Welcome to the webpage of Kihoon Seong
I am a H.C. Wang assistant professor at Cornell University, working with Philippe Sosoe. Between July 2022 and June 2023, I was a postdoc at the Max Planck Institute under the supervision of Felix Otto. I received my Ph.D. at KAIST in August, 2022, under the guidance of Soonsik Kwon (KAIST) and Tadahiro Oh (University of Edinburgh). I am one of the organizers of the probability seminar at Cornell.
Email: kihoonseong@cornell.edu
Research Interests
Transport properties of Gibbs and Gaussian measures under the flow of Hamiltonian PDEs: invariance, quasi-invariance, and singularity
Construction of Gibbs measures (constructive quantum field theory)
Rough paths, singular stochastic parabolic and dispersive/hyperbolic PDEs
Papers
(with P. Sosoe) Law of large numbers for focusing Gibbs measures
(with B. Gess, P. Tsatsoulis) Low-temperature expansions for the Euclidean Φ^4_2-measure
Exponential ergodicity for the stochastic hyperbolic sine-Gordon equation on the circle
Phase transition of singular Gibbs measures for three-dimensional Schrödinger-wave system
(with F. Otto, M. Tempelmayr) Lecture notes on tree-free regularity structures, Mat. Contemp. 58 (2023), 150–196.
(with T. Robert, L. Tolomeo, Y. Wang) Focusing Gibbs measures with harmonic potential, to appear in Ann. Inst. Henri Poincaré Probab. Stat.
Invariant Gibbs dynamics for the two-dimensional Zakharov-Yukawa system, J. Funct. Anal. 286, (2024), no. 4, 81 pp
(with J. Forlano) Transport of Gaussian measures under the flow of one-dimensional fractional nonlinear Schrödinger equations, Comm. Partial Differential Equations, 47 (2022), no. 6, 1296--1337.
(with T. Oh, L. Tolomeo) A remark on Gibbs measures with log-correlated Gaussian fields, Forum Math. Sigma. 12 (2024), e50, 40 pp.
(with T. Oh) Quasi-invariant Gaussian measures for the cubic fourth order nonlinear Schrödinger equation in negative Sobolev spaces, J. Funct. Anal. 281 (2021), no. 9, 49 pp.
Low regularity a priori estimates for the fourth order cubic nonlinear Schrödinger equation, Commun. Pure Appl. Anal. 19 (2020), no. 12, 5437--5473.
Well-Posedness and Ill-Posedness for the Fourth order cubic nonlinear Schrödinger equation in negative Sobolev spaces, J. Math. Anal. Appl. 504 (2021), no. 1, 125342, 41 pp.
Other articles
Oberwolfach report: Langevin Dynamics of Lattice Yang-Mills measures: Quantum field theory and stochastic PDEs
HORIZON (webzine issued by KIAS (Korea Institute for Advanced Study)): 편미분 방정식을 이용한 양자장 이론의 건설 [1]: 무한 차원 깁스 측도와 확률 편미분방정식
Talks
2024
April 2024, Probability Seminar, University of Rochester, USA
April 2024, Analysis Seminar, Cornell University, USA
April 2024, Probability Seminar, University of Tennessee, USA
March 2024, Differential Equations Seminar, University of Michigan, USA
February 2024, Analysis and PDE Seminar, University of Massachusetts Amherst, USA
2023
December 2023, Oberwolfach, QFT and Stochastic PDEs, Germany
October 27, 2023, Probability and Statistical Physics Seminar, University of Chicago, USA
August 28, 2023, Probability seminar, Cornell University, USA
August 10, 2023, the Frontiers in Stochastic Analysis, University of Illinois Chicago, USA
June 22, 2023, AG Analysis-Probability seminar, Max Planck Institute for Mathematics, Leipzig, Germany
April 21, 2023, Oberseminar Mathematical Physics, LMU Munich, Germany
April 20, 21, 2023, (online) Conference on Probability and PDEs, KAIST, South Korea
2022
September 19, 2022, (online) Workshop on Probability and PDE, POSTECH, South Korea
September 7, 2022, New Faces Seminar, Max Planck Institute for Mathematics, Leipzig, Germany
July 27, 2022, IST, Summer School- Lightning talks by PhD students, Austria
June 17, 2022, Dispersive Day, The Maxwell Institute for Mathematical Sciences, Edinburgh, UK
June 9, 2022, Sogang University, Analysis Seminar, South Korea
February 11, 2022, University of Rochester, Analysis Seminar, USA
January 17, 2022, Max Planck Institute for Mathematics, Leipzig, Germany
2021
March 10, 2021, Online Seminars on PDEs and Harmonic Analysis, South Korea
February 8,9,16,17,18, 2021, SAARC Seminar, KAIST, Daejeon, South Korea
2020
February 13, 2020, KIAS Analysis Seminar, Seoul, South Korea
2019
December 13,14, 2019, Workshop on Harmonic Analysis Techniques for PDEs, Jeonbuk National University, South Korea
Education
Ph.D. in Mathematical Science, KAIST, 2019.08~2022.08
Visiting student to University of Edinburgh, 2020.03~2020.09
M.S. in Mathematical Science, KAIST, 2017.08~2019.08
B.A. in History, B.A. in Economics, and B.S. in Mathematics (Triple major), Sogang University, 2012.03~2017.08
Teaching
(Instructor) MATH 4710, Probability, Spring 2024, Cornell University
(Instructor) MATH 1110, Calculus I, Fall 2023, Cornell University
(Instructor) Summer School on PDEs and Randomness (6 hours tutorial session), May 22-24, Max Planck Institute
(Teaching Assistant) MAS491, Introduction to Contemporary Mathematics, Fall 2021, KAIST
(Teaching Assistant) MAS540, Real Analysis, Spring 2021, KAIST
(Teaching Assistant) MAS491, Introduction to Contemporary Mathematics, Fall 2020, KAIST
(Teaching Assistant) MAS491, Introduction to Contemporary Mathematics, Fall 2019, KAIST
(Teaching Assistant) MAS540, Real Analysis, Spring 2019, KAIST
(Teaching Assistant) MAS491, Introduction to Contemporary Mathematics, Fall 2018, KAIST
(Teaching Assistant) MAS491, Introduction to Contemporary Mathematics, Fall 2017, KAIST