James Pascaleff
This webpage is out of date. I have moved to the University of Illinois at UrbanaChampaign.
The University of Texas at Austin
Department of Mathematics, RLM 8.100
2515 Speedway Stop C1200
Austin, TX 787121202
Office: RLM 11.166
Telephone: (512) 4711135
Email: jpascaleff@math.utexas.edu
(PGP public key)
I am an RTG postdoctoral fellow in the Department of Mathematics at the University of Texas at Austin. Previously, I was a student at MIT, where I received my PhD under the supervision of Denis Auroux. You can see my full CV here.
During the period 1 June–15 August 2014, I am in Bonn as a guest of the Max Planck Institute for Mathematics.
Spring 2014 teaching: Lagrangian Floer Homology (M 392C)
Research
I am interested in symplectic geometry, Floer theory and mirror symmetry. Currently I've been thinking about Floer theory for log CalabiYau surfaces, following work of GrossHackingKeel. My thesis concerns special Lagrangian torus fibrations (the Strominger–Yau–Zaslow conjecture) and the Floer cohomology of Lagrangian sections of the torus fibration in certain cases where this fibration has singularities.
Articles
 My arXiv and google scholar pages.

Floer cohomology of gequivariant Lagrangian branes.
(with YankÄ± Lekili, arXiv:1310.8609, submitted) 
On the symplectic cohomology of log Calabi–Yau surfaces.
(arXiv:1304.5298, submitted)Log CalabiYau manifolds (the complement YD of an effective anticanonical divisor D in a projective manifold Y) have a rich symplectic geometry. They are the subject of a mirror symmetry conjecture: there is a mirror variety M, and the Floer theory of YD is reflected in the algebraic geometry of M. For instance, following Gross–Hacking–Keel and Gross–Siebert, one expects to find the ring of regular functions on M sitting inside the symplectic cohomology of YD.
This article contains some results towards this conjecture in complex dimension two. There is a basis for degree zero symplectic cohomology indexed by integral points in a certain SL(2,Z)manifold (related to the GrossHackingKeel theta functions). We also include a discussion of wrapped Floer cohomology of certain Lagrangian submanifolds, and a description of the product structure in a particular case. We also show that, after enhancing the coefficient ring, the degree–zero symplectic cohomology defines a family degenerating to a singular surface obtained by gluing together several affine planes.

Floer cohomology in the mirror of the projective plane and a binodal cubic curve.
Duke Math. J., to appear. (arXiv:1109.3255, or thesis version)This paper explores an example of homological mirror symmetry, relating Lagrangian branes in a LandauGinzburg model (X^{∨}, W) to coherent sheaves on the projective plane. The LandauGinzburg model is regarded as the mirror to the pair consisting of the projective plane along with a chosen anticanonical divisor, which we take to be the union of a conic and a line. This is the binodal cubic curve of the title. The topology of X^{∨} and the superpotential W reflect this particular choice, whereas, for example, taking the anticanonical divisor to be the union of three transverse lines gives rise to the the "HoriVafa" mirror.
This LandauGinzburg model is interesting from the point of view of the StromingerYauZaslow (SYZ) picture of mirror symmetry, because the total space X^{∨} carries a special Lagrangian torus fibration with a singularity. The Lagrangian submanifolds we consider are sections of this torus fibration, meaning that they correspond to line bundles on the mirror projective plane, in line with general expectations from the SYZ picture.
The algebra structure on the Floer cohomology of these Lagrangian submanifolds is computed, and matched with the algebra structure on the homspaces of the corresponding line bundles. The tools here are symplectic techniques developed by Seidel for counting pseudoholomorphic sections of Lefschetz fibrations. One of the later sections describes the "tropical" interpretation of the result: the Lagrangian Floer cohomology has a natural basis in bijection with integral points in an affine manifold, and the algebra structure counts particular tropical curves in this manifold. In the last section we show how our computation can be used to describe the wrapped Floer cohomology of the Lagrangian submanifolds as well.
Seminars & workshops
 Graduate Geometry and Topology Current Literature Seminar: see departmental calendar (20122013 schedule)
As a graduate student, I coorganized two workshops:
 Graduate Symplectic Field Theory workshop mentored by Tobias Ekholm (August 30September 3, 2010).
 2011 MITRTG Geometry workshop with David Nadler (June 1317, 2011).
Teaching
Graduate course:
 Spring 2014: Lagrangian Floer Homology (M 392C)
Undergraduate courses taught at UT Austin:
 Fall 2013: Differential and Integral Calculus (M 408C)
 Spring 2013: Multivariable Calculus (M 408M)
 Fall 2012: Advanced Calculus for Applications I (M 427K)
 Spring 2012: Probability I (M 362K)
 Fall 2011: Sequences, Series, and Multivariable Calculus (M 408D)