서울대학교 수리과학부

1. Education

• • University of California, Los Angeles
  • Ph.D. Applied Mathematics, 1996 ​
  • KAIST M.S. Applied Mathematics, 1988 ​
  • Seoul National University B.A. Mathematics, 1986
    

2. 주요 연구 분야

• • Numerical Analysis
  • Image Processing Computational Fluid Dynamics
  • Scientific Computing
  • Deep Learning
  • Computer Vision
  • Mathematical Modeling
  • Numerical Algorithm

Academic positions

09/2021– Associate professor, Seoul National University, South Korea

09/2017– now Assistant professor, Seoul National University, South Korea

04/2017–08/2017 Postdoctoral fellow, Ruhr-Universität Bochum, Germany

04/2014–04/2017 Postdoctoral fellow, Universität Münster, Germany

Research  interests

Combinatorics: combinatorial Laplace operators, matroids complexes, simplicial networks 

Applied algebraic topology: discrete harmonic spaces, topological data analysis

Commutative Algebra: face ring of simplicial complexes, homological algebra



Research interests:

Representation theory of Lie (super)algebras and their quantum groups

Algebraic combinatorics related to representation theory

Education 

• B.S. : Seoul National University, February 1994

• M.S. : Seoul National University, February 1996  

• Ph.D. : Seoul National University, August 2001

Employment

• Full-time Instructor, Korea Air Force Academy (July 1998-June 2000)

• Research Fellow, Korea Institute for Advanced Study (September 2001-March 2003)

• Assistant Professor, Dept. of Math., University of Seoul (April 2003-March 2007)

• Associate Professor, Dept. of Math., University of Seoul (April 2007-March 2012)

• Professor, Dept. of Math., University of Seoul (April 2012-August 2012)

• Professor, Dept. of Math., Sungkyunkwan University (September 2012-August 2015)

• Professor, Dept. of Math., Seoul National University (September 2015- )

Awards

• Teaching Excellence Awards in University of Seoul (2006, 2009)

• Research Excellence Awards in University of Seoul (2006, 2007, 2008, 2009)

• Distinguished Paper Award in the Korean Mathematical Society (2011)

• Teaching Excellence Awards in College of Natural Sciences, Seoul National University (2017, Spring) 

• Teaching Excellence Awards in College of Natural Sciences, Seoul National University (2017, Fall) 

Grants

• 2005-2007 Co-I KRF-2005-070-C00004 (National Research Foundation of Korea)

• 2008-2011 Co-I KRF-2008-314-C00004 (National Research Foundation of Korea)

• 2011-2015 PI NRF-2011-0006735 (National Research Foundation of Korea)

• 2015-2020 PI SSTF-BA1501-01 (Samsung Science and Technology Foundation)

• 2019-2023 2019R1A2C1084833  (National Research Foundation of Korea) 

• 2020-2027 2020R1A5A1016126 (National Research Foundation of Korea) SRC



Employment

Associate Professor, Seoul National University, 2015-present

Assistant Professor, Seoul National University, 2011-2015

Research Fellow, Korea Institute for Advanced Study, 2010-2011

L.E.Dickson Instructor, University of Chicago, 2007-2010

Education

Ph.D. in Mathematics, Princeton University, 2001-2007

Thesis Advisor: Prof. J ́anos Koll ́ar

B.A. in Mathematics, Seoul National University, 1995-1999

Education



Education:

2004 Ph.D in Mathematics (Probability)
Department of Mathematics, University of Washington, USA

1998 M. A. in Mathematics (Probability) 
Department of Mathematics, Korea University, South Korea

1996 B. A. in Mathematics (with summa cum laude)
Department of Mathematics, Korea University, South Korea

Employment:

Since 2013.9: Professor in Seoul National University.

2008.10-2013.8: Associate Professor in Seoul National University.

2006.9-2008.9: Assistant Professor in Seoul National University.

