Email: cbj5212@gmail.com    bchoi@postech.ac.kr

Curriculum Vitae 

Research Interests

Geometric analysis:  differential geometry, PDE, calculus of variation and gradient flow 

Employment

Assistant professor at POSTECH, South Korea (2021.07 - ) 

CMC fellow at Korea Institute for Advanced Study, South Korea (2021.05 - 2021.06) 

Postdoctoral research fellow at University of Toronto, Canada (2019.08 - 2021.04)

Education

PhD in Mathematics, Columbia University, New York, USA (2011.09 - 2019.05)

- Adviser: Panagiota Daskalopoulos

- Military leave of absence (2013.06- 2016.08)

BS in Mathematical Science, KAIST, Daejeon, South Korea (2007.02 - 2011.02)

- Summa Cum Laude

Publications/accepted for publication

• Classification of bubble-sheet ovals in R^4, with P. Daskalopoulos, W. Du, R. Haslhofer, and N. Sesum.  (2022)
  to appear in Geom. Topol. [journal][arXiv]

• Uniqueness of ancient solutions to Gauss curvature flow asymptotic to a cylinder, with K. Choi and P. Daskalopoulos,
  to appear in J. Diff. Geom. [journal][arXiv]

• Finite-dimensional leading order dynamics for the fast diffusion equation near extinction, with C. Seis. (2023)
  Discrete Contin. Dyn. Syst.  [journal][arXiv]

• Asymptotics near extinction for nonlinear fast diffusion on a bounded domain, with R. McCann and C. Seis,
  Arch. Ration. Mech. Anal. (ARMA) (2023) [journal][arXiv]

• A note on blowup limits in 3d Ricci flow, with R. Haslhofer,
  Math. Res. Lett. (2023) [journal][arXiv]

• Hitting estimates on Einstein manifolds and applications, with R. Haslhofer,
  J. reine angew. Math. (Crelle's journal).(2022) [journal][arXiv]

• Inverse mean curvature flow with singularities, with P.-K. Hung,
  IMRN (2022) [journal][arXiv]

• Convergence of Gauss curvature flows to translating solitons, with K. Choi and P. Daskalopoulos,
  Adv. Math. (2022) [journal][arXiv]

• Heat flow on time-dependent manifolds, with J. Gao, R. Haslhofer, and D. Sigal,
  J. Geom. Anal. (2022) [journal][arXiv]

• Evolution of non-compact hypersurfaces by inverse mean curvature, with P. Daskalopoulos,
  Duke Math. J. (2021) [journal][arXiv]

• Convergence of Curve Shortening Flow to Translating Soliton, with K. Choi and P. Daskalopoulos,
  Amer. J. Math.(2021) [journal][arXiv]

• Type II singularities on complete non-compact Yamabe flow, with P. Daskalopoulos and J. King,
  J. reine angew. Math. (Crelle's journal).(2021) [journal][arXiv]

• A note on the selfsimilarity of limit flows, with R. Haslhofer and O. Hershkovits,
  Proc. Amer. Math. Soc.(2021) [journal][arXiv]

• Diffusion of biological organisms; Fickian and Fokker-Planck type diffusions, with Y.-J. Kim,
  SIAM J. Appl. Math.(2019) [journal]

• Yamabe flow: steady solitons and type II singularities, with P. Daskalopoulos,
  Nonlinear Anal.(2018) [journal][arXiv]

Preprints

• Thom's gradient conjecture for nonlinear evolution equations, with P.-K. Hung. (2024)
  - This is major improvement over the previous preprint 'Asymptotics for slowly converging evolution equations' with P.-K. Hung.

• Monge-Ampère equations with right-hand sides of polynomial growth,  with K. Choi and S. Kim. (2024)
  - a part of this result was shown in the 2021 preprint by the same authors.

• Continuous family of surfaces translating by powers of Gauss curvature, with K. Choi and S. Kim. (2024)
  - a part of this result was shown in the 2021 preprint by the same authors.

• Asymptotics for slowly converging evolution equations, with P.-K. Hung. (2023)

• On existence of hypersurfaces translating by powers of Gauss curvature. (2022)

• Ricci limit flows and weak solutions, with R. Haslhofer. (2021)

• Translating surfaces under flows by sub-affine-critical powers of Gauss curvature, with K. Choi and S. Kim.  (2021)

• Multi-D fast diffusion equation via diffusive scaling of generalized Carleman kinetic equation, with K.-A. Lee. (2015)

Grants, honors, and awards

• Y-KAST member, Korean Academy of Science and Technology (2023-)

• Samsung Science and Technology Foundation Grant P.I. (2023-)

• NRF Science Research Center CM2LA Participating Researcher (RS-2023-00219980) (2023-)

• National Research Foundation of Korea  (NRF-2022R1C1C1013511) (2022-2027)

• KIAS associate member (2022-)

• Sangsan Young Mathematician Award, Korean Mathematical Society (2021)

• POSCO Science Fellow, TJ Park Foundation (2022-2023)

• Basic Science Research Institute, POSTECH (NRF-2021R1A6A1A10042944)  (2021-2022)

• Columbia Faculty Fellow, Columbia University (2011-2019)

• Samsung Scholarship for doctoral study, Samsung Scholarship Foundation (2011- 2019)

• Presidential Science Scholarship from the Korean President, Korea Student Aid Foundation (2007 - 2011)

Notes

Parabolic Krylov-Safonov Harnack Inequality 

- This is based on a talk I gave in graduate student geometric analysis seminar, Columbia University, Fall 2017. Most of the proof ideas and outlines are from the note of former colleague M. Connor.