Marco Gualtieri

Marco Gualtieri is a leading Canadian mathematician who received his B.Sc. from McGill and his D. Phil in 2004 from Oxford University. After spending several years (2005-2008) as a Moore instructor at MIT, he accepted the offer of Assistant Professor with the Department of Mathematics at the University of Toronto. In 2013, he was promoted to Associate Professor.

In the 11 years since his doctorate, Gualtieri has published 16 substantial papers in leading journals (including a single author paper of nearly 50 pages in the very prestigious Annals of Mathematics). Gualtieri is considered a world leader in differential geometry, and specifically, generalized complex geometry.

In 2001, Oxford mathematician Nigel Hitchin discovered the concept of generalized complex geometry, a type of structure which includes both usual complex geometry and symplectic geometry as special cases, and which allows one to interpolate between the two. As Hitchin’s student, Gualtieri picked up on this important new development and soon became its leading exponent, developing it and expanding greatly its scope. In a series of brilliant papers, he has given new methods for constructing generalized complex manifolds and has introduced a new theory of generalized Kahler manifolds.

His work contains many beautiful theorems, such as the local classification of generalized complex structures, the reduction theory for generalized complex and generalized Kahler structures, and specific existence and non-existence theorems for these structures. Experts speak of him as “a brilliant geometer”, “one of the best and most promising differential geometers in the world”, and say that his work is “deep and profound”.

Gualtieri’s work goes beyond pure mathematics. He is compared to MIT mathematician Isadore Singer in his ability to unite mathematics and physics. Much of Gualtieri’s work has application to the geometric study of quantum field theory. Edward Witten of the Institute for Advanced Study, considered by some to be the top physicist of our times, speaks of Gualtieri as being very influential amongst physicists.

Gualtieri’s work has been recognized by numerous prestigious prizes including the Lichnerowicz Prize in 2010, the Andre Aisenstadt Prize in 2012, the Coxeter-James Prize of the Canadian Mathematical Society in 2014 and the Simons Fellowship in 2015.

With all these achievements to date, leading mathematicians feel that even greater things are yet to come. Gualtieri is seen as a person who is constantly expanding his intellectual horizons and exploring new areas, such as in his recent paper on Stokes groupoids. Moreover, he is an excellent communicator and so a popular speaker at conferences and seminars, explaining seemingly complicated concepts in a simple and down-to-earth way.

Full of new and exciting ideas, Gualtieri conducts his research in close collaboration with a large group of students and postdoctoral researchers, establishing his ability to inspire students to do outstanding research. To facilitate this, he has created the Geometric Structures Laboratory, a collaborative research lab at the University of Toronto which focuses on projects at the interface between geometry and physics, with a special focus on generalized complex geometry, singular differential equations, and quantum field theory.