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## A Formula For the Gromov--Witten Potential of an Elliptic Curve

Moscow Mathematical Journal. 2023. Vol. 23. No. 3. P. 309-317.

An algorithm to determine all the Gromov–Witten invariants of any smooth projective curve was obtained by Okounkov and Pandharipande in 2006. They identified stationary invariants with certain Hurwitz numbers and then presented Virasoro type constraints that allow to determine all the other Gromov–Witten invariants in terms of the stationary ones. In the case of an elliptic curve, we show that these Virasoro type constraints can be explicitly solved leading to a very explicit formula for the full Gromov–Witten potential in terms of the stationary invariants.

Providence : American Mathematical Society, 2018

This volume contains the proceedings of the 2016 AMS von Neumann Symposium on Topological Recursion and its Influence in Analysis, Geometry, and Topology, which was held from July 4–8, 2016, at the Hilton Charlotte University Place, Charlotte, North Carolina.
The papers contained in the volume present a snapshot of rapid and rich developments in the emerging ...

Added: February 20, 2019

Malygina E., Кунинец А. А., Раточка В. Л. et al., Прикладная дискретная математика 2023 № 62 С. 83-105

We consider the basic theory of algebraic curves and their function fields necessary for constructing algebraic geometry codes and a pair of codes constituting error-correction pair which is used in a precomputation step of the decoding algorithm for the algebraic geometry codes. Also, we consider the decoding algorithm and give the necessary theory to prove ...

Added: March 19, 2024

Serge Lvovski, Moscow Mathematical Journal 2019 Vol. 19 No. 3 P. 597-613

We show that if we are given a smooth non-isotrivial family of curves of genus 1 over C with a smooth base B for which the general fiber of the mapping J : B → A 1 (assigning j-invariant of the fiber to a point) is connected, then the monodromy group of the family (acting ...

Added: August 30, 2019

Matveeva A., Poberezhny V. A., Математические заметки 2017 Т. 101 № 1 С. 91-100

A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and an explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic. ...

Added: October 18, 2016

Poberezhny V. A., Matveeva A., Journal of Geometry and Physics 2017 Vol. 114 P. 384-393

We consider a generalization of Riemann–Hilbert problem on elliptic curves. For a given elliptic curve and irreducible representation of free group with two generators we construct explicitly a semistable vector bundle of degree zero obeying a logarithmic connection such that its monodromy over fundamental parallelogram is equivalent to given free group representation, monodromy along a−cycle is ...

Added: October 26, 2016

Lebedev P. A., Nesterenko A., Черновик статьи 2014

В работе предложен алгоритм вычисления явного вида эндоморфизма эллиптической кривой, который может использоваться для ускорения операций по вычислению кратной точки. Приведены детали авторской реализации и результаты её производительности. В статье впервые представлены решения поставленной задачи для степени соответствующего многочлена Гильберта выше пятой. ...

Added: October 23, 2014

Matveeva A., Poberezhny V. A., Mathematical notes 2017 Vol. 101 No. 1 P. 115-122

A one-dimensional generalization of the Riemann–Hilbert problem from the Riemann sphere to an elliptic curve is considered. A criterion for its positive solvability is obtained and the explicit form of all possible solutions is found. As in the spherical case, the solutions turn out to be isomonodromic. ...

Added: May 22, 2017

Dunin-Barkowski P., Mulase M., Norbury P. et al., Journal fuer die reine und angewandte Mathematik 2017 Vol. 2017 No. 726 P. 267-289

We construct the quantum curve for the Gromov–Witten theory of the complex projective line. ...

Added: March 3, 2015

Takebe T., International Journal of Modern Physics A 2004 Vol. 19, May suppl. P. 418-435

Trigonometric degeneration of the Baxter-Belavin elliptic r matrix is described by the degeneration of the twisted WZW model on elliptic curves. The spaces of conformal blocks and conformal coinvariants of the degenerate model are factorised into those of the orbifold WZW model. ...

Added: August 14, 2014

Netay I. V., Savvateev A. V., Bulletin of the Korean Mathematical Society 2017 Vol. 54 No. 5 P. 1597-1617

The paper is devoted to the description of family of scalene triangles for which the triangle formed by the intersection points of bisectors with opposite sides is isosceles. We call them Sharygin triangles. It turns out that they are parametrized by an open subset of an elliptic curve. Also we prove that there are infinitely ...

