New!
The microlocal Riemann-Hilbert correspondence for complex contact manifolds
+ Laurent Côté, Christopher Kuo, David Nadler
On Fukaya categories and prequantization bundles
+ Tatsuki Kuwagaki, Adrian Petr
Quiver Hecke algebras from Floer homology in Coulomb branches
+ Mina Aganagic, Ivan Danilenko, Yixuan Li, Peng Zhou
+ Tobias Ekholm
The Hamiltonian reduction of hypertoric mirror symmetry
+ Michael McBreen, Peng Zhou
Skein valued cluster transformation in enumerative geometry of Legendrian mutation
+ Matthias Scharitzer
On the Hochschild cohomology of Tamarkin categories
+ Christopher Kuo, Bingyu Zhang
Adjoints, wrapping, and morphisms at infinity
+ Tatsuki Kuwagaki
Symplectic geometry:
Skein-valued enumeration of holomorphic curves with boundary
+ Tobias Ekholm
+ Tobias Ekholm
Skein recursion for holomorphic curves and invariants of the unknot
+ Tobias Ekholm
Colored HOMFLYPT counts holomorphic curves
+ Tobias Ekholm
Quantum mirrors of cubic planar graph Legendrians
+ Matthias Scharitzer
Localization of the wrapped Fukaya category
Covariantly functorial wrapped Floer theory on Liouville sectors
+ Sheel Ganatra, John Pardon
Publ. math. IHES 131 (2020), 73-200
Sectorial descent for wrapped Fukaya categories
+ Sheel Ganatra, John Pardon
Journal of the American Mathematical Society 37 (2024), 499-635
DOI: https://doi.org/10.1090/jams/1035
Microlocal Morse theory of wrapped Fukaya categories
+ Sheel Ganatra, John Pardon
Annals of Math (2) 199(3) (May 2024), 943-1042.
DOI: 10.4007/annals.2024.199.3.1
Microlocal sheaf theory
Microlocal category for Weinstein manifolds via h-principle
Pub. RIMS 57.3-4 (Kashiwara 70) (2021)
Sheaf quantization in Weinstein symplectic manifolds
+ David Nadler
+ Laurent Côté, Christopher Kuo, David Nadler
Mirror Symmetry
Mirror symmetry for very affine hypersurfaces
+ Benjamin Gammage
Acta Mathematica 229.2 (2022), 287-346
Calabi-Yau structures on topological Fukaya categories
+ Alex Takeda
Homological mirror symmetry at large volume
+ Benjamin Gammage
Tunisian Journal of Mathematics 5.1 (2023), 31-71
Toric mirror symmetry revisited
Comptes Rendus Mathématique 360 (2022), 751-759
Microsheaves and Hitchin systems
Microsheaves from Hitchin fibers via Floer theory
Invariance of microsheaves on stable Higgs bundles
+ David Nadler
Legendrian knots
Legendrian knots and constructible sheaves
+ David Treumann, Eric Zaslow
Inventiones Mathematicae 207.3 (2017), 1031-1133
+ Lenhard Ng, Daniel Rutherford, Steven Sivek, Eric Zaslow.
Geometry and Topology 24.5 (2020), 2149-2286
The cardinality of the augmentation category
+ Lenhard Ng, Daniel Rutherford, Steven Sivek,
Mathematical Research Letters 24.6 (2017), 1845-1874.
Conormal torus and usual knots
The conormal torus is a complete knot invariant
Forum of Mathematics, Pi, 7 (2019), e6
A complete knot invariant from contact homology
+ Lenhard Ng, Tobias Ekholm,
Inventiones mathematicae 211 (2018), 1149-1200.
Cluster varieties
Cluster varieties from Legendrian knots
+ David Treumann, Harold Williams, Eric Zaslow.
Duke Mathematical Journal 168.15 (2019), 2801-2871.
On the combinatorics of exact Lagrangian surfaces
+ David Treumann, Harold Williams.
Assorted notes and sketches
Arboreal singularities from Lefschetz fibrations
in Proceedings of the Gökova Geometry-Topology Conferences, 2018/2019
(International Press, 2021), 90-104.
