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Marie-Louise Michelsohn (born October 8, 1941) is a professor of mathematics atState University of New York at Stony Brook.
Michelsohn attended theBronx High School of Science. She attended theUniversity of Chicago for her undergraduate and graduate studies, including her PhD.
She spent a year as a visiting professor atUniversity of California at San Diego. She spent a year l'Institut des Hautes Études Scientifiques outside of Paris, France. She then joined the faculty of State University of New York at Stony Brook.
Michelsohn's PhD was in the field oftopology. As of 2020, she has published twenty articles, on topics includingcomplex geometry,spin manifolds and theDirac operator, and the theory ofalgebraic cycles. Half of her work has been in collaboration withBlaine Lawson. With Lawson, she wrote a textbook onspin geometry which has become the standard reference for the field.
In her most widely-known work, published in 1982, Michelsohn investigated the notion of abalanced metric on acomplex manifold. These arehermitian metrics for which the penultimate power of the associatedKähler form is closed, i.e.
in whichω is the Kähler form andn is the complex dimension. Note that, even though it is reported in multiple sources that Michelsohn introduced balanced metrics, this is not true as these metrics had already been studied before under the namesemi-Kähler, she introduced the alternative terminology, which has now become standard as her paper is the first comprehensive investigation of such property. It is trivial to see that every Kähler metric is a balanced metric. As for Kähler metrics, the above definition of a balanced metric automatically places cohomological restrictions on the underlying manifold; byStokes' theorem, every codimension-one complex subvariety is homologically nontrivial. For instance, theCalabi-Eckmann complex manifolds do not support any balanced metrics. Michelsohn also recast the definition of a balanced metric in terms of thetorsion tensor and in terms of theDirac operator. In parallel to a work of Reese Harvey andBlaine Lawson's on Kähler metrics, Michelsohn obtained a full characterization, in terms of the cohomological theory ofcurrents, of which complex manifolds admit balanced metrics.
Balanced metrics are, in part, of interest due to their role in theStrominger system arising fromstring theory.
Michelsohn is also an accomplished middle and long-distance runner. She holds fivemasters athletics world records including through three age divisions of the2000 metres steeplechase which she has held since 2002.[1] In addition to the world records, she holds 6 more outdoorAmerican records and 10 indoor American records, running the table of all official indoor distances 800 metres and above in both the W65 and W70 divisions.[2]
