My research centers around mathematical gauge theory and its applications to low-dimensional topology. I received my PhD in 2015 at UCLA, advised by Ciprian Manolescu. Before joining the faculty at the University of Miami, I was an NSF postdoctoral fellow, spending time at Brandeis University with Danny Ruberman, and at the Simons Center for Geometry and Physics in Stony Brook with Simon Donaldson.
My research is part of a program which began in the early 1980s with the work of Donaldson, who used instantons, solutions to certain non-linear PDE, to uncover surprising results about the topology of smooth 4-manifolds. To better understand Donaldsons invariants of 4-manifolds obtained by cut-and-paste methods along 3-manifolds, in the late 1980s Floer introduced instanton homology, an invariant associated to certain 3-manifolds. There are now many versions of Floer homology, some of them even defined for knots and links. Much of my research goes towards understanding these invariants, with a view towards concrete topological applications in dimensions 3 and 4.
In my free time, I enjoy spending time with my family, listening to music, playing my guitar, and watching movies.
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