Assistant Professor of Mathematics
Dept. of Mathematics, Brown University
151 Thayer St. Providence, RI, 02912
mann @ math [dot] brown [dot] edu
Office: 312 Kassar
Research: Topology, geometry, geometric group theory, dynamics...
I work on actions of infinite groups on manifolds and the moduli spaces of such actions: character varieties, spaces of flat bundles or foliations, and spaces of left-invariant orders on groups.
As part of this, I've worked on the relationship between the algebraic and topological structure of diffeomorphism and homeomorphism groups, the large-scale geometry of such groups (e.g. subgroup distortion and dynamical consequences of this), and rigidity phenomenon for group actions, often arising from some geometric structure.
In simple English: I work with abstract spaces and try to understand their shape and the structure of their symmetries or how flexible or rigid they are. Sometimes the spaces are themselves collections of mathematical objects (for example, you could think about the space of all 1-variable functions, or the space of all solutions to a problem or...). This gives us new tools to understand these objects.