Office: Herman Brown Hall, Room 452 Email: kk43 "at" rice "dot" edu
About
I received my Ph.D. from UCLA in 2014, where my advisor was Mario Bonk.
My primary research interests are in conformal and quasiconformal geometry, analysis of metric spaces, and applications of these techniques to the study of hyperbolic groups. Much of my work is directly related to, or motivated by, the quasiconformal geometry found on the boundary of hyperbolic groups. I am particularly interested in uniformization and rigidity problems in this area.
Geometry/Analysis Seminar, Rice University, September 2016. Talk title: Hausdorff dimension and rigidity for convex-cocompact actions on negatively-curved spaces
Undergraduate Colloquium, Rice University, September 2016. Talk title: Conformal maps and circle packings
Metric Spaces: Analysis, Embeddings into Banach Spaces, Applications, Texas A&M University, July 2016.
AMS Sectional Conference, Session on Probability and Complex Analysis inspired by Schramm and Loewner, April 2016. Talk title: Hölder domains, John domains, and conformal dimension
AMS Sectional Conference, Session on Geometric Measure Theory, March 2016. Talk title: Lower codimension-1 mass bounds in metric manifolds
Geometry Seminar, Indiana University Bloomington, March 2016. Talk title: Entropy-rigidity for hyperbolic groups
Interactions between Analysis and Geometry Reunion Conference, IPAM, December 2015. Talk title: Conformal dimension and boundaries of planar domains
Texas Geometry and Topology Conference, Rice University, November 2015. Co-organizer; Topic: Metric and conformal geometry
Analysis and Probability Seminar, University of Connecticut, October 2015. Talk title: Conformal dimension of boundaries of planar domains
Workshop on Analysis and Geometry in Metric Spaces Workshop, ICMAT, June 2015.
Rainwater Seminar, University of Washington, May 2015. Talk title: Conformal dimension of boundaries of John domains
Geometric Groups on the Gulf Conference, March 2015. Talk title: Entropy-rigidity for hyperbolic groups
Undergraduate writings
Some examples for students thinking about summer math programs
Compact widths in metric trees (with A. G. Aksoy) Function Spaces IX , 15--25, Banach Center Publ. 92, Polish Acad. Sci. Inst. Math., Warsaw, 2011 A paper coming from a summer research project at Claremont McKenna College in 2008; my first official publication!
Analytic Methods in Additive Number Theory (my undergraduate thesis) An exposition on Fourier analysis, its use in additive number theory, and a walk through Gowers' proof of Szemerédi's theorem for progressions of length four.
On the index of constant mean curvature hypersurfaces (with E. Colberg, A. M. de Jesus, and G. Silva Neto) My first dabble into differential geometry. I didn't know what a manifold was before this summer. From the 2008 Brazil IRES program.
A cubical antipodal theorem (with A. Mazel-Gee, T. Sondjaja, and F. E. Su) A combinatorial analog for cubes of a classical topological fact about spheres. From the 2007 Claremont REU program.