- Ben Cooper
Ben studies invariants of Fukaya categories which yield constructions similar to those used to define quantum invariants of 3-manifolds, elliptic Hall algebras and categorifications of quantum groups. His long term objective is to construct a presentation of a categorification of the derived Hall algebra and relate this construction to the skein algebras of surfaces, contact categories and the Bordered Heegaard-Floer categories of surfaces. The short term goal is to perform an extensive study of the derived Hall algebras of Fukaya categories Ha(F(S)).
- Isabel Darcy
Isabel's research focuses on applied and computational topology. She is using topological data analysis to analyze brain fMRIs in collaboration with her graduate student Maria Gommel and Peg Nopoulos, a Professor of Psychiatry, Pediatrics & Neurology. She also uses knot theory to study locally knotted proteins and to determine the shape of DNA bound by proteins.
- Hao Fang
Hao's research interest lies in differential geometry and geometric analysis. He has been working on geometric problems related to algebraic geometry, PDE and topology. He is especially interested in Kahler and conformal geometry. Recently, he has been working on geometric properties of conic manifolds, which are special examples of incomplete manifolds.
- Mohammad Farajzadeh-Tehrani
Mohammad's research interests lie in symplectic and complex algebraic geometry. More specifically, foundational problems in symplectic topology, applications of moduli spaces of pseudoholomorphic curves, and degeneration techniques in symplectic/algebraic geometry. He is also interested in problems related to Calabi-Yau manifolds, such as Mirror Symmetry. He enjoys interdisciplinary conversations, especially if the topic can be related to geometry and topology. One of his long term goals is to bring techniques of logarithmic geometry into symplectic topology.
- Charles Frohman
Charlie is broadly interested in topology and geometry. He has made contributions to geometric group theory, minimal surface theory, gauge theory, and quantum topology.
- Keiko Kawamuro
Keiko specializes in low-dimensional topology. Generalizing Birman-Menasco's braid foliations, she with Tetsuya Ito introduced a notion of open book foliations, which is a tool to study mapping classes. With open book foliations she studies 3-dimensional contact structures, knots and links, and the relations between various positivities on mapping classes and contact/symplectic properties.
- Maggy Tomova (Associate Dean for the Natural, Mathematical, and Social Sciences)
Maggy studies 3- and 4-dimensional manifolds and submanifolds embedded in them. Heegaard splittings, decompositions of a 3-manifold into two compressions bodies, have helped elucidate the structure of these manifolds. Trisections of 4-manifolds, a new tool introduced by Gay and Kirby, allows us to similarly decompose a 4-manifold into three simple pieces. Maggy's recent research efforts have been focused on exploring ways in which our understanding of Heegaard splittings can guide us in our study of trisections.
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