An algebraic approach to the algebraic Weinstein conjecture
in Symplectic geometry - A Festschrift in honour of Claude Viterbo’s 60th birthday,
Journal of fixed point theory and applications 24, Article number: 25 (2022)
Algebraic geometry:
Character varieties.
The weights of the tautological classes of the character varieties
IMRN (2016). (DOI: 10.1093/imrn/rnv363)
Higher discriminants and applications.
Higher discriminants and the topology of algebraic maps
+ Luca Migliorini,
Algebraic Geometry 5 (1) (2018) 114–130.
A support theorem for Hilbert schemes of planar curves
+ Luca Migliorini,
Journal of the European Mathematical Society 15.6 (2013), 2353--2367.
A support theorem for Hilbert schemes of planar curves, II
+ Luca Migliorini, Filippo Viviani
Compositio Mathematica 157.4 (2021), 835--882.
Equidistribution on the space of rank two vector bundles over the projective line
+ Jacob Tsimerman
Duke Mathematical Journal 166.18 (2017), 3461-3504.
Notes on equidistribution and Brill-Noether asymptotics
Deletion-contraction triangles for Hausel-Proudfoot varieties
+ Zsuzsanna Dancso, Michael McBreen
To appear in Journal of the European Mathematical Society
Hilbert schemes of points on singular plane curves.
... and curve counting
Hilbert schemes of points on a locally planar curve and the Severi strata of its versal deformation
Compositio Mathematica 148.2 (2012), 531--547.
A short proof of the Goettsche conjecture
+ Martijn Kool and Richard Thomas
Geometry and Topology 15.1 (2011), 397--406.
+ Steven Kleiman
in A celebration of Algebraic Geometry -- in honor of Joe Harris’s 60th birthday,
(AMS 2013), 429--449.
Refined curve counting on complex surfaces
+ Lothar Goettsche
Geometry and Topology 18.4 (2014) 2245--2307.
The chi-y genera for relative Hilbert schemes for linear systems on K3 and Abelian surfaces
+ Lothar Goettsche
Algebraic Geometry 4.2 (2015).
... and knot invariants
The Hilbert scheme of a plane curve singularity and the HOMFLY polynomial of its link
+ Alexei Oblomkov
Duke Mathematical Journal, 161.7 (2012), 1277-1303.
The Hilbert scheme of a plane curve singularity and the HOMFLY homology of its link
+ Alexei Oblomkov, Jacob Rasmussen, (with an appendix by Eugene Gorsky)
Geometry & Topology 22 (2018), 645–691. (DOI 10.2140/gt.2018.22.645)
Large N duality, Lagrangian cycles, and algebraic knots
+ Duiliu-Emanuel Diaconescu, Cumrun Vafa
Communications in Mathematical Physics 319.3 (2013), 813--863.
Torus knots and the Rational DAHA
+ Eugene Gorsky, Alexei Oblomkov, Jacob Rasmussen
Duke Mathematical Journal 163.14 (2014), 2709-2794.
In a different lifetime, I worked on quantum circuits. I don't have an undergraduate or master's degree, but I think of the first five of these papers as my undergraduate thesis, and the sixth and seventh as my master's thesis.
Quantum circuits.
Synthesis of reversible logic circuits
+ Aditya Prasad, Igor Markov, John Hayes.
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 22.6 (2003), 710-722.
Data structures and algorithms for simplifying reversible circuits
+ Aditya Prasad, Igor Markov, John Hayes, and Ketan Patel,
ACM Journal on Emerging Technologies in Computing Systems (JETC) 2.4, 277-293
Minimal universal two-qubit controlled-not based circuits
+ Igor Markov and Steven Bullock
Physical Review A 69.6 (2004), 062321.
Recognizing small-circuit structure in two-qubit operators
+ Igor Markov and Steven Bullock
Physical Review A 70.1 (2004), 012310.
Quantum circuits for incompletely specified two-qubit operators
+ Igor Markov
Quantum Information and Computation 5.1 (2004), 48-56.
Synthesis of quantum logic circuits
+ Igor Markov and Steven Bullock
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 25.6 (2006), 1000-1010.
On the CNOT-cost of Toffoli gates
+ Igor Markov
Quantum Information and Computation 9.5-6 (2009), 461--486.