Professor in the School of Mathematics at Korea Institute for Advanced Study
Contact Information
 School of Mathematics, Korea Institute for Advanced Study, Building 1 Room 1308
85 Hoegiro, Dongdaemungu, Seoul 02455, Republic of Korea
 namgyu(at)kias(dot)re(dot)kr
 +82−2−958−2637
Employment
 Professor, KIAS, Jan. 2016 – Present
 Associate Professor, Seoul National University, Mar. 2014 – Dec. 2015
 Assistant Professor, Seoul National University, Mar. 2010 – Feb. 2014
 Olga Taussky  John Todd Instructor, Caltech, Aug. 2007 – Feb. 2010
 C.L.E. Moore Instructor, M.I.T., Jul. 2004 – Jun. 2007
Education
Awards and Honors
 Clay Liftoff Fellow, Clay Mathematics Institute, 2004
 Prize Teaching Fellow, Yale University, 2004 – 05
Preprint(s)
Publications
 (with Y. Ameur
and N. Makarov)
Rescaling Ward's identities in the random normal matrix model,
arXiv:1410.4132, 58 pp.
To appear in Constr. Approx.
 (with G. Ivanov, and A. Vasiliev)
Slit holomorphic stochastic flows and Gaussian free field,
Complex Anal. Oper. Theory 10 (2016), no. 7, 1591−1617.
 (with H. Tak)
Conformal field theory of dipolar SLE with the Dirichlet boundary condition,
Anal. Math. Phys. 3 (2013), no. 4, 333−373.
 (with N. Makarov)
Gaussian free field and conformal field theory,
Astérisque, 353 (2013), viii+136 pp.
(This monograph can be purchased from the
Société Mathématique de France or the
AMS bookstore.)
 (with Y. Ameur)
On a problem for Ward's equation with a MittagLeffler potential,
Bull. Sci. Math. 137 (2013), no. 7, 968−975.

Conformal field theory of dipolar SLE(4) with mixed boundary condition,
J. Korean Math. Soc. 50 (2013), no. 4, 899−916.
 The law of the iterated logarithm for SLE,
Int. Math. Res. Not. 2007, no. 18, Art. ID rnm060, 22 pp.
 On the quantitative boundary behavior of SLE,
Universality and renormalization,
185−198, Fields Inst. Commun. 50, Amer. Math. Soc., Providence, RI, 2007.
 Boundary behavior of SLE,
J. Amer. Math. Soc.
20 (2007), no. 1, 185−210.
 (with S. Chung and D. Kim)
Oscillatory integrals as ultradistributions,
Integral Transform. Spec. Funct. 12 (2001), no. 1, 37−52.
Selected Talks
 [03/17/17] SLE, GFF and LQG in NYC, Columbia University, NYC, USA
 [06/14/16] Recent developments in SLE, Institut MittagLeffler, Djursholm, Sweden
 [06/10/16] 2016 Stochastic Analysis Workshop, Korea University, Seoul, Korea
 [02/24/16] 4th BielefeldSNU Joint Workshop in Mathematics, Bielefeld, Germany
 [06/18/15] Geometry of Random Walks and SLE: A Birthday Conference for Greg Lawler, Isaac Newton Institute, Cambridge, UK
 [05/27/15] Analysis Seminar, KTH, Stockholm, Sweden
 [05/14/15] CMC Colloquium, Korea Institute for Advanced Study (KIAS), Seoul, Korea
 [02/26/15] 3rd BielefeldSNU Joint Workshop in Mathematics, Seoul National University, Seoul, Korea
 [04/17/14] Colloquium, Seoul National University, Seoul, Korea
 [01/28/14] Analysis Seminar, University of Bergen, Bergen, Norway
 [04/09/13] Conformal Invariance in Continuous and Discrete Systems, Simons Center for Geometry and Physics, Stony Brook, USA
 [06/01/12] 6th KMS Probability Workshop, Seoul National University, Seoul, Korea
 [04/28/12] Invited Lecture in Probability Section, Spring Meeting of the Korean Mathematical Society, Seoul, Korea
 [02/01/12] Analysis Seminar, Caltech, Pasadena, USA
 [12/12/11] Workshop on Geometric Analysis and Mathematical Physics, Institut MittagLeffler, Djursholm, Sweden
 [10/26/11] Analysis Seminar, Caltech, Pasadena, USA
 [09/06/10] 34th Conference on Stochastic Processes and Their Applications, Osaka, Japan
 [05/26/10] Conformal Maps from Probability to Physics, Ascona, Switzerland
 [03/11/10] Colloquium, Seoul National University, Seoul, Korea
 [02/10/10] Probability Seminar, UCLA, Los Angeles, USA
 [12/08/09] Reunion Conference II on Random Shapes, Institute for Pure and Applied Mathematics (IPAM), Lake Arrowhead, USA
 [12/02/09] Mathematical Physics Seminar, Caltech, Pasadena, USA
 [09/16/09] Analysis, PDE and Mathematical Physics Seminar, Michigan State University, East Lansing, USA
 [12/12/08] Reunion Conference I on Random Shapes, IPAM, Lake Arrowhead, USA
 [08/05/08] Workshop on Stochastic Loewner Evolution and Scaling Limits, Centre de recherches mathématiques, Montréal, Canada
 [10/03/07] Mathematical Physics Seminar, Caltech, Pasadena, USA
 [03/29/07] Workshop on Random Shapes, Representation Theory, and Conformal Field Theory, IPAM, Los Angeles, USA
 [05/05/06] Workshop on SLE and Loop Measures, Cornell University, Ithaca, USA
 [09/20/05] Workshop on Percolation, SLE, and Related Topics, Fields Institute, Toronto, Canada
 [06/21/05] Workshop on Geometric Methods in Analysis and Probability, Erwin Schrödinger Institute, Vienna, Austria
 [03/16/05] Workshop on Dynamics, Probability, and Conformal Invariance, Banff International Research Station, Banff, Canada
 [11/10/03] Analysis Seminar, Yale University, New Haven, USA
Conferences Organized