Added: April 11, 2018

Pavlov A., Buchweitz R., L’ENSEIGNEMENT MATHÉMATIQUE 2021

We give normal forms of determinantal representations of a smooth projective plane cubic in terms of Moore matrices. Building on this, we exhibit matrix factorizations for all indecomposable vector bundles of rank 2 and degree 0 without nonzero sections, also called Ulrich bundles, on such curves. ...

Added: November 13, 2021

Радомский А. О., Известия РАН. Серия математическая 2023 Т. 87 № 1 С. 119-160

We obtain some results related to Romanoff’s theorem. ...

Added: February 15, 2023

Ornea L., Verbitsky M., Mathematische Zeitschrift 2021 Vol. 299 P. 2287-2296

A compact complex manifold V is called Vaisman if it admits an Hermitian metric which is conformal to a K\"ahler one, and a non-isometric conformal action by C. It is called quasi-regular if the C-action has closed orbits. In this case the corresponding leaf space is a projective orbifold, called the quasi-regular quotient of V. It is known that the set ...

Added: November 14, 2021

Oblomkov A., Okounkov A., Pandharipande R., Communications in Mathematical Physics 2020 Vol. 374 No. 3 P. 1321-1359

We propose an explicit formula for the GW/PT descendent correspondence in the stationary case for nonsingular connected projective threefolds. The formula, written in terms of vertex operators, is found by studying the 1-leg geometry. We prove the proposal for all nonsingular projective toric threefolds. An application to the Virasoro constraints for the stationary descendent theory of ...

Added: May 15, 2020

Serge Lvovski, Springer, 2020

This is a brief textbook on complex analysis intended for the students of upper undergraduate or beginning graduate level. The author stresses the aspects of complex analysis that are most important for the student planning to study algebraic geometry and related topics. The exposition is rigorous but elementary: abstract notions are introduced only if they ...

Added: October 27, 2020

Takebe T., Kuroki G., Journal of Physics A: Mathematical and Theoretical 2001 Vol. 34 No. 11 P. 2403-2413

We construct a Gaudin type lattice model as the Wess-Zumino-Witten model on elliptic curves at the critical level. Bethe eigenvectors are obtained by the bosonisation technique. ...

Added: August 14, 2014

Buff X., Goncharuk Nataliya, Journal of Modern Dynamics 2015 Vol. 9 P. 169-190

We investigate the notion of complex rotation number which was introduced by V.I.Arnold in 1978. Let f: R/Z -> R/Z be a (real) analytic orientation preserving circle diffeomorphism and let omega in C/Z be a parameter with positive imaginary part. Construct a complex torus by glueing the two boundary components of the annulus { z ...

Added: October 10, 2013

A. O. Radomskii, Izvestiya: Mathematics 2023 Vol. 87 No. 1 P. 113-153

We obtain some results related to Romanoff’s theorem. ...

Added: September 8, 2023

Dunin-Barkowski P., , in : Proceedings of Symposia in Pure Mathematics. Vol. 100: Topological Recursion and its Influence in Analysis, Geometry, and Topology.: Providence : American Mathematical Society, 2018. P. 231-295.

We describe a way of producing local spectral curves for arbitrary
semisimple cohomological field theories (and Gromov-Witten theories in particular) and global spectral curves for semisimple cohomological field theories
satisfying certain conditions. By this we mean that applying the topological
recursion procedure on the spectral curve reproduces the total potential of the
corresponding cohomological field theory. ...

Added: February 20, 2019

Sirotin V., Arkhipova M., Dubrova T. A. et al., Bielsko-Biala : University of Bielsko-Biala Press, 2016

The main attributes of modern enterprises should be the flexibility and the ability of forecasting the future. Constant adaptation to the changing environment and the rapidity of undertaking certain actions which are conditioned by specific situations determine the rules for the future position of market competition. Effective and efficient adjustment of the company in line ...

Added: November 2, 2016

Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216

Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...

Added: December 4, 2017

Furmanov K. K., Nikol'skii I. M., Computational Mathematics and Modeling 2016 Vol. 27 No. 2 P. 247-253

Added: December 22, 2016

Buchstaber V., Limonchenko I., / Cornell University. Series math "arxiv.org". 2018. No. 1808.08851.

We introduce the notions of algebraic and geometric direct families of polytopes and develop a theory of such families. The theory is then applied to the problem of existence of nontrivial higher Massey products in cohomology of moment-angle-complexes. ...

Added: September 29, 2019

Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18

Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...

Added: November 16, 2020