New!
Skein-valued mirror curves for toric CY3 strips
+ Mingyuan Hu
Microsheaf composition of Lagrangian correspondences
+ Wenyuan Li, David Nadler
Skein traces from curve counting
+ Tobias Ekholm, Pietro Longhi, Sunghyuk Park
Operadic twisting as an adjunction
+ Guillaume Laplante-Anfossi, Adrian Petr
Aganagic's invariant is Khovanov homology
+ Elise LePage
The skein valued mirror of the topological vertex
+ Tobias Ekholm, Pietro Longhi
A universal characterization of the curved homotopy Lie and associative algebras
+ Guillaume Laplante-Anfossi, Adrian Petr
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
Symplectic geometry:
Skein-valued enumeration of holomorphic curves with boundary
+ Tobias Ekholm
+ Tobias Ekholm
To appear in Communications in Analysis and Geometry
+ Tobias Ekholm
Skein recursion for holomorphic curves and invariants of the unknot
+ Tobias Ekholm
Comptes Rendus. Mathématique 363 (G13), 1543-1554
Colored HOMFLYPT counts holomorphic curves
+ Tobias Ekholm
Proc. Nat. Acad. Sci. USA 122.50 (2025) e2510118122
DOI: https://doi.org/10.1073/pnas.2510118122
Quantum mirrors of cubic planar graph Legendrians
+ Matthias Scharitzer
Skein valued cluster transformation in enumerative geometry of Legendrian mutation
+ 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 (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
On the Hochschild cohomology of Tamarkin categories
+ Christopher Kuo, Bingyu Zhang
The microlocal Riemann-Hilbert correspondence for complex contact manifolds
+ 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
Compositio Mathematica 161.5 (2025) 1128-1214.
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.
The Hamiltonian reduction of hypertoric mirror symmetry
+ Michael McBreen, Peng Zhou
to appear in Advances in Mathematics.
Toric mirror monodromies and Lagrangian spheres
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)
Adjoints, wrapping, and morphisms at infinity
+ Tatsuki Kuwagaki
Comptes Rendus Mathématique, Volume 363 (2025), 205-212.
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
Journal of the European Mathematical Society 26.7 (2023), 2565-2653.
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.