Random Conformal Geometry and Related Fields,
(with Tom Alberts and Fredrik Viklund),
June 18−22, 2018, KIAS, Seoul, Korea.
This conference will focus on recent developments in SchrammLoewner evolution and its connections to random Gaussian fields and classical conformal field theory from theoretical physics.
Together, these subjects have been one of the most active areas in statistical mechanics in the last fifteen years.
The mathematical theory behind random conformal geometry is rich and intimately intertwined with theoretical physics, combinatorics, operator theory, spectral theory, and many other disciplines where new connections are regularly emerging.

TokyoSeoul Conference in Mathematics  Probability Theory,
(with Shigeki Aida, JongHae Keum, and Toshitake Kohno),
December 8−9, 2017, The University of Tokyo, Japan.

Geometry, Analysis and Probability
in Honor of Peter W. Jones,
(with Christopher Bishop,
Raanan Schul,
and
Ignacio UriarteTuero),
May 8−12, 2017, KIAS, Seoul, Korea.
Over the last four decades Peter Jones has demonstrated the power of using ideas from real and harmonic analysis to solve difficult problems
in complex and functional analysis, geometric measure theory, conformal dynamics, conformal probability and geometrically based applied mathematics.
Although much of this work is highly technical, it is usually motivated by simple geometric or analytic ideas.
The conference will explore the areas listed above from the perspectives of both established experts and younger researchers,
with an emphasis on interactions between areas and the basic themes that recur in each of them.
Specific topics will include recent advances in harmonic measure, SchrammLoewner Evolutions (SLE), Gaussian Free Fields (GFF), rectifiability, and the analysis of big data.
 Workshop on Probability Theory and its Applications,
(with Panki Kim),
December 13−16, 2016, KIAS, Seoul, Korea.
 Summer School on Algebraic Geometry and Conformal Field Theory,
(with YoungHoon Kiem),
August 21−26, 2016, Korea.

Everything is Complex in Honor of Nikolai G. Makarov,
(with Ilia Binder,
Alex Poltoratski, and
Stanislav Smirnov),
March 6−11, 2016, SaasFee, Switzerland.

The 11th Hokkaido University and Seoul National University Symposium on Mathematics,
(with ShinIchiro Ei),
November 27, 2015, Seoul National University, Seoul, Korea.

