My research focuses on geometric analysis, calculus of variations, and nonlinear partial differential equations, with a primary focus on variational methods in geometric problems.
Papers
 Stability of standard double bubble under volume preserving mean curvature flow, in preparation.
 Some remarks on the existence of soap bubbles under volume preserving mean curvature flow, in preparation.
 Asymptotic behavior of polygon flow (joint with D. Glickenstein), to appear in Journal of Geometric Analysis, preprint at arXiv: math.DG /1610.03598 (2016), doi: 10.1007/s122200179940y.
 The monotonicity of eigenvalues and energy functionals under RicciHarmonic flow, Master Thesis.
Talks  (Expected) “Asymptotic behavior of polygon flows”, Special Session on Geometric Analysis and Geometric Flows, Joint Mathematics Meetings, San Diego, California, Jan. 10–13, 2018.
 “Defects in pattern formation”, Analysis Dynamics and Applications Seminar, Department of Mathematics, University of Arizona, November 7, 2017.
 “Curve shortening evolution on polygons”, Undergraduate Research Seminar, Department of Mathematics, University of Arizona, March 27, 2017.
 “Asymptotic behavior of polygon flows”, 9th Minimeeting on Differential Geometry in CIMAT, Mexico, December 12, 2016.
 “Asymptotic behavior of polygon flows”, Geometry Seminar, Arizona State University, October 28, 2016.
 “Asymptotic behavior of solutions to a polygon flow,” Analysis Dynamics and Applications Seminar, Department of Mathematics, University of Arizona, September 6, 2016.
 “Evolution of curves and polygons”, Grad Research Blitz, Department of Mathematics, University of Arizona, April 8, 2016.
 “Semidiscrete geometric flow of some graphs”, RTG Mini Conference, Department of Mathematics, University of Arizona, December 12, 2013.
Workshop and Conference Attended  Aug. 21–25, 2017, “Maryland Analysis and Geometry Atelier”, University of Maryland, College Park, MD.
 Jul. 24–28, 2017, “2017 PIMS Conference on Geometric Analysis” (in part celebrates Professor GangTian’s 60th birthday), University of British Columbia, Vancouver, Canada.
 May 15–19, 2017, “Shanks Conference on Lowdimensional Topology and Geometry” (in conjunction with the 32nd annual Shanks Lecture), Vanderbilt University, Nashville, TN.
 Apr. 28–May 2, 2017, “JDG 2017 Harvard Conference on Geometry and Topology” (in celebration of the50th anniversary of the Journal of Differential Geometry), Harvard University, Cambridge, MA.
 Apr. 22, 2017, “Junior Geometry and Topology in the Midwest Workshop”, University of WisconsinMadison, Madison, WI.
 Apr. 7–9, 2017, “Geometry and Analysis on Manifold Conference 2017”, University of CaliforniaSanta Barbara, Santa Barbara, CA.
 Mar. 31–Apr. 2, 2017, “32nd Annual Geometry Festival”, Duke University, Durham, NC.
 Feb. 11–12, 2017, “24th SCGAS Geometric Analysis Conference”, University of CaliforniaSan Diego, San Diego, CA.
 Dec. 12–14, 2016, “9th Minimeeting on Differential Geometry”, CIMAT, Guanajuato, Mexico.
 Apr. 8, 2016, “Grad Research Blitz”, University of Arizona, Tucson, AZ.
 Jan. 25–31, 2016, “23rd SCGAS Winter School and Conference”, University of CaliforniaIrvine, Orange County, CA.
 Dec. 12, 2013, “RTG Mini Conference”, University of Arizona, Tucson, AZ.
 Mar. 9–13, 2013, “Arizona Winter School”, University of Arizona, Tucson, AZ.
 Oct. 27–28, 2012, “Special Session on Geometric Analysis and Riemannian Geometry”, AMS Fall Western Sectional Meeting, Tucson, AZ.
 Aug. 3–7, 2012, “Integration Workshop 2012”, University of Arizona, Tucson, AZ.

