[3] In 2016 he was awarded a European Research Council (ERC) grant, and in 2018 he received the Doctorate Honoris Causa from the Université Côte d'Azur.

In 2018, he won the Fields Medal "for his contributions to the theory of optimal transport, and its application to partial differential equations, metric geometry, and probability".

[10] Then, in a joint work with Eric Carlen, he addressed the stability analysis of some Gagliardo–Nirenberg and logarithmic Hardy–Littlewood–Sobolev inequalities to obtain a quantitative rate of convergence for the critical mass Keller–Segel equation.

[14] More recently, in collaboration with Alice Guionnet, he introduced and developed new transportation techniques in the topic of random matrices to prove universality results in several-matrix models.

[15] Also, together with Joaquim Serra, he proved the De Giorgi's conjecture for boundary reaction terms in dimension lower than five, and he improved the classical results by Luis Caffarelli on the structure of singular points in the obstacle problem.