Recent Progress in Random Conformal Geometry (ICM 2014 Satellite Conference),
(with Pierre Nolin and Fredrik Viklund),
August 11−12, 2014, COEX, Seoul, Korea.
The last decade has seen remarkable advancement in the understanding of planar lattice models and their scaling limits.
A wide range of ideas and techniques from probability, analysis, and physics, including the SLE process, discrete complex analysis, random planar maps, quantum gravity, and conformal field theory, come together in this field.
The workshop will bring together leading researchers in these areas to interact and to present and discuss recent advances.
Seminars at KIAS
12/13/2017 InJee Jeong (KIAS): A modification of the moment method and Plancherel random partitions
We will begin by reviewing how a certain modification of the moment method was utilized to obtain limit theorems concerning fluctuations of extreme eigenvalues of various random matrix ensembles.
Then we describe how to apply the method to analyze the asymptotic behavior of the first, second, and so on rows of stochastically decaying partitions.
This is based on joint work with Sasha Sodin.
08/16/2017 Paul Jung (KAIST): Levy Khintchine random matrices and the Poisson weighted infinite skeleton tree
We study a class of Hermitian random matrices which includes Wigner matrices, heavytailed random matrices, and sparse random matrices such as adjacency matrices of ErdosRenyi graphs with $p=1/N.$
Our matrices have real entries which are i.i.d. up to symmetry.
The distribution of entries depends on $N,$ and we require sums of rows to converge in distribution; it is then wellknown that the limit must be infinitely divisible.
We show that a limiting empirical spectral distribution (LSD) exists, and via local weak convergence of associated graphs, the LSD corresponds to the spectral measure associated to the root of a graph which is formed by connecting infinitely many Poisson weighted infinite trees using a backbone structure of special edges.
One example covered are matrices with i.i.d. entries having infinite second moments, but normalized to be in the Gaussian domain of attraction.
In this case, the LSD is a semicircle law.
08/07/2017 Sanghyun Kim (SNU): Free products in Diff($S^1$)
We prove that $(F_2 X Z) * Z$ does not embed into Diff$^{\,2}(S^1).$
Then we classify RAAGs that admit faithful smooth actions on the circle, answering a question raised in a paper of M. Kapovich.
(Joint with T. Koberda)
03/30/2017 Sanghyun Kim (SNU): Flexibility of PSL(2,R) representations
Which finitely presented groups arise as subgroups of PSL(2,R)?
The general (indiscrete) case of this question is wideopen.
We propose a class of torsionfree groups, called "flexible groups"; these groups admit uncountably many, independent, indiscrete faithful representations into PSL(2,R).
We prove a combination theorem for this class of groups.
A key underlying idea is a version of KleinMaskit combination theorem.
This is a joint work with Thomas Koberda and Mahan MJ.
08/19/2016 Kunwoo Kim (Postech): Multifractal structure of the tall peaks for stochastic PDEs
Solutions to a large family of stochastic PDEs (SPDEs) exhibit tall peaks on some small regions and this phenomenon is called intermittency.
In this talk, we consider the geometric structure of the tall peaks for two types of SPDEs: intermittent SPDEs (SPDEs with nonlinear noise) and nonintermittent SPDEs (SPDEs with additive noise).
Using the BarlowTaylor macroscopic Hausdorff dimension, we will show that there are infinitely many length scales in the tall peaks for both types of SPDEs.
This is based on an ongoing work with Davar Khoshnevisan and Yimin Xiao.
08/03/2016 Jose Luis Romero (University of Vienna): Gabor analysis and sampling and interpolation
Gabor systems are structured function systems consisting of timefrequency translates of a window function. I will discuss some of the central problems in Gabor analysis and progress towards them.
In particular, I will present recent results on stability of the spanning properties of such systems under deformations of the underlying set of timefrequency nodes.
The deformations that we consider are in general nonlinear and, in particular, include the standard jitter error and linear deformations of phase space.
The proofs involve a characterization of Gabor frames and Gabor Riesz sequences in the style of Beurling's characterization of sets of sampling for bandlimited functions ('without inequalities').
07/25/2016 Insuk Seo (UC Berkeley): Limit theory and large deviation principle for interacting Brownian motions
Consider a system of interacting Brownian motions.
Because of the complex nature of interactions among particles, it is difficult to obtain the typical or atypical behavior of a single particle.
Varadhan and his coworkers have extensively studied such a problem for interacting particle systems on lattice.
In the first part of the presentation, we review the theory proposed by Varadhan et al., which is now called the hydrodynamic limit theory.
In the second part or the presentation, we explain our recent generalization of this theory to a system of interacting Brownian motions and discuss the universality of the results.
