I work on algebraic aspects of symplectic geometry and number theory. This is a list of my papers. A chronological list is available on the arXiv. Here they are grouped by theme.
You might also be interested in my CV.
Three most recent papers
A. Representations of finite groups on modules over K-theory. 2015 preprint. Has an appendix by Akhil Mathew.
B. with Vivek Shende and Eric Zaslow, Legendrian knots and constructible sheaves. 2014 preprint.
You are welcome to read the project description for my 2015-2018 NSF grant, which builds on Paper B.
C. with Akshay Venkatesh, Functoriality, Smith theory, and the Brauer homomorphism. to appear in Annals of Math. The published version leaves out the material on the "small c" c-group, and the case-by-case construction of sigma-dual homomorphisms.
Applications of Smith theory
(Paper C. is also an application of Smith theory.)
D. with Robert Lipshitz, Noncommutative Hodge-to-de Rham spectral sequence and the Heegard Floer homology of double covers. To appear in the Journal of the European Mathematical Society.
E. Smith theory and geometric Hecke algebras. 2011 preprint.
F. A topological approach to induction theorems in Springer theory. Published in Representation Theory, 2009. Link to published version.
Mirror symmetry papers
Most of this work is explained in the project description for my 2012-2015 NSF grant.
G. with Nicolò Sibilla and Eric Zaslow, Ribbon graphs and mirror symmetry. Published in Selecta Mathemematica, 2014. Link to published version.
H. with Helge Ruddat, Nicolò Sibilla, and Eric Zaslow, Skeleta of affine hypersurfaces. Published in Geometry & Topology, 2014. Link to published version.
Paper H. proves the conjecture of a 2011 preprint with Eric Zaslow, Polytopes and Skeleta, which was never submitted.
I. with Bohan Fang, Chiu-Chu Melissa Liu, and Eric Zaslow, A categorification of Morelli's theorem. Published in Inventiones Mathematicae, 2011. Link to published version
J. with Bohan Fang, Chiu-Chu Melissa Liu, and Eric Zaslow, T-duality and homological mirror symmetry of toric varieties. Published in Advances in Math, 2012. Link to published version.
K. Morse theory and toric vector bundles. To appear in Transactions of the American Mathematical Society.
L. with Bohan Fang, Chiu-Chu Melissa Liu, and Eric Zaslow, The coherent constructible correspondence for toric Deligne-Mumford stacks. Published in IMRN, 2014. Link to published version.
M. with Bohan Fang, Chiu-Chu Melissa Liu, and Eric Zaslow, The coherent-constructible correspondence and Fourier-Mukai transforms. Published in Acta Mathematica Sinica, 2011. Link to published version
N. with Bohan Fang, Chiu-Chu Melissa Liu, and Eric Zaslow, The coherent constructible correspondence and homological mirror symmetry for toric varieties. A survey article, published in Geometry and Analysis Vol. 2, 2010.
O. Staggered t-structures on toric varieties. Published in J. Algebra 2010. Link to published version.
P. with Pramod Achar, Purity and decomposition theorems for staggered sheaves. Published in JIMJ, 2012. Link to published version.
Q. with Pramod Achar, Baric structures on triangulated categories and coherent sheaves. Published in IMRN, 2010. Link to published version.
Sheaves of categories
(Paper G. is also about sheaves of categories.)
R. Stacks similar to the stack of perverse sheaves. Published in Transactions of the AMS, 2010. Link to published version.
S. Exit paths and constructible stacks. Published in Compositio Mathematica, 2009. Link to published version.
Remarks on the nonequivariant coherent-constructible correspondence for toric varieties, 2010 preprint. Outdated after this paper of Scherotzke and Sibilla.
with Eric Zaslow, Polytopes and Skeleta, 2011 preprint. The conjecture has been proven in Paper H. We still have plans for the "Kashiwara-Schapira sheaf."
with Davesh Maulik, Constructible functions and Lagrangian cycles on orbifolds. 2011 preprint. No excuse really, we are just behind.