About me
I am a Ph.D. Candidate (4th year) at Cornell University. I was a student of William P. Thurston who recently passed away. Here you can see some of my memories about him. 

I am currently staying at UC Davis as a visiting graduate student under the guidance of Joel Hass. 

Collaborators
Lucien Clavier (Cornell)

Sebastian Hurtado (UC Berkeley) 

Eric Samperton (UC Davis)

Research Area 

My main research areas are Low-dimensional Topology, Geometric Group Theory and Complex Dynamical Systems. In particular, I am interested in the group actions on the circle with dense invariant laminations. Main motivation is the following theorem of Thurston (which is a simplified statement of the universal circle theorem).

This theorem was generalized to the case of essential laminations by Calegari-Dunfiled. One of the most outstanding questions is the converse of this statement. Namely, if a 3-manifold group acts faithfully on the circle with a pair of transverse dense invariant laminations, can one find an essential lamination associated with it? Another rather ambitious question is how to characterize various 3-manifold groups purely in terms of invariant laminations? Recently, I found an answer to an analogous question in one lower dimension: a torsion-free discrete group acting faithfully on the circle by orientation-preserving homeomorphisms is conjugated into PSL(2,R) if and only if it admits a pants-like collection of three pairwise transverse very-full invariant laminations. I am trying to generalize the result to 3-manifold groups.

I am also interested in the limit sets of Kleinian groups. You can get a lot of beautiful pictures of limit sets with Opti. I am studying about Teichmuller theorey and hyperbolic structures on 3-manifolds as well. 

For more detail, please see my research statement. 

The following is one of my favorite quotes. 

Teaching
2011 Fall MATH 2230: Theoretical Linear Algebra and Calculus

2011 Spring MATH 6510: Algebraic Topology 1
2010 Fall  MATH 3560: Groups and Geometry

2010 Fall Olivetti Club

Talks

2013 May. 21. A Characterization of Mobius Group Actions via Invariant Laminations (Mathematics Seminar, KIAS) [Abstract]

2013 Apr. 21. Groups acting on the circle with dense invariant laminations (USTARS, Purdue University)

2013 Apr. 9. Thurston's view on the space of complex polynomials (Geometry/Topology Seminar, UC Davis) [Abstract][Slides]

2013 Mar. 8. Groups acting on the circle with dense invariant laminations (Informal Geometry Seminar, Stanford)

2013 Mar. 5. Groups acting on the circle with dense invariant laminations (Geometry/Topology Seminar, UC Davis) [Abstract]

2013 Jan. 18. Groups acting on the circle with dense invariant laminations (Seminar COOL, IHP, Paris) [Abstract]

2013 Jan. 15. Groups acting on the circle with dense invariant laminations (Séminaires systèmes dynamiques et géométrie, Université d'Angers) [Abstract]

2011 Nov.15. Universal Circle (Cornell Olivetti club) [Poster] 

2011 Nov.12. Space of closed subgroups of PSL(2, C) in Hausdorff topology (Binghamton graduate conference)

2011 Apr.16. Thurston's topological characterization of rational maps (37th Annual New York Regional Graduate Mathematics Conference)
2010 Nov.16  Fenchel-Nielsen coordinates of Teichmuller space (Cornell Olivetti club) [Poster] [Slides]
2010 Nov.9 Grid graphs and Lattice surfaces Part2 (Cornell seminar in Analysis) [Slides]

2010 Nov.6 Veech groups of Translation surfaces (Binghamton graduate conference)

2010 Nov.4 Grid graphs and Lattice surfaces Part1 (Cornell seminar in Analysis)

Talks in Kleinian group seminar at Cornell 
2011 Nov11. The space of 1-generator closed subgroups of PSL(2,C) and its boundary, part 2 (joint talk with Lucien Clavier)

2011 Nov.4. The space of 1-generator closed subgroups of PSL(2,C) and its boundary, part 1 (joint talk with Lucien Clavier)

2011 Oct.14. Boundary groups of QF (the space of quasi-fuchsian groups) 

2011 Sep.30. More precise algorithm to detect discrete groups
2011 Sep.23. Finding discrete groups using the centers of isometric circles
2011 Sep.16. Geometry of Kleinian manifolds corresponding to once punctured torus groups, Part 2
2011 Sep.2. Geometry of Kleinian manifolds corresponding to once punctured torus groups, Part 1
2011 Aug.26. Discreteness Criterion in OPTi and Jorgensen's parametrization 

Talks in Berstein seminar at Cornell 

Conferences (Presented)
2011 Nov. 12-13. Graduate Conference in Algebra and Topology, Binghamton University, http://www.math.binghamton.edu/grads/gradconf/index.html
2011 Apr. 15-16. 37th Annual New York Regional Graduate Mathematics Conference, http://students.syr.edu/mgo/MGOConference.html
2010 Nov. 6-7. Graduate Conference in Algebra and Topology, Binghamton University, http://www.math.binghamton.edu/grads/gradconf/index.html

Conferences (Attended)
2012 Jul. 1-21, PCMI Summer School in Geometric Group Theory, PCMI. 

2012 May. 5-9, Topology festival, Cornell University. 

2012 Apr. 5-8, G^3 conference, Pensacola beach http://www.math.uiuc.edu/~mineyev/ggg/
2012 Mar. 3-4, The Redbud Topology Conference, Oklahoma State University http://www.math.okstate.edu/~jjohnson/redbud/
2011 Sep. AMS Sectional Meeting, Cornell University.
2011 Apr. 2-3. Ninth Annual Graduate Student Topology and Geometry Conference, Michigan State Univ http://math.msu.edu/related/gstgc/
2011 Mar. 17-18. FPSG '11 Finitely Presented Solvable Groups Conference, The CIity Collge of New York http://rio.sci.ccny.cuny.edu/caissny.org/fpsg2011.php
2011 Mar. 24-27. The Triennial Ahlfors-Bers Colloquium http://math.rice.edu/Conferences/ABC2011/
2010 Oct. 9-11. Approaches to Group Theory (Ken Brown's birthday conference), Cornell http://www.math.cornell.edu/~approachtogroups/
2010 Sep. 24-26. Geometry and Analysis of Riemann Surfaces and Their Moduli (Scott Wolpert's birthday conference), University of Maryland, http://mypage.iu.edu/~cjudge/service/scottfest/

2010 Jun. 26 - Jul. 17. Geometry, Topology, and Dynamics of Character Varieties, IMS, Singapore

2010 May 7-10. Topology Festival, Cornell

2010 Apr. 11-13. Stochastic Analysis and Mathematical Physics (A conference in honor of Len Gross)

2012 Oct. 22-26. Lipschitz metric on Teichmuller space, AIM, Palo Alto, USA (Link)

2010 Aug 2-4. Workshop for Young Mathematicians in Korea, KAIST

2010 Apr. 10. Mathematics and Design Workshop, Cornell University, Ithaca, USA 

2010 Jan. 7-8. Invitation to geometry for undergraduate students, KIAS, Seoul, Korea 

2. Go to your webmail https://recursion.math.cornell.edu/cgi-bin/openwebmail/openwebmail.pl

3. Click the webdick button on the menu bar. You can create the index.html file by going into the html directory.  Then enter index.html in TargetName, and click NewFile.  GO back into the html directory and you should see the file. You can enter content by clicking on the file's EditHTML link. Further directions could be found at http://www.math.cornell.edu/ADMIN/Computers/webdisk.html

4. To have a link to your webpage on your page in the department's website (In my case, http://www.math.cornell.edu/People/Grads/baik.html ), you should contact Mikki.