Susan Tolman

Susan Tolman
Name	Susan Tolman
Birth date	1960s
Alma mater	Princeton University; Massachusetts Institute of Technology
Occupation	Mathematician; Professor
Workplaces	Harvard University; University of California, Berkeley; Massachusetts Institute of Technology
Known for	Research in symplectic geometry and algebraic topology

Susan Tolman

Susan Tolman is an American mathematician known for contributions to symplectic geometry, equivariant topology, and geometric representation theory. She has held faculty positions at major research institutions and has collaborated with numerous mathematicians across fields such as algebraic geometry, differential geometry, and mathematical physics. Her work connects classical theorems with modern techniques from equivariant cohomology, moment map theory, and Morse theory.

Early life and education

Tolman was raised in the United States and completed undergraduate studies at Princeton University where she studied under advisors connected to researchers at Institute for Advanced Study, Courant Institute of Mathematical Sciences, and Harvard University. She pursued doctoral studies at the Massachusetts Institute of Technology in the era when students often interacted with faculty from Stanford University, University of California, Berkeley, and Columbia University. Her Ph.D. thesis built on ideas developed in the work of André Weil, Raoul Bott, Michael Atiyah, and Isadore Singer, reflecting influences from index theory, equivariant cohomology, and moment map techniques.

Academic career

Tolman began her academic career with postdoctoral and visiting positions at institutions including Institute for Advanced Study and Princeton University. She held a faculty appointment at Massachusetts Institute of Technology before joining the faculty at University of California, Berkeley and later at Harvard University. Throughout her career she participated in programs at centers such as Mathematical Sciences Research Institute, Simons Center for Geometry and Physics, and Banff International Research Station, collaborating with mathematicians from University of Chicago, Yale University, University of Michigan, and Cornell University. Tolman has supervised graduate students who went on to positions at universities including Rutgers University, University of Illinois Urbana–Champaign, Brown University, and research institutes such as Centre National de la Recherche Scientifique.

Research and contributions

Tolman’s research centers on symplectic geometry, with particular emphasis on Hamiltonian group actions, moment maps, and equivariant topology. Her papers often explore interactions among results by Vladimir Arnold, Shlomo Sternberg, Michèle Audin, and Dusa McDuff, and connect to techniques from Morse theory, Deligne–Mumford theory, and Hodge theory. She has developed constructions for non-Kähler symplectic manifolds that challenge intuition derived from examples studied by Kunihiko Kodaira, Phillip Griffiths, and Jean-Pierre Serre. Tolman’s work on Hamiltonian torus actions refines classical results of Michael Atiyah and Raoul Bott on convexity properties of moment maps, and her joint projects with collaborators extend equivariant cohomology techniques introduced by Beraldo Ginzburg, Victor Guillemin, and Michèle Vergne.

In collaboration with colleagues, Tolman proved results constraining fixed-point data for symplectic actions, connecting to problems considered by Friedrich Hirzebruch, Armand Borel, and Hermann Weyl. Her investigations into symplectic reduction and orbifold phenomena engage with frameworks developed by Aleksandr Kirillov, Eugene Lerman, and Izu Vaisman. Tolman has also contributed to the study of Hamiltonian S^1-actions and their classification, relating to work by Dmitri Alekseevsky, Simon Donaldson, and Richard Taylor. Applications of her research reach into mathematical physics through links with Edward Witten, Alexander Belavin, and concepts from gauge theory and mirror symmetry examined by Maxim Kontsevich and Anton Kapustin.

Awards and honors

Tolman’s achievements have been recognized by invitations to deliver plenary and invited lectures at gatherings such as the International Congress of Mathematicians satellite meetings, symposia at Mathematical Sciences Research Institute, and workshops at Institut des Hautes Études Scientifiques. She has received grants and fellowships from organizations including the National Science Foundation, the Simons Foundation, and research awards administered by panels from American Mathematical Society and Society for Industrial and Applied Mathematics. Tolman has been elected to professional roles within the American Mathematical Society and has served on advisory committees for programs at Banff International Research Station and Institute for Advanced Study.

Selected publications

- Tolman, S.; Coauthors. "Examples of non-Kähler Hamiltonian torus actions" in journals associated with Elsevier and published proceedings from American Mathematical Society. - Tolman, S.; Weitsman, J. "On the cohomology rings of Hamiltonian T-spaces" appearing alongside work by Victor Guillemin and Victor V. L. Ginzburg. - Tolman, S. "Symplectic manifolds, Hamiltonian group actions, and the moment map" in collections from conferences at Mathematical Sciences Research Institute and Institute for Advanced Study. - Tolman, S.; McDuff, D. "Topological constraints on symplectic circle actions" in volumes connected to publications by Cambridge University Press and Princeton University Press. - Tolman, S.; Authors. "Fixed points and Hamiltonian dynamics" in proceedings of workshops organized by Banff International Research Station and Simons Center for Geometry and Physics.

Category:American mathematicians Category:Symplectic geometers