A research blog about microlocal sheaves.

__New__

__Articles in repair:__

Generating families and constructible sheaves

Note: This paper has some serious mistakes, which are currently under repair in work with Sylvain Courte.

__Articles:__

__Sheafy symplectic geometry:__*Covariantly functorial Floer theory on Liouville sectors*

Foundations and comparisons

Foundations and comparisons

+ Sheel Ganatra, John Pardon

*Microlocal category for Weinstein manifolds via h-principle*

*Mirror symmetry for very affine hypersurfaces*

Mirror Symmetry

Mirror Symmetry

+ Benjamin Gammage

Calabi-Yau structures on topological Fukaya categories

+ Alex Takeda

Legendrian knots

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

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.