2004.8-2006.8 : J. L. Doob Research Assistant Professor in University of Illinois at Urbana-Champaign

Professional Societies:

2024-2025: Chair of Committee for Conferences on Stochastic Processes for Bernoulli Society          

2018-2020: Chairman of Probability and Statistics Committee, Korean Mathematical Society          

2013.7-Present:  Editor for Journal of Korean Mathematical Society          

2016-2025: Spokesperson in International Research Training Group 2235 (Seoul)          

2020-2027: Committee for Conferences on Stochastic Processes for Bernoulli Society        

2022-2025: Member of the East Asian and Pacific Regional Committee of the Bernoulli Society






Employment

• • Department of Mathematical Sciences, Seoul National University, Seoul, Korea

  • Assistant Professor, September 2017 - present

• • Department of Mathematical Sciences, Worcester Polytechnic Institute, Worcester, MA, USA

  • Postdoctoral Scholar, August 2015 - July 2017

  • - Mentor: Stephan Sturm

Education

• • Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

  • Ph.D. in Mathematics, 2015

  • - Advisor : Jonathan Goodman

  • Department of Mathematical Sciences, Seoul National University, Seoul, Korea

  • B.S. in Mathematics, 2009



Thesis Directed

Ph. D

Master 

Employment 

• Assistant Professor, Department of Mathematical Sciences, Seoul National University, August 2023- Present 

• CMC Fellow (Hyo Chul Myung Assistant Professor), June E Huh Center for Mathematical Challenges, Korea Institute for Advanced Study, July 2022-July 2023 (Independent Researcher supported by HCMC)

• Project Research Fellow, Department of Mathematics, Korea Institute for Advanced Study, September 2021-June 2022(Group leader: Prof. Nam-Gyu Kang)

Education 

• Ph.D., Mathematics, Seoul National University, August 2021 (Advisors: Prof. Nam-Gyu Kang,  Prof. Panki Kim)

• Bielefeld-Seoul International Research Training Group 2235 on the graduate exchange program, September 2016-August 2021 (Mentor: Prof. Gernot Akemann) 

Fellowships and Grants 

• POSCO Science Fellowship,  PI, POSCO TJ Park Foundation, 35 million Korean won per year, March 2023- February 2025

• KIAS Individual Grant,  PI, Korea Institute for Advanced Study via the Center for Mathematical Challenges (SP083201), 35 million Korean won per year (cf. 20 million Korean won for conference organization), July 2022- July 2023 

• KIAS Student Fellow,  Korea Institute of Advanced Study (KIAS), January 2017- August 2021 

Honours and Awards 

• 14th POSCO Science Fellowship, POSCO TJ Park Foundation, 2022

• KIAS Academic Award, Korea Institute for Advanced Study, 2022

• Excellent Teaching Assistant, Faculty of Liberal Education-Seoul National University, 2017

Academic Positions

Research Interests : vertex algebras and integrable systems.

Education :

2008-2013 Ph.D. in Mathematics, Massachusetts Institute of Technology (thesis advisor : Victor Kac)

2004-2007 B.S. in Mathematics, Seoul National University

Awards and Honors:

2016-present : National Research Foundation of Korea (NRF), Junior research fellowship

2008-2013 : Samsung Scholarship

2007 : Valedictorian at graduation ceremony of Seoul National University

2007 : President Prize, Seoul National University

2006-2007 : SK scholarship

2005-2007 : Honor Prize, college of Natural Science in Seoul National University

Curriculum Vitae   (Extended version)

• 02. 2023 -             : Vice President for Academic Affairs,  Seoul National University
• 09. 2020 -             : Director,  Mathematical Sciences Division for Future Human Resources Development
• 06. 2020 - 06. 2022 : Associate Dean for Academic Affairs,  College of Natural Sciences, SNU 
• 12. 2017 - 12. 2019 : Chair, Department of Mathematical Sciences, SNU 
• 06. 2016 - 06. 2017 : Visiting Professor, Department of Mathematics, University of Connecticut 
• 06. 2014 - 06. 2016 : Associate Dean for Research Affairs,  College of Natural Sciences, SNU 
• 03. 2012 -             : Professor, Seoul National University 
• 03. 2009 - 02. 2012 : Associate Professor, Seoul National University 
• 03. 2003 - 02. 2009 : Associate Professor, Sejong University
• 11. 2002 - 03. 2003 : Research Fellow, KIAS
• 06. 2001 - 06. 2002 : Visiting Research Scholar,  Ohio State University
• 03. 1999 - 06. 2001 : Research Fellow, KIAS
• 03. 1994 - 02. 1999 : Ph.D. Mathematics(Number Theory), Seoul National University 
• 03. 1992 - 02. 1994 : B.S. Mathematics, Seoul National University 

