Faculty

Biography

Academic Positions:

• Visiting Professor, Department of Mathematics, Princeton University (Spring 2019).
• Full Professor, Department of Mathematics, University of Rochester (2016-Now).
• Associate Professor, Department of Mathematics, University of Rochester (2009-2016).
• Research Member, MSRI, Berkeley (Spring 2016).
• Research Member, Harvard University (Spring 2016 - Postponed).
• Ruth I. Michler Fellow, Department of Mathematics, Cornell University (Spring 2015).
• Visiting Associate Professor (Spring 2013) Department of Mathematics, Princeton University.
• Research Member (Winter 2007) Geometric Evolution Equations Program, MSRI, Berkeley.
• Assistant Professor (2006-2009) Department of Mathematics, University of Rochester.
• Visiting Fellow (Winter 2005) Department of Mathematics, Princeton University.
• Research Member (Winter 2004) MSRI, Berkeley.
• Ralph Boas Assistant Professor (2002-2005) Department of Mathematics, Northwestern University.
• Research Scholar (Fall 2001) Conformal Field Theory program, IPAM, UCLA.
• Visiting Assistant Professor (2000-2002) Department of Mathematics, Cornell University.
• Teaching Assistant (1994-2000) Department of Mathematics, Michigan State University.

Memberships:

• American Mathematical Society
• Association For Women in Mathematics

Teaching Experience:

• Princeton University Spring 2013
• University of Rochester 2006-Now
• Northwestern University 2002-2006
• Cornell University 2000-2002
• Michigan State University 1994-2000

Research Overview

My research is related to the geometry and topology of manifolds with special holonomy and calibrated geometry, analysis of deformation and elliptic theory on noncompact manifolds, high dimensional complex geometry and singularity theory, supersymmetry and Calabi-Yau manifolds, special Lagrangian submanifolds and the applications in mirror symmetry, associative and coassociative submanifolds of G_2 manifolds and the connections with M-Theory.

Research Interests

• Differential geometry
• geometric analysis
• mathematical physics

Courses Offered (subject to change)

• MTH 164:  Multidimensional Calculus
• MTH 557:  Special Topics in Differential Geometry
• MTH 453:  Differential Geometry

Selected Publications

• Contact Structures on G_2-Manifolds and Spin 7-Manifolds, (with M. Firat Arikan and Hyunjoo Cho) (In preparation) (available at http://xxx.lanl.gov/abs/1207.2046)
• Remarks on Hamiltonian Structures in G_2-Geometry, (with Hyunjoo Cho and Albert J. Todd) (http://xxx.lanl.gov/abs/1309.1984,  to appear in Journal of Mathematical Physics)
• Diffeomorphisms of 7-Manifolds with Coclosed G_2-Structure, (with Albert J. Todd) (http://xxx.lanl.gov/abs/1212.2261. (Part 2 of the sequel, to appear in Jour. of Math. Physics)
• Existence of Compatible Contact Structures on $G_2$-manifolds, (with M. Firat Arikan and Hyunjoo Cho) (Asian Journal of Math., Volume 17, No. 2, (2013), pp. 321-334.)
• Diffeomorphisms of 7-Manifolds with Closed G_2-Structure, (with Hyunjoo Cho and Albert J. Todd) (http://arxiv.org/abs/1112.0832, Part 1 of the sequel, to appear in Jour. of Math. Physics)
• A Note on Closed G_2-Structures and 3-Manifolds, (with Hyunjoo Cho and Albert J. Todd) (http://xxx.lanl.gov/abs/1112.0830, to appear in Turkish Journal of Math)
•  Deformations of Asymptotically Cylindrical Special Lagrangian Submanifolds with Moving Boundary, (with Albert J. Todd) (Part 2, Proc. Gokova Geometry-Topology, (2010), 99-124, Int. Press.)
• Deformations of Asymptotically Cylindrical Special Lagrangian Submanifolds with Fixed Boundary, (with Albert J. Todd) (Part 1, Proc. Gokova Geometry-Topology, (2010), 99-124, Int. Press.)
• Mirror Duality in a Joyce Manifold, (with Selman Akbulut and Baris Efe) (Advances in Mathematics, 223, (2010), pp. 444-453)
• New Spin(7) holonomy metrics admiting G_2 holonomy reductions and M-theory/IIA dualities. (with Osvaldo Santillan) (Phys. Rev. D., 79, (2009), no. 8, 086009)