# Kunwoo Kim

Pohang University of Science and Technology (POSTECH)

77 Cheongam-Ro, Nam-Gu

Pohang, Gyeongbuk, Korea 37673

Email: kunwoo at postech dot ac dot kr

## 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

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

## Editorship

Editorial Board Member (since 2021 - ), Stochastic Models

## Other activites

Organizer for 2018 Probability Workshop in Gyeongju , 11th KMS Probability Workshop, 2021 Workshop on Stochastic Analysis and PDE, 2021 BK21 Four POSTECH Math Workshop, Workshop in Kinetic theory, thermodynamics and contact topology

Department Colloquium Chair, POSTECH, Fall 2016 ~ Spring 2017

Stochastic Seminar Organizer, University of Utah, Fall 2012 ~ Spring 2015

Referee for Acta Mathematica Scientia, Annals of Probability, Annals of Applied Probability, Annales de l'Institut Henri Poincaré, Discrete and Continuous Dynamical Systems Series B, Electronic Journal of Probability, Electronic Communications in Probability, Journal of the Korean Mathematical Society, Journal of Theoretical Probability, Mathematical Reviews, Nonlinearity, SIAM Journal on Mathematical Analysis, Statistics & Probability Letters, Stochastics, Stochastic Partial Differential Equations, Stochastic Processes and their Applications, Transactions of the American Mathematical Society

Parabolic Anderson model with space-time white noise