Awards

• 04. 2008 : KMS(The Korean Mathematical Society) Excellent Research Paper Award 
• 06. 2008 : Scientists of the Month (Korea Science and Engineering Foundation)

I was a research associate at Imperial College London for Jan 2021 - Feb 2024 under the supervision of professor Richard Thomas, and a research fellow at KIAS (Korea Institute for Advanced Study) for Sep 2017 - Jan 2021. I got my PhD at KAIST (Korea Advanced Institute of Science and Technology) under the supervision of professor Bumsig Kim.

I was visiting Fields Institute for Jun-Dec 2019 as a postdoc under the supervision of professor David Favero and UC Berkeley for Jan-May 2018 as a visiting scholar hosted by professor Alexander Givental.

My research interest is intersection theory, Gromov-Witten theory, quasimap theory and Donaldson-Thomas theory

I am an assistant professor at Seoul National University. Before that, I was a C.L.E. Moore instructor at MIT. I got a  Ph.D.  degree at the University of Wisconsin-Madison under the supervision of Shaoming Guo. My research interests lie in Fourier analysis. Especially, I am interested in restriction estimates, decoupling inequalities, and their applications to number theory and geometric measure theory.

Feel free to contact me if you are interested in working with me. Here are some lists of articles relevant to my research area.

Decouplings: Article 1, Article 2  

Restriction and Kakeya: Article 1, Article 2, Article 3, Article 4, Article 5, Article 6  

Research

Geometric Langlands Theory and Supersymmetric Gauge Theory

• Geometric Langlands Twists of N=4 Gauge Theory from Derived Algebraic Geometry (joint with Chris Elliott)

• A Physical Origin for Singular Support Conditions in Geometric Langlands Theory (joint with Chris Elliott)

• Quantum Geometric Langlands Categories from N = 4 Super Yang-Mills Theory (joint with Chris Elliott)

Aspects of Supergravity and Superstring Theories

• Dispersionless Integrable Hierarchy via Kodaira-Spencer Gravity (joint with Weiqiang He, Si Li, and Xinxing Tang)

• Twisted S-duality (joint with Surya Raghavendran)

Developments of BV Formalism

• Degenerate Classical Field Theories and Boundary Theories (joint with Dylan Butson)

• Asymptotic Freedom in the BV Formalism (joint with Chris Elliott and Brian Williams)

Career

Assistant Professor, Seoul National University, March 2022 - present

Assistant Professor, Sungkyunkwan University, September 2019 - February 2022

Postdoctoral Researcher, Universität Heidelberg, September 2012 - August 2019
Mentor: Anna Wienhard

Research Member, Mathematical Sciences Research Institute, March - May 2015
MSRI program: Dynamics on moduli spaces of geometric structures

Postdoctoral Researcher, Seoul National University, April - August 2012
Mentor: Seonhee Lim

Visiting Researcher, Institut Henri Poincaré, January - March 2012
IHP program: Geometry and analysis of surface group representations

Postdoctoral Researcher, Seoul National University, September 2010 - December 2011
Mentor: Seonhee Lim

Visiting Student, University of Melbourne, February - August 2009
Advisor: Craig D. Hodgson

Mandatory Military Service, Korea, December 2001 - January 2004

Education 

PhD, Mathematics, KAIST, March 2006 - August 2010 
Advisor: Suhyoung Choi 
Thesis Title: Projective deformations of hyperbolic Coxeter 3-orbifolds 

