Math., vol. 316, pp. 710–747, 2017.

[38]   S. Serfaty and J. Serra, “Quantitative stability of the free boundary in the obstacle problem,” Anal. PDE, vol. 11, no. 7, pp. 1803–1839, 2018.

[39]   X. Ros-Oton and J. Serra, “The boundary Harnack principle for nonlocal elliptic operators in non-divergence form,” Potential Anal., vol. 51, no. 3, pp. 315–331, 2019.

[40]   E. Cinti, F. Glaudo, A. Pratelli, X. Ros-Oton, and J. Serra, “Sharp quantitative stability for isoperimetric inequalities with homogeneous weights,” 2020. https://arxiv.org/pdf/2006.13867.pdf.

[41]   S. Dipierro, X. Ros-Oton, J. Serra, and E. Valdinoci, “Non-symmetric stable operators: regularity theory and integration by parts,” 2020. https://arxiv.org/pdf/2012.04833.pdf.

[42]   J. Serra, “The geometric structure of interfaces and free boundaries,” 2021. Aparecerá en la Newsletter de la EMS. Elaborado por invitación de los editores de la revista, describe a grandes rasgos la investigación del autor y su significación.

[43]   A. Figalli, X. Ros-Oton, and J. Serra, “The singular set in the Stefan problem,” 2021. Preprint.