Collaborators

My papers on the arxiv, and at google scholar.

A talk where I explain some things I am thinking about

A (presently defunct)
research blog about microlocal sheaves.


New

Microlocal Morse theory of wrapped Fukaya categories
+ Sheel Ganatra, John Pardon

Structural results in wrapped Floer theory
+ Sheel Ganatra, John Pardon

Arboreal singularities from Lefschetz fibrations



Articles:


Sheafy symplectic geometry:

Foundations and comparisons

Covariantly functorial wrapped Floer theory on Liouville sectors
+ Sheel Ganatra, John Pardon


Microlocal category for Weinstein manifolds via h-principle


Mirror Symmetry

Mirror symmetry for very affine hypersurfaces
+ Benjamin Gammage


Calabi-Yau structures on topological Fukaya categories
+ Alex Takeda


Legendrian knots


Legendrian knots and constructible sheaves
+ David Treumann, Eric Zaslow
Inventiones Mathematicae (DOI: 10.1007/s00222-016-0681-5).

Augmentations are sheaves
+ Lenhard Ng, Daniel Rutherford, Steven Sivek, Eric Zaslow.

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

A complete knot invariant from contact homology
+ Lenhard Ng, Tobias Ekholm,
Inventiones Mathematicae (DOI: 10.1007/s00222-017-0761-1).


Cluster varieties

Cluster varieties and Legendrian knots
+ David Treumann, Harold Williams, Eric Zaslow.

On the combinatorics of exact Lagrangian surfaces
+ David Treumann, Harold Williams.







Algebraic geometry (I haven't done this in awhile):

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. (
doi:10.14231/AG-2018-004)

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

Equidistribution on the space of rank two vector bundles over the projective line
+ Jacob Tsimerman
Duke Mathematical Journal 166.18 (2017), 3461-3504.


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.

On the Goettsche threshold
+ Steven Kleiman
“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.