MSc, Mathematics, KAIST, March 2002 - February 2006 
Advisor: Gyo Taek Jin 
Thesis Title: A study on trisecants of spatial graphs 

BSc, Mathematics (Summa cum laude), KAIST, March 1998 - February 2002

Research Interests 

Geometry and Topology: Geometric structures on manifolds and orbifolds, Representation varieties, 
Hyperbolic and real projective geometry, Discrete subgroups of Lie groups, Coxeter groups, Knot theory

Published or Accepted papers 

Convex cocompactness for Coxeter groups
with Jeffrey Danciger, François Guéritaud, Fanny Kassel and Ludovic Marquis,  to appear in Journal of the European Mathematical Society

Cusped Borel Anosov representations with positivity
with Tengren Zhang,  Geometriae Dedicata 218 (2024), article number 54 

Hitchin components for orbifolds
with Daniele Alessandrini and Florent Schaffhauser,  Journal of the European Mathematical Society 25 (2023), 1285-1347

Deformation spaces of Coxeter truncation polytopes
with Suhyoung Choi and Ludovic Marquis,  Journal of the London Mathematical Society 106 (2022), 3822-3864

A small closed convex projective 4-manifold via Dehn filling
with Ludovic Marquis and Stefano Riolo,  Publicacions Matemàtiques 66 (2022), 369-403

Convex projective generalized Dehn filling
with Suhyoung Choi and Ludovic Marquis,  Annales Scientifiques de l'École Normale Supérieure 53 (2020), 217-266

Anti-de Sitter strictly GHC-regular groups which are not lattices
with Ludovic Marquis,  Transactions of the American Mathematical Society 372 (2019), 153-186

Pappus theorem, Schwartz representations and Anosov representations
with Thierry Barbot and Viviane Pardini Valério,  Annales de l'Institut Fourier 68 (2018), 2697-2741

Convex projective structures on nonhyperbolic three-manifolds
with Samuel A. Ballas and Jeffrey Danciger,  Geometry & Topology 22 (2018), 1593-1646

Collar lemma for Hitchin representations
with Tengren Zhang,  Geometry & Topology 21 (2017), 2243-2280

Projective deformations of weakly orderable hyperbolic Coxeter orbifolds
with Suhyoung Choi,  Geometry & Topology 19 (2015), 1777-1828

Projective deformations of hyperbolic Coxeter 3-orbifolds
with Suhyoung Choi and Craig D. Hodgson,  Geometriae Dedicata 159 (2012), 125-167



Education:

• Ph.D. in mathematics, Sep. '93 - Sep. '98, Courant Institute, New York University, New York, NY,USA ( Academic Advisor: Luis Caffarelli)

• B.A. in Mathematics, Mar. '88 - Feb. '91, Seoul National University, Seoul, Korea

Professional Experience:

• Sep., 2011-Present, Professor, Derpartment of Mathematical Sciences, Seoul National University, Korea

• Dec., 2020-Present, Chairman, Derpartment of Mathematical Sciences, Seoul National University, Korea

• Sep. 2009-August. 2020, Affiliate Professor, Korea Institute for Advanced Study (KIAS), Korea

• April. 2006-Aug. 2011, Associate Professor, Derpartment of Mathematical Sciences, Seoul National University, Korea

• Fall, 2005, Adjunct Professor, Derpartment of Mathematics, Yale University, USA

• Spring, 2005, Adjunct Professor, Derpartment of Mathematics, University of Texas at Austin, USA

• Dec. 2001-Mar. 2006, Assistant Professor, Derpartment of Mathematics, Seoul National University, Korea

• Fall , 2000 -Fall 2001, Lecturer, Derpartment of Mathematics, University of Texas at Austin, USA

• Spring, 1999-Spring 200, Visiting Assistant Professor, Derpartment of Mathematics, University of California at Irvine, USA

Honors:

• Fellow of The Korean Academy of Science and Technology (2022 -Present)

• Invited Section Lecturer, ICM 2014, Seoul, Korea

• Scientists of the Month, National Research Foundation of Korea, September, 2012

• Excellent Research Paper Award, The Korean Mathematical Society, April, 2008

• Research Award, School of Natural Science, Seoul Nation University, June, 2006



Research area

Harmonic analysis and partial differential equations



Publications

-(with T.Lam and M. Shimozono) On the coproduct in affine Schubert calculus, arXiv:1906.08118. LMS Lecture note series 473, Facets of algebraic geometry (Fulton 80 volume). 2 (2022)115--146.

