As announced in Gross and Siebert (in Algebraic geometry: Salt Lake City 2015,
Proceedings of Symposia in Pure Mathematics, vol 97, no 2. AMS, Providence, pp 199–230 …

We construct “quantum theta bases,” extending the set of quantum cluster monomials, for
various versions of skew-symmetric quantum cluster algebras. These bases consist …

Abstract Gross, Pandharipande and Siebert have shown that the 2–dimensional Kontsevich–
Soibelman scattering diagrams compute certain genus-zero log Gromov–Witten invariants of …

Block and Göttsche have defined aq-number refinement of counts of tropical curves in R^ 2
R 2. Under the change of variables q= e^ iu q= e iu, we show that the result is a generating …

The skein algebra of a marked surface, possibly with punctures, admits the basis of (tagged)
bracelet elements constructed by Fock-Goncharov and Musiker-Schiffler-Williams. As a …

We prove aq-refined tropical correspondence theorem for higher genus descendant
logarithmic Gromov–Witten invariants with a λ g class in toric surfaces. Specifically, a …

The Kauffman bracket skein algebra is a quantization of the algebra of regular functions on
the SL 2 character variety of a topological surface. We realize the skein algebra of the 4 …

In, we established a series of correspondences relating five enumerative theories of log
Calabi–Yau surfaces, ie pairs (Y, D) with Y a smooth projective complex surface and D= D …

Abstract In the Gross–Siebert mirror symmetry program, certain enumerations of tropical
disks are encoded in combinatorial objects called scattering diagrams and broken lines …

Let $(S, E) $ be a log Calabi-Yau surface pair with $ E $ a smooth divisor. We define new
conjecturally integer-valued counts of $\mathbb {A}^ 1$-curves in $(S, E) $. These log BPS …