via the hessian. These metrics have the special property of projective invariance, so that projective transformation from one given domain to another becomes an isometry of the corresponding metrics. Pseudo-differential operators Joseph Kohn and Nirenberg introduced the notion of pseudo-differential operators. Nirenberg and François Trèves investigated the famous Lewy's example for a non-solvable linear PDE of second order, and discovered the conditions under which it is solvable, in the context of both partial differential operators and pseudo-differential operators. Their introduction of local solvability conditions with analytic coefficients has become a focus for researchers such as R. Beals, C. Fefferman, R.D. Moyer, Lars Hörmander, and Nils Dencker who solved the pseudo-differential condition for Lewy's equation. This opened up further doors into the local solvability of linear partial differential equations. Major publications Books and surveys. Articles. References External links Homepage of Louis Nirenberg Simons Foundation, Science Lives: Louis Nirenberg Allyn Jackson. Interview with Louis Nirenberg. Notices Amer. Math. Soc. 49 (2002), no. 4, 441–449. YanYan Li. The work of Louis Nirenberg. Proceedings of the International Congress of Mathematicians. Volume I, 127–137, Hindustan Book Agency, New Delhi, 2010. Simon Donaldson. On the work of Louis Nirenberg. Notices Amer. Math. Soc. 58 (2011), no. 3, 469–472. Tristan Rivière. Exploring the unknown: the work of Louis Nirenberg on partial differential equations. Notices Amer. Math. Soc. 63 (2016), no. 2, 120–125. Recent applications of Nirenberg's classical ideas. Communicated by Christina Sormani. Notices Amer. Math. Soc. 63 (2016), no. 2, 126–134. Martin Raussen and Christian Skau. Interview with Louis Nirenberg. Notices Amer. Math. Soc. 63 (2016), no. 2, 135–140. (Coordinated by Robert V. Kohn and Yanyan Li.) Louis Nirenberg (1925–2020). Notices Amer. Math. Soc. 68 (2021), no. 6, 959–979. 1925 births 2020 deaths 20th-century American mathematicians 21st-century American mathematicians Abel Prize laureates Anglophone Quebec people Canadian emigrants to the United States New York University alumni Fellows of the American Mathematical Society Jewish American scientists Jewish Canadian scientists Members of the French Academy of Sciences Members of the United States National Academy of Sciences National Medal of Science laureates Courant Institute of Mathematical Sciences faculty PDE theorists People from Hamilton, Ontario Scientists from Ontario McGill University Faculty of Science alumni Courant Institute of Mathematical Sciences alumni 20th-century Canadian mathematicians American people of Ukrainian-Jewish descent 21st-century Canadian mathematicians Canadian people of Ukrainian-Jewish descent Members of the American Philosophical Society