- Linear relations on LLT polynomials and their k-Schur positivity for k=2, Journal of Algebraic Combinatorics, 53 (2021), 973-990

- (with T. Lam and M. Shimozono) Back stable Schubert calculus, Compositio Math. 157 (2021), 883-962.

- Positivity of Cylindric skew Schur functions, Journal of Combinatorial Theory, Series A, 168 (2019), 26-49.

- Combinatorial description of the cohomology of the affine flag variety, Transactions of the American Mathematical Society, 371 (2019), 4029-4057

- Chern class of Schubert cells in the flag manifold and related algebras, Journal of Algebraic Combinatorics, 2017, https://doi.org/10.1007/s10801-017-0773-3

- Combinatorial description of the cohomology of the affine flag variety, Extended abstract, Proceedings of FPSAC 2016, http://www.lix.polytechnique.fr/~pilaud/FPSAC16/final_83.

- Pieri rule for the affine flag variety, Extended abstract, Proceedings of FPSAC 2015, http://fpsac2015.sciencesconf.org/70975.

- Pieri rule for the affine flag variety, Advances in Mathematics, 304 (2017), 266-284.

- (with A. Barvinok and I. Novik) Explicit constructions of centrally symmetric k-neighborly polytopes and large strictly antipodal sets,

Discrete & Computational Geometry, 49 (2013), 429--443.

- (with A. Barvinok and I. Novik) Centrally symmetric polytopes with many faces,

Israel Journal of Mathematics, Israel Journal of Mathematics, 195 (2013), 457--472.

- (with A. Barvinok and I. Novik) Neighborliness of the symmetric moment curve, Mathematika, 59 (2013), 223--249.

Preprints

-(with Jaeseong Oh and Brendon Rhoades) Two conjectures for Macdonald polynomials: The stretching symmetry and Haglund's conjecture, arXiv:2203.04590

-(with Sue Kyong Y. Soh) Explicit formulas for e-positivity of chromatic quasisymmetric functions, arXiv:2201.13080.

-(with T. Lam and M. Shimozono) Back stable K-theory Schubert calculus, arXiv:2018.10202.

-Crystal structure on King tableaux and semistandard oscillating tableaux, arXiv:1910.04459.

- Local neighborliness of the symmetric moment curve, arXiv:1102.5143.

EDUCATION



Research Interest : homogeneous dynamics and number theory, geometric group theory

Seminar organized : Dynamics & Number Theory and Topological Data Analysis 

Upcoming and recent conference organized: 



Research topics

• Dynamics of singular and critical data
  
• Stability, instability and singularity formation
  
• Inviscid limit. 

Employment

Education

Grants

• National Research Foundation of Korea, 2022.03–2027.02
  
• New Faculty Startup Fund, 2021.04–2023.03
  
• Samsung Science and Technology Foundation, 2020.12–2025.11
  
• National Research Foundation of Korea, 2019.06–2022.08
  
• Science Fellowship of POSCO TJ Park Foundation, 2019.01–2021.12
  
• KIAS Individual Grant, 2017.11–2021.02

Publications:

