Results 11 to 20 of about 287 (57)

Manifold Ways to Darboux-Halphen System [PDF]

, 2018
Many distinct problems give birth to Darboux-Halphen system of differential equations and here we review some of them. The first is the classical problem presented by Darboux and later solved by Halphen concerning finding infinite number of double ...
Morales, John Alexander Cruz, Movasati, Hossein, Nikdelan, Younes, Roychowdhury, Raju, Torres, Marcus A. C.   +4 more
core   +3 more sources

Stokes matrices for the quantum differential equations of some Fano varieties [PDF]

, 2014
The classical Stokes matrices for the quantum differential equation of projective n-space are computed, using multisummation and the so-called monodromy identity. Thus, we recover the results of D.
B Dubrovin, B Dubrovin, D Guzzetti, E Zaslow, H Iritani, K Ueda, S Cecotti, S Tanabé   +7 more
core   +2 more sources

Genus one enumerative invariants in del-Pezzo surfaces with a fixed complex structure [PDF]

, 2016
We obtain a formula for the number of genus one curves with a fixed complex structure of a given degree on a del-Pezzo surface that pass through an appropriate number of generic points of the surface.
Biswas, Indranil, Mukherjee, Ritwik, Thakre, Varun   +2 more
core   +3 more sources

Open WDVV equations and Frobenius structures for toric Calabi-Yau 3-folds

Forum of Mathematics, Sigma
Let X be a toric Calabi-Yau 3-fold and let $L\subset X$ be an Aganagic-Vafa outer brane. We prove two versions of open WDVV equations for the open Gromov-Witten theory of $(X,L)$ .
Song Yu, Zhengyu Zong
doaj   +1 more source

Theory of Submanifolds, Associativity Equations in 2D Topological Quantum Field Theories, and Frobenius Manifolds

, 2006
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of ...
B. Dubrovin, O. I. Mokhov, O. I. Mokhov
core   +2 more sources

A mirror theorem for Gromov-Witten theory without convexity

Forum of Mathematics, Sigma
We prove a genus zero Givental-style mirror theorem for all complete intersections in toric Deligne-Mumford stacks, which provides an explicit slice called big I-function on Givental’s Lagrangian cone for such targets.
Jun Wang
doaj   +1 more source

On the injectivity radius in Hofer's geometry

, 2014
In this note we consider the following conjecture: given any closed symplectic manifold $M$, there is a sufficiently small real positive number $\rho$ such that the open ball of radius $\rho$ in the Hofer metric centered at the identity on the group of ...
Lalonde, François, Savelyev, Yakov
core   +1 more source

Relative quantum cohomology of the Chiang Lagrangian

Forum of Mathematics, Sigma
We compute the open Gromov-Witten disk invariants and the relative quantum cohomology of the Chiang Lagrangian $L_\triangle \subset \mathbb {C}P^3$ .
Anna Hollands, Elad Kosloff, May Sela, Qianyi Shu, Jake P. Solomon   +4 more
doaj   +1 more source

Logarithmic asymptotics of the genus zero Gromov-Witten invariants of the blown up plane

, 2005
We study the growth of the genus zero Gromov-Witten invariants GW_{nD} of the projective plane P^2_k blown up at k points (where D is a class in the second homology group of P^2_k).
Di Francesco, Eugenii Shustin, Greuel, Göttsche, Hofer, Ilia Itenberg, Kollár, Kontsevich, McDuff, McDuff, McDuff, Viatcheslav Kharlamov   +11 more
core   +6 more sources

The (n,1)-Reduced DKP Hierarchy, the String Equation and W Constraints [PDF]

, 2014
The total descendent potential of a simple singularity satisfies the Kac-Wakimoto principal hierarchy. Bakalov and Milanov showed recently that it is also a highest weight vector for the corresponding W-algebra.
van de Leur, Johan
core   +2 more sources