07/18/2016 Kijung Lee (Ajou University): Modeling: random interruptions to Heat diffusion
In the inhomogeneous heat equation
$$u_t(t,x) = \Delta u(t,x)+f(t,x),$$
the term $f$ models the interruptions to the heat diffusion along time and on space locations.
Especially, the effect of $f$ in time direction is more troublesome and the regularity of $u$ is subject to the regularity of $f.$
In this talk we discuss a type of modeling of $f$ in the form $N_t(\omega)g(t,x),$
where $N$ is a random noise process which can be whiter than the white noise.
We also discuss a regularity relation between $N, g$ and $u.$
06/27/2016 Seonhee Lim (SNU): Asymptotics of heat kernel in Riemannian manifolds of negative curvature
We will show the asymptotics of the heat kernel $p(t,x,y)$ as $t$ goes to infinity for Riemannian manifolds of negative curvature.
We will explain how to use dynamics of the geodesic flow and certain Gibbs measures. This is a joint work with F. Ledrappier.
03/22/2016 Kyeonghun Kim (Korea Univ.): An introduction to $L_p$theory of stochastic PDEs
Stochastic partial differential equations (SPDEs) are differential equations which include the effects of random forces and environments.
The theory of SPDE was started in 1970s, and $L_p$theory of SPDE was first introduced by Krylov in 1994.
Since then, $L_p$theory has become one of main approaches to study the regularity of solutions to SPDEs.
In this talk, I will give a short description on SPDEs and introduce classical $L_p$theory of secondorder SPDEs.
I will also introduce recent results on SPDEs having nonlocal operators.
03/16/2016 Panki Kim (SNU): Factorization of harmonic functions and Martin boundary for nonlocal operators in metric measure spaces
In this talk we consider a large class of nonlocal operators on metric measure spaces.
We first show that a uniform and scale invariant boundary Harnack principle holds.
Then we study Martin boundaries corresponding to nonlocal operators.
If infinity is accessible from an open set D, then there is only one Martin boundary point of D associated with it, and this point is minimal.
Under suitable further assumptions there is only one Martin boundary point associated with infinity, and that this point is minimal if and only if infinity is accessible from D.
This is based on joint works with Renming Song and Zoran Vondracek.
03/14/2016 Ji Oon Lee (KAIST): Comparison Methods in Random Matrix Theory
The local eigenvalue statistics of a large class of random matrices exhibits the same limiting behaviour, and such property is known as the universality.
A typical strategy to prove the universality is to first compute the local statistics for the simplest case, usually the Gaussian case, and compare the given model with the simple model.
In this talk, I will explain the comparison methods and how we can apply them to prove universality for complicated models such as deformed Wigner matrices or sample covariance matrices with general population.
03/02/2016 Sanghyun Kim (SNU): No finite index subgroups of mapping class groups act faithfully on the circle by $C^2$ diffeomorphisms
One intriguing direction of research in surface theory is the analogy between mapping class groups and higher rank lattices.
However, current understanding of finite index subgroups of mapping class groups are still rudimentary.
We prove the result in the title, which was originally asked by Farb, and which is analogous to Ghys and BurgerMonod theorem about obstructions of higher rank lattice actions on the circle.
(Joint work with Hyungryul Baik and Thomas Koberda)
Previous Teaching
Teaching at SNU
 3341.202, Mathematical Analysis 2, Fall 2014; Fall 2015
 033.002, Calculus II, Fall 2014; Fall 2015
 3341.201, Mathematical Analysis 1, Spring 2014; Spring 2015
 3341.348, Functions of Several Variables, Spring 2015
 881.425, Real Variables, Spring 2011; Spring 2012; Spring 2014
 3341.721A, Topics in SchrammLoewner Evolutions, Fall 2012
 881.313, Set Theory and Mathematical Logic, Spring 2011; Spring 2012
 881.004, Complex Variables, Fall 2011
 3341.721A, Topics in Conformal Field Theory, Fall 2010
 3341.503, Real Analysis, Spring 2010
 010.101, Calculus I, Spring 2010
Teaching at Caltech
 Lecturer, Ma 192a, Topics in Conformal Field Theory, Fall 2009
 Lecturer, Ma/ACM 144a, Probability, Winter 2008; Fall 2009
 Lecturer, Ma 191c, Topics in SchrammLoewner Evolutions, Spring 2009
 Lecturer, Ma/ACM 142b, Ordinary and Partial Differential Equations, Winter 2009
 Lecturer, Ma/ACM 144b, Probability, Spring 2008
Teaching at MIT
 Recitation, 18.02/02A, Calculus of Functions of Several Variables, Fall 2004; Winter 2007
 Lecturer, 18.440, Probability and Random Variables, Spring 2005; Fall 2006
 Lecturer, 18.125, Measure and Integration, Spring 2006
 Recitation, 18.01A/02A, Calculus of Functions of One Variable / Calculus of Functions of Several Variables, Fall 2005
Teaching at Yale
 Lecturer, math115a, Calculus of Functions of One Variable II, Fall 2003
 Lecturer, math112a, Calculus of Functions of One Variable I, Fall 2002
 Lecturer, math120a/120b, Calculus of Functions of Several Variables, Spring 1999; Fall 1999; Spring 2001
