Columbia University
Department of Mathematics
Recent Doctoral Theses

Knot Floer homology and categorification
Allison Gilmore, May 2011 (Advisor: P. Ozsváth)

Moduli spaces of dynamical systems on Pn
Alon Levy, May 2011 (Advisor: S. Zhang)

On using graphical calculi
Joelle Brichard, May 2011 (Advisor: M. Khovanov)

An algebraic circle method
Thibaut Pugin, May 2011 (Advisor: J. de Jong)

F-virtual abelian varieties of GL2-type and Rallis inner product formula
Chenyan Wu, May 2011 (Advisor: S. Zhang)

Bordered sutured Floer homology
Rumen Zarev, May 2011 (Advisor: P. Ozsváth)

Bounds for the spectral mean value of central values of L-functions
Qing Lu, May 2011 (Advisor: D. Goldfeld)

Lattice subdivisions and tropical oriented matroids featuring Δn-1 × Δd-1
Lindsay Piechnik, May 2011 (Advisor: D. Bayer)

Monopole Floer homology, link surgery, and odd Khovanov homology
Jonathan Bloom, May 2011 (Advisor: P. Ozsváth)

Soergel diagrammatics for dihedral groups
Ben Elias, May 2011 (Advisor: M. Khovanov)

Approximate converse theorem
Min Lee, April 2011 (Advisor: D. Goldfeld)

On Hamilton's Ricci flow and Bartnik's construction of metrics of prescribed scalar curvature
Chen-Yun Lin, May 2010 (Advisor: M.-T. Wang)

Action-Maslov homomorphism for monotone symplectic manifolds
Mark Branson, May 2010 (Advisor: D. McDuff)

The discrete Dirac operator and the discrete generalized Weierstrass representation in pseudo-Euclidean spaces
Dmitry Zakharov, May 2010 (Advisor: I. Krichever)

On the twisted Floer homology of mapping tori of periodic diffeomorphisms
Evan Fink, May 2010 (Advisor: P. Ozsváth)

Rational curves on Fano threefolds of Picard number one
Mingmin Shen, May 2010 (Advisor: A.J. de Jong)

Applications of Heegaard Floer homology to knot and link concordance
Adam Simon Levine, May 2010 (Advisor: P. Ozsváth)

Managing volatility risk: innovation of financial derivatives, stochastic models and their analytical implementation
Chenxu Li, May 2010 (Advisor: I. Karatzas)

Functional Itô calculus and applications
David-Antoine Fournie, May 2010 (Advisor: R. Cont; Sponsor: I. Karatzas)

Computations of Heegaard Floer homology: torus bundles, L-spaces, and correction terms
Thomas David Peters, May 2010 (Advisor: P. Ozsváth)

Computations and structures in sl(n)-link homology
Daniel Krasner, December 2009 (Advisor: M. Khovanov)

Convex duality in singular control -- optimal consumption choice with
intertemporal substitution and optimal investment in incomplete markets

Helena Kauppila, September 2009 (Advisors: P. Bank and I. Karatzas)

On the mean curvature flow of graphs of symplectomorphisms
of Kähler-Einstein manifolds; application to complex projective spaces

Ivana Medos, May 2009 (Advisor: M.-T. Wang)

Geometry of rational curves on algebraic varieties
Matthew DeLand, May 2009 (Advisor: A.J. de Jong)

Bessel and volatility-stabilized processes
Irina Goia, May 2009 (Advisor: I. Karatzas)

Finite atomic lattices and their relationship to resolutions of monomial ideals
Sonja Mapes, May 2009 (Advisor: D. Bayer)

Remarks on some non-linear heat flows in Kähler geometry
Donovan McFeron, May 2009 (Advisor: D. Phong)

On Λ-adic Saito-Kurokawa lifting and its application
Zhi Li, May 2009 (Advisor: E. Urban)

Probability on graphs and groups: theory and applications
Natalia Mosina, May 2009 (Advisor: I. Karatzas)

Splice diagrams. Singularity links and universal abelian covers
Helge Møller Pedersen, May 2009 (Advisor: W. Neumann)

The Hilbert-Chow morphism and the incidence divisor
Joseph Ari Ross, May 2009 (Advisor: A.J. de Jong)

Modularity of generating functions of special cycles on Shimura varieties
Wei Zhang, May 2009 (Advisor: S. Zhang)