• Simple labeled graph C*-algebras are associated to disagreeable labeled spaces, J. Math. Anal. App., 461(2018), 1391-1403. (with G. H. Park).
• Purely infinite labeled graph C*-algebras, Ergod. Th. & Dynam. Sys. to appear (with E. J. Kang and G. H. Park).
• Finite simple labeled graph C*-algebras of Cantor minimal subshifts, J. Math. Anal. App. 446(2017), 395-410 (with E. J. Kang, S. H. Kim, and G. H. Park).
• Finite groups acting on higher dimensional noncommutative tori, J. Funct. Anal. 268(2015), 473-499 (with J. H. Lee).
• AF labeled graph C*-algebras, J. Funct. Anal. 266(2014), no. 4, 2153-2173 (with E. J. Kang and S. H. Kim).
• The structure of gauge-invariant ideals of labelled graph C*-algebras, J. Funct. Anal. 262(2012), no. 4, 1759-1780 (with S. H. Kim and G. H. Park)
• On simple labelled graph C*-algebras, J. Math. Anal. App. 386(2012), 631-640 (with S. H. Kim).
• Topological entropy and the AF core of a graph C*-algebra, J. Math. Anal. App. 354(2009), 664-673 (with G. H. Park).
• Cancellation for inclusions of C*-algebras of finite depth, Indiana Univ. Math. J. 58(2009), 1537-1564 (with N. C. Phillips, H. Osaka, and T. Teruya). 
  
• On the stability of a fixed point algebra C*^gamma of a gauge action on a graph C*-algebra, J. Korean Math. Soc. 46(2009), 657-673
• Saturated actions by finite dimensional Hopf *-algebras on C*-algebras, Intern. J. Math. 19(2008), 125-144 (with G. H. Park).
• Topological entropy and AF subalgebras of graph C*-algebras, Proc. Amer. Math. Soc. 134(2006), 215-228. (with G. H. Park)
• Dynamical systems in graph C*-algebras, Intern. J. Math. 16(2005), 999-1015 (with G. H. Park).
• Topological entropy for the canonical completely positive maps on graph C*-algebras, Bull. Australian Math. Soc. 70(2004), 101-116 (with G. H. Park).
• Stable rank and real rank of graph C*-algebras, Operator Algebras and Applications, Advanced Studies in Pure Mathematics 38, pp. 97-106, Mathematical Society of Japan 2003.
• Graph C*-algebras and topological entropy, Trends in Mathematics, vol 6, no.2, 41-49, Information Center for Mathematical Sciences, December 2003.
• Real rank of C*-algebras associated with graphs, J. Australian Math. Soc. 77(2004),141-147.
• Real rank of graph C*-algebras, Operator Algebras and Mathematical Physics, Constanta(Romania), 203-208, The Theta Foundation, 2003.
• Graph C*-algebras with real rank zero, J. Funct. Anal. 188(2002), 216-226 (with G. H. Park).
• Minimal index of a C*-crossed product by a finite group, Proc. Amer. Math. Soc. 129(2001), 2031-2038 (with G. H. Park).
• Stable rank and real rank of graph C*-algebras, Pacific J. Math. 200(2001), 331-343 (with G. H. Park and D. Y. Shin).
• Extremally rich graph C*-algebras, Comm. Korean Math. Soc. 15(2000), 159-171.
• Extremal richness of the crossed products of simple C*-algebras by finite groups, J. Australian Math. Soc. 64(1998), 285-301 (with H. Osaka).
• Exponential rank of C*-algebras, Bull. Korean Math. Soc. 34(1997),395-401 (with G. H. Park).
• Purely infinite simple C*-crossed products II, Canad. Math. Bull. 39(1996),203-210 (with K. Kodaka and H. Osaka).
• Purely infinite simple C*-crossed products, Proc. Amer. Math. Soc. 123(1995), 3075-3078.
• Projections in some simple C*-crossed products, Proc. Amer. Math. Soc. 123(1995), 3317-3321 (with G. H. Park).
• Topologically free actions and purely infinite C*-crossed products, Bull. Korean Math. Soc. 31(1994), 167-172.
• Full hereditary C*-subalgebras of crossed products, Bull. Korean Math. Soc. 30(1993), 193-199.
• On purely infinite C*-algebras, Proc. Amer. Math. Soc. 117(1993), 679-682 (with S. G. Lee).
• Purely infinite C*-algebras and full hereditary C*-subalgebras, Ph. D. Thesis, Seoul National University, February 1992.





