Mobius II by M.C.Escher   

 My main research interests are in low dimensional topology and geometry, and gauge and Floer theoretic invariants for them. More specifically, my study focuses on the TQFT aspects of Ozsváth and Szabó's Heegaard Floer theory in dimensions (3+1). These include the study of knot concordance group, and the interplay between 4-manifolds and their boudary 3-manifolds

Research papers:
Irreducible 3-manifolds that cannot be obtanined by 0-surgery on a knot
   with Matt Hedden, Min Hoon Kim, and Tom Mark, in preparation, 2018.
Spherical 3-manifolds bounding rational homology balls
   with Dong Heon Choe, in preparation, 2018.
On intersection forms of definite 4-manifolds bounded by a rational homology 3-sphere
   with Dong Heon Choe, Topology and its Applications 238 (2018), arxiv:1704.04419
An infinite-rank summand of knots with trivial Alexander polynomial
   with Min Hoon Kim, to appear in Journal of Symplectic Geometry, arxiv:1604.04037, 2016.
Some computations and applications of Heegaard Floer correction terms
   MSU Thesis, 2014.
On independence of iterated Whitehead doubles in the knot concordance group
   Journal of Knot Theory and Its Ramifications 27 (2018) no. 1, arxiv:1311.2050