Alessio Figalli

Alessio Figalli (2016)

Alessio Figalli (born April 2, 1984 in Rome ) is an Italian mathematician who deals with partial differential equations . He is the recipient of the Fields Medal .

biography

Figalli studied at the University of Pisa and the Scuola Normale Superiore in Pisa with Giovanni Alberti and Luigi Ambrosio , graduating in 2006. In 2007 he received his doctorate with Ambrosio at the Scuola Normale Superiore in Pisa and with Cédric Villani at the Ecole Normale Superieure de Lyon (Optimal transportation and action minimizing measures). In 2007/08 he was the CNRS charge de recherche at the University of Nice and from 2008 professor at the École polytechnique . In 2009 he completed his habilitation in Nice (Optimal transport, Euler equations, Mather and DiPerna-Lions theories). At the end of 2009 he went to the University of Texas at Austin as an Associate Professor , where he became a professor in 2011. He has been a professor at ETH Zurich since 2016 .

Together with Young-heon Kim and Robert J. McCann, he proved the regularity of the mappings for optimal transport on products of spheres and with Guido De Philippis the regularity (see Sobolev space ) of solutions to the Monge-Ampere equation . The latter result was also highlighted as groundbreaking in the acknowledgment for the Fields Medal and is almost optimal in terms of known counterexamples. He also initiated the study of singular sets of images of optimal transport and achieved initial results by showing that they have Lebesgue measure zero. He also applied the theory of optimal transport to geometric inequalities (such as the isoperimetric inequality or the Brunn-Minkowski inequality ), without additional regularity assumptions for the geometrical objects under consideration and without exploiting Euclidean symmetries. The application to the Wulff inequality provides information about the structure of crystals at low energies. ${\displaystyle W^{2,1}}$

In 2012 he received the EMS award . In the laudation, his “outstanding contributions to the regularity theory of images in optimal transport, quantitative geometric and functional inequalities and partial solutions to the Mather and Mané conjectures in the theory of dynamic systems” were recognized.

In 2012 Figalli held the Cours Peccot at the Collège de France . In 2008 he received the Giuseppe Borgia Prize from the Accademia Nazionale dei Lincei and the Carlo Miranda Prize from the Academy of Sciences in Naples. In 2014 he was invited speaker at the ICM in Seoul (Quantitative stability results for the Brunn-Minkowski inequality). In 2015 Figalli was awarded the Stampacchia Medal of the Unione Matematica Italiana . In 2017 he received an Antonio Feltrinelli Prize . In 2018 he received the Fields Medal for contributions to the theory of optimal transport and its application to partial differential equations, metric geometry and probability theory (laudation).

Figalli is married to the mathematician Mikaela Iacobelli.

Fonts (selection)

• with Fabrizio Maggi, Aldo Pratelli: A mass transportation approach to quantitative isoperimetric inequalities. In: Inventiones Mathematicae . Volume 182, No. 1, 2010, pp. 167-211, doi : 10.1007 / s00222-010-0261-z .
• with Jose A. Carrillo, Marco DiFrancesco, Thomas Laurent, Dejan Slepčev: Global-in-time weak measure solutions and finite-time aggregation for nonlocal interaction equations. In: Duke Mathematical Journal. Volume 156, No. 2, 2011, pp. 229-271, doi : 10.1215 / 00127094-2010-211 .
• with Ludovic Rifford, Cédric Villani : Nearly round spheres look convex. In: American Journal of Mathematics . Volume 134, No. 1, 2012, pp. 109-139, JSTOR 41426421 .
• with Guido De Philippis : regularity for solutions of the Monge-Ampère equation. In: Inventiones Mathematicae. Volume 192, No. 1, 2013, pp. 55-69, doi : 10.1007 / s00222-012-0405-4 . ${\displaystyle W^{2,1}}$
• with Guido De Philippis: The Monge-Ampère equation and its link to optimal transportation. In: Bulletin of the American Mathematical Society . Volume 51, No. 4, 2014, pp. 527-580, doi : 10.1090 / S0273-0979-2014-01459-4 .
• with Gonzalo Contreras, Ludovic Rifford: Generic hyperbolicity of Aubry sets on surfaces. In: Inventiones Mathematicae. Volume 200, No. 1, 2015, pp. 201-261, doi : 10.1007 / s00222-014-0533-0 .
• with Ludovic Rifford: Closing Aubry sets. I, II. In: Communications on Pure and Applied Mathematics. Volume 68, No. 1, 2015, pp. 210-285, doi : 10.1002 / cpa.21511 ; No. 3, 2015, pp. 345-412, doi : 10.1002 / cpa.21512 .
• The Monge-Ampère Equation and Its Applications. European Mathematical Society, Zurich 2017, ISBN 978-3-03719-170-5 .

Web links

• Alessio Figalli's website. Retrieved August 3, 2020.
• Kevin Hartnett: A Traveler Who Finds Stability in the Natural World. Quanta Magazine, August 1, 2018, accessed August 3, 2020.
• Videos by and about Alessio Figalli in the AV portal of the Technical Information Library

Individual evidence

1. ^ A. Figalli: Optimal transport, Euler equations, Mather and DiPerna-Lions theories. (PDF; 413 kB), accessed on August 3, 2020.
2. ^ A. Figalli, Young-Heon Kim, Robert J. McKann: Regularity of optimal transport maps on multiple products of spheres. In: Journal of the European Mathematical Society. Volume 12, No. 4, 2010, pp. 1009-1040, doi : 10.4171 / JEMS / 221 .
3. ^ Regularity for solutions of the Monge-Ampère equation. In: Inventiones Mathematicae. Volume 192, No. 1, 2013, pp. 55-69. ${\displaystyle W^{2,1}}$
4. ↑ Laudation for the EMS Prize. Retrieved August 3, 2020.
5. ↑ "For contributions to the theory of optimal transport and its applications in partial differential equations, metric geometry and probability." Official website. Retrieved August 3, 2020.
6. ↑ Joachim Laukenmann: The mathematician on cloud nine. In: Tages-Anzeiger . December 1, 2018, accessed August 3, 2020.