Research 

Research interests : 
Applied Analysis, Collective Dynamics, Hyperbolic Conservation Laws, Kinetic Theory.


CV - Publications - Talks 

Professional Activities 

Editorial Board 

Networks and Heterogeneous Media (NHM) (Editor in Chief from 2017 January) 



Bulletin of the Korean Mathematical Society (Managing editor from 2019 January) 



Kinetic and Related Models (KRM) (Associate editor) 



Ricerche di Matematica (Associate editor from 2016 April ) 



SN Partial Differential Equations and Applications (Associate editor from 2020 January) 

• Ordinary Differential Equations and Practice, 
  
  Zoom link

Education



Employment

Education



Papers and preprints

• Surfaces, braids, Stokes matrices, and points on spheres.[arXiv]
  With Yu-Wei Fan. Submitted.
• Surface group representations in SL2(C) with finite mapping class orbits.[arXiv]
  With Indranil Biswas, Subhojoy Gupta, and Mahan Mj. Geometry & Topology, to appear.
• The rank two p-curvature conjecture on generic curves.[arXiv]
  With Anand Patel and Ananth Shankar. Advances in Mathematics, to appear. 
• Arithmetic of curves on moduli of local systems.[arXiv]
  Algebra Number Theory, 14(10), 2575-2605 (2020).
• Nonlinear descent on moduli of local systems.[arXiv]
  Israel Journal of Mathematics, 240, 935-1004 (2020).
• Global geometry on moduli of local systems for surfaces with boundary.[arXiv]
  Compositio Mathematica, 156(8), 1517-1559 (2020). 
• The uncertainty principle and a generalization of a theorem of Tao.
  With Ram M. Murty. Linear Algebra and its Applications, 437(1), 214-220 (2012).
• Another Proof of the Infinitude of the Prime Numbers.
  American Mathematical Monthly, 117(2), 181 (2010).

Markov Processes

• singular diffusions (unbounded drifts, reflection problems on rough state spaces, in particular on subsets of infinite dimensional state spaces and moving domains)
• uniqueness problems (pathwise uniqueness, (sub-)martingale problems)
• path regularity (non-explosion, recurrence)
• existence of standard and Hunt processes associated to strongly continuous semigroups on L²-spaces

Symmetric, non-symmetric and generalized Dirichlet forms

• general development

Analysis

• elliptic and parabolic regularity for singular partial differential equations
• analytic and non-analytic strongly continuous semigroups and operator theory

Tools and computations 

Conley-Zehnder indices in prequantization bundles (also known as Boothby-Wang bundles)

This pdf-file contains some details on how to compute the Conley-Zehnder/Maslov index of periodic Reeb orbits in a prequantization bundle. We work out a simple relation between this index and the first Chern class of the symplectic manifold (the quotient by the circle action). This is often helpful in symplectic homology computations.CZ_index_BW_bundle.pdf

Some explicit computations

This pdf-file contains some explicit computations of symplectic/contact homology of some well-known manifolds.SHnames.pdf

Notes and slides 

Talk/tutorial on TDA: mapper and persistent homology 

Slides for two talks on TDA in Busan: TDA_tutorial2019busan1.pdf TDA_tutorial2019busan2.pdf

Lecture on singularity theory and exotic spheres

Notes for a lecture given at the 1st International Undergraduate Mathematics Summer School, Peking University 2018:singularity.pdf

Talk on Sasakian geometry and symplectic topology

Notes for a talk given at the conference ``Differential Geometry, Geometric Analysis and PDEs'', Academica Sinica, Taipei 2018: sasaki_einstein.pdf

Slides from a talk in Cologne (September 2014)

PDF-file from my talk in Cologne: surface_cologne.pdf

Slides from a talk at the astronomy colloquium at SNU (May 2021)

PDF-file from my talk: symplectic_celestial.pdf

Slides from a zoom talk given at Shanghai Jiao Tong University (March 2022)

PDF-file from my talk: holo_convex2022_3.pdf