Kenneth L. Baker
I earned a Ph.D. in Mathematics from the University of Texas in 2004 under John Luecke in my hometown Austin, Texas. After doing post-docs at the University of Georgia and the Georgia Institute of Technology, I joined the University of Miami in 2008.
As a Low Dimensional Topologist, I primarily study relationships among curves, surfaces, and spaces of dimensions 3 and 4 and their knotting. More specifically, I tend to focus upon problems of Dehn surgery, a transformation between two 3-manifolds based upon a knotted loop in each of them. Much of my research derives motivation from the elusive Berge Conjecture which posits a characterization of Dehn surgeries on knots in S^3 that produce knots in lens spaces.
This leads me to studies of fibrations and contact structures on 3-manifolds, Dehn surgeries on hyperbolic knots producing non-hyperbolic 3-manifolds, sliceness and concordances of knots, branched coverings, and various measures of complexity of knots and 3-manifolds. My approach often finds inspiration in a visual sense of rhythm and symmetry and insight through drawing on blackboards and crafting models on computer.
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