Kunwoo Kim

About me

I received my Ph.D. in May 2012 from the University of Illinois at Urbana-Champaign under the guidance of Richard Sowers. 

From July 2012 to June 2015, I was a Wylie assistant professor at the University of Utah. After that, I was an MSRI postdoctoral fellow at MSRI in Berkeley for Fall 2015 and a postdoctoral fellow at the Technion - Israel Institute of Technology in January 2016. 

I am now an associate professor (tenure-track) at POSTECH (Pohang University of Science and Technology) in Korea. 

Research Interests

My main research interest lies in probability and stochastic analysis. In particular, I am working on stochastic partial differential equations and their qualitative properties.

Publications

• On the support of solutions to nonlinear stochastic heat equations  (with B. Han and J. Yi),), 31 pages, submitted (arXiv).

• Small-ball constants, and exceptional flat points of SPDEs  (with D. Khoshnevisan and C. Mueller), 37 pages, submitted (arXiv).

• On the valleys of the stochastic heat equation (with D. Khoshnevisan and C. Mueller), Annals of Applied Probability, 34(1B), (2024), 1177-1198.

• The compact support property for solutions to the stochastic partial differential equations with colored noise (with B. Han and J. Yi), SIAM Journal on Mathematical Analysis, 55(6), (2023), 7665-7703.

• Phase Analysis for a family of Stochastic Reaction-Diffusion Equations (with D. Khoshnevisan, C. Mueller, S. Shiu), Electronic Journal of Probability, 28, (2023), 1-66. 

• Dissipation in Parabolic SPDEs II: Oscillation and decay of the solution (with D. Khoshnevisan and C. Mueller), Ann. Inst. Henri Poincaré Probab. Stat., 59(3), (2023), 1610-1641.

• Small ball estimates for the Hölder semi-norm of the stochastic heat equation (with M. Foondun and M. Joseph), Probability Theory and Related Fields, 185, (2023), no.1-2, 553-613.

• Limit theorems for time-dependent averages of nonlinear stochastic heat equations (with J. Yi), Bernoulli, 28, (2022), no.1, 214-238.

• Stochastic comparisons for stochastic heat equation  (with L. Chen), Electronic Journal of Probability, 25 (2020), 1-38. 

• Dissipation in parabolic SPDEs (with D. Khoshnevisan, C. Mueller, S. Shiu), Journal of  Statistical Physics, Volume 179 (2020), no. 118, 502-534.

• Dense blowup for parabolic SPDEs (with L. Chen, J. Huang and D. Khoshnevisan), Electronic Journal of Probability, Volume 24 (2019), no. 118, 1-33.

• Nonlinear stochastic heat equation driven by spatially colored noise: moments and intermittency (with L. Chen),  Acta Mathematica Scientia, 39(3), 2019, 645-668.

• On the large-scale structure of the tall peaks for stochastic heat equations with fractional Laplacian, Stochastic Processes and their Applications, Volume 129, Issue 6 (2019), 2207-2227.

• The dimension of the range of a transient random walk (with N. Georgiou, D. Khoshnevisan and A. Ramos), Electronic Journal of Probability, Volume 23 (2018), no. 83, 1-31.

• A macroscopic multifractal analysis of parabolic stochastic PDEs (with D. Khoshnevisan and Y. Xiao), Communications in Mathematical Physics, 360 (2018), no.1, 307-346. 

• A Boundedness Trichotomy for the Stochastic Heat Equation (with L. Chen and D. Khoshnevisan), Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 53 (2017), no. 4, 1991–2004..

• Intermittency and multifractality: A case study via parabolic stochastic PDEs (with D. Khoshnevisan and Y. Xiao), Annals of Probability, 45 (2017), no. 6A, 3697-3751. 

• On comparison principle and strict positivity of solutions to the nonlinear stochastic fractional heat equations (with L. Chen), Annales de l'Institut Henri Poincaré, Probabilités et Statistiques,  53 (2017), no. 1, 358–388..

• Dissipation and high disorder (with L. Chen, M. Cranston and D. Khoshnevisan), Annals of Probability, 45 (2017), no.1 82-99. 

• Decorrelation of total mass via energy (with L. Chen and D. Khoshnevisan), Potential Analysis, Volume 45, Issue 1 (2016), Page 157-166.

• Non-linear noise excitation of intermittent stochastic PDEs and the topology of LCA groups (with D. Khoshnevisan), Annals of Probability, Volume 43, No.4 (2015), Page 1944-1991.

• Non-linear noise excitation and intermittency under high disorder (with D. Khoshnevisan), Proceedings of the AMS, Volume 143 (2015), page 4073-4083.

• A stochastic Stefan problem (with R. Sowers and Z. Zheng), Journal of Theoretical Probability, Volume 25, Issue 4 (2012), Page 1040-1080.

• Numerical analysis of the stochastic moving boundary problem (with R. Sowers), Stochastic Analysis and Applications, Volume 30, Issue 6 (2012), Page 963-996.

• A stochastic moving boundary value problem (with C. Mueller and R. Sowers), Illinois Journal of Mathematics, Volume 54, Issue 3 (2010), Page 927-962 (2012).

Teaching

Current teaching (Spring 2024)

• Math 719 Brownian motion and Stochastic analysis 

Past Teaching 

• Graduate course: Probability Theory, Partial Differential Equations, Mathematical Statistics, Stochastic calculus and Financial Mathematics,  Statistical Inference I and II, Real Analysis I

• Undergraduate course: Theory of Ordinary Differential Equations, Introduction to Probability, Introduction to Probability and Statistics, Calculus I, Calculus for Business, A Mathematical World, Freshman Research Participation, Introduction to Analysis I and II

Awards and Honors

• TJ Park Science Fellowship for Young Professors (POSCO TJ Park Foundation), January 2017 ~ December 2018

• Itô Travel Awards (IMU), September 2015

• AMS Travel Grants (UIUC), January 2011

• Hohn-Nash Awards (UIUC), Spring 2010

• University Fellowship (UIUC), Spring 2010

• Schark Fellowship (UIUC), Spring 2009

• University Fellowship (UIUC), Spring 2008

• Conference Travel Grants (UIUC), Spring 2009, 2011