Columbia University
Department of Mathematics
Recent Doctoral Theses

The parity of analytic ranks among quadratic twists of elliptic curves over number fields
Nava Balsam, May 2015 (Advisor: D. Goldfeld)

A proof of Looijenga's conjecture via integral-affine geometry
Philip Engel, May 2015 (Advisor: R. Friedman)

Singular solutions to the Monge-Ampère equation
Connor Mooney, May 2015 (Advisor: O. Savin)

Quantum algebras and cyclic quiver varieties
Andrei Negut, May 2015 (Advisor: A. Okounkov)

Partial differential equations and variational approaches to constant scalar curvature metrics in Kähler geometry
Daniel Rubin, May 2015 (Advisor: D. Phong)

A Minkowski-type inequality for hypersurfaces in the Reissner-Nordstrom-anti-de Sitter manifold
Zhuhai Wang, May 2015 (Advisor: M.-T. Wang)

On a spectral bound for congruence subgroup families in SL(3,Z)
Timothy Heath, February 2015 (Advisor: D. Goldfeld)

Equivariant Gromov-Witten theory of GKM orbifolds
Zhengyu Zong, February 2015 (Advisor: C.-C. M. Liu)

Three-manifold mutations detected by Heegaard Floer homology
Corrin Clarkson, May 2014 (Advisor: R. Lipshitz)

Canonical metrics in Sasakian geometry
Tristan Collins, May 2014 (Advisor: D. Phong)

Bordered Heegaard Floer homology and graph manifolds
Jonathan Hanselman, May 2014 (Advisor: R. Lipshitz)

Pro-p-Iwahori-Hecke algebras in the mod-p local Langlands program
Karol Kozioł, May 2014 (Advisor: R. Ollivier)

Constant scalar curvature of toric fibrations
Thomas Nyberg, May 2014 (Advisor: D. Phong)

Rational normal curves on complete intersections
Xuanyu Pan, May 2014 (Advisor: J. de Jong)

Demazure-Lusztig operators and metaplectic Whittaker functions on covers of the general linear group
Anna Puskas, May 2014 (Advisors: D. Goldfeld/G. Chinta)

On a triply-graded generalization of Khovanov homology
Krzysztof Putyra, May 2014 (Advisor: M. Khovanov)

Self-duality and singularities in the Yang-Mills flow
Alex Waldron, May 2014 (Advisor: P. Daskalopoulos)

A Spacetime Alexandrov theorem
Ye-Kai Wang, May 2014 (Advisor: M.-T. Wang)

Multiple Dirichlet series for affine Weyl groups
Ian Whitehead, May 2014 (Advisor: D. Goldfeld)

Towards a definition of Shimura curves in positive characteristics
Jie Xia, May 2014 (Advisor: J. de Jong)

The arithmetic and geometry of genus four curves
Hang Xue, May 2014 (Advisor: S. Zhang)

A geometric construction of a Calabi quasimorphism on projective space
Andre Rubens Franca Carneiro, May 2013 (Advisor: D. McDuff)

p-adic Heights of Heegner points on Shimura curves
Daniel Disegni, May 2013 (Advisor: S. Zhang)

Odd symmetric functions and categorification
Alexander Ellis, May 2013 (Advisor: M. Khovanov)

Properties of Hamiltonian torus actions on closed symplectic manifolds
Andrew Fanoe, May 2013 (Advisor: D. McDuff)

Singular theta lifts and near-central special values of Rankin-Selberg L-functions
Luis Emilio Garcia Martinez, May 2013 (Advisor: S. Zhang)

Localization and Heegaard Floer homology
Kristen Hendricks, May 2013 (Advisor: P. Ozsvath/R. Lipshitz)

Del Pezzo surfaces with irregularity and intersection numbers on quotients in geometric invariant theory
Zachary Maddock, May 2013 (Advisor: J. de Jong)

Hopfological algebra
You Qi, May 2013 (Advisor: M. Khovanov)

Purity of the stratification by Newton polygons and Frobenius-periodic vector bundles
Yanhong Yang, May 2013 (Advisor: J. de Jong)

Local regularity of the complex Monge-Ampere equation
Yu Wang, May 2013 (Advisor: D. Phong)

Sato-Tate problem for GL(3)
Fan Zhou, May 2013 (Advisor: D. Goldfeld)

Limiting properties of certain geometric flows in complex geometry
Adam Jacob, May 2012 (Advisor: D. Phong)

Arithmetic inner product formula for unitary groups
Yifeng Liu, May 2012 (Advisor: S. Zhang)

Forbidden substructures in graphs and trigraphs, and related coloring problems
Irena Penev, May 2012 (Advisor: M. Chudnovsky)

Bordered Heegaard Floer homology, satellites, and decategorification
Tsvetelina Petkova, May 2012 (Advisor: P. Ozsváth)

On Fourier-Mukai type functors
Alice Rizzardo, May 2012 (Advisor: J. de Jong)

The asymptotic cone of Teichmüller space: thickness and divergence
Harold Sultan, May 2012 (Advisor: W. Neumann)

Eigenvarieties and twisted eigenvarieties
Zhengyu Xiang, May 2012 (Advisor: E. Urban)

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)