[图书][B] Higher Airy Structures, 𝒲 Algebras and Topological Recursion
We define higher quantum Airy structures as generalizations of the Kontsevich–Soibelman
quantum Airy structures by allowing differential operators of arbitrary order (instead of only …
quantum Airy structures by allowing differential operators of arbitrary order (instead of only …
Flat F-manifolds, F-CohFTs, and integrable hierarchies
We define the double ramification hierarchy associated to an F-cohomological field theory
and use this construction to prove that the principal hierarchy of any semisimple …
and use this construction to prove that the principal hierarchy of any semisimple …
Semisimple flat F-manifolds in higher genus
In this paper, we generalize the Givental theory for Frobenius manifolds and cohomological
field theories to flat F-manifolds and F-cohomological field theories. In particular, we define a …
field theories to flat F-manifolds and F-cohomological field theories. In particular, we define a …
Open/closed Correspondence and Extended LG/CY Correspondence for Quintic Threefolds
K Aleshkin, CCM Liu - arXiv preprint arXiv:2309.14628, 2023 - arxiv.org
We show that Walcher's disk potential for the quintic threefold can be represented as a
central charge of a specific Gauged Linear Sigma Model which we call the extended quintic …
central charge of a specific Gauged Linear Sigma Model which we call the extended quintic …
Extended r-spin theory in all genera and the discrete KdV hierarchy
In this paper we construct a family of cohomology classes on the moduli space of stable
curves generalizing Witten's r-spin classes. They are parameterized by a phase space which …
curves generalizing Witten's r-spin classes. They are parameterized by a phase space which …
Open -spin theory II: The analogue of Witten's conjecture for -spin disks
A Buryak, E Clader, RJ Tessler - Journal of Differential Geometry, 2024 - projecteuclid.org
We conclude the construction of $ r $-spin theory in genus zero for Riemann surfaces with
boundary. In particular, we define open $ r $-spin intersection numbers, and we prove that …
boundary. In particular, we define open $ r $-spin intersection numbers, and we prove that …
Open WDVV equations and Virasoro constraints
A Basalaev, A Buryak - Arnold Mathematical Journal, 2019 - Springer
In their fundamental work, Dubrovin and Zhang, generalizing the Virasoro equations for the
genus 0 Gromov–Witten invariants, proved the Virasoro equations for a descendent …
genus 0 Gromov–Witten invariants, proved the Virasoro equations for a descendent …
Riemann–Hilbert–Birkhoff inverse problem for semisimple flat FF‐manifolds and convergence of oriented associativity potentials
G Cotti - Journal of the London Mathematical Society, 2024 - Wiley Online Library
In this paper, we address the problem of classification of quasi‐homogeneous formal power
series providing solutions of the oriented associativity equations. Such a classification is …
series providing solutions of the oriented associativity equations. Such a classification is …
Open r-spin theory III: A prediction for higher genus
A Buryak, E Clader, RJ Tessler - Journal of Geometry and Physics, 2023 - Elsevier
In our previous two papers, we constructed an r-spin theory in genus zero for Riemann
surfaces with boundary and fully determined the corresponding intersection numbers …
surfaces with boundary and fully determined the corresponding intersection numbers …
The point insertion technique and open -spin theories I: moduli and orientation
RJ Tessler, Y Zhao - arXiv preprint arXiv:2310.13185, 2023 - arxiv.org
The papers arXiv: 2003.01082 [math-ph], arXiv: 1809.02536 [math. SG], arXiv: 2211.16302
[math-ph], arXiv: 2203.02423 [math. AG] constructed an intersection theory on the moduli …
[math-ph], arXiv: 2203.02423 [math. AG] constructed an intersection theory on the moduli …