Related papers: Steenrod operations in Gromov--Witten theory: a co…
Gromov-Witten invariants have been constructed to be deformation invariant, but their behavior under other transformations is subtle. In this note we show that logarithmic Gromov-Witten invariants are also invariant under appropriately…
This expository article is an introduction to logarithmic Gromov--Witten (GW) theory. We discuss how to study the GW theory of a smooth projective variety via simple normal crossings degenerations. We survey several approaches to…
Open Gromov-Witten invariants are defined as cycles of the multi-curve chain complex, well defined up to isotopy.
We construct a new type of geometric knot theory, plumbers' knots, and solve the problems of distinguishing and enumerating such knots at a fixed level of complexity. (v2) Minor edits, added theorem 3.18. (v3) Substantial revisions,…
Notes for a short lecture series, covering exploded manifolds, the moduli stack of curves in exploded manifolds, and a tropical gluing formula for Gromov-Witten invariants: a gluing formula providing a degeneration formula for Gromov-Witten…
Two typos in the published paper are pointed out. Both are just typos and the calculations in that paper are based on the correct formulism.
In the present text we discuss basic aspects of the Seiberg - Witten theory mainly focusing the attantion on some geometrical details which could make the introduction to the subject more illustrative. At the same time we list there natural…
Polyfold theory, as developed by Hofer, Wysocki, and Zehnder, is a relatively new approach to resolving transversality issues that arise in the study of $J$-holomorphic curves in symplectic geometry. This approach has recently led to a…
Resubmitted as hep-ph/9502316. Removed from hep-th. Incorrigibly inept submitter publicly excoriated.
In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has…
Recent progress towards an understanding of the piNN system within chiral perturbation theory is reported. The focus lies on an effective field theory calculation and its comparison to phenomenological calculations for the reaction NN->d…
This paper has been withdrawn by the author due to a crucial error in equation.
The CP symmetry is a fundamental discrete symmetry in chiral gauge theory. Therefore this symmetry is expected to be kept also on the lattice. However, it has been pointed out by Hasenfratz that the chiral fermion action in Luscher's…
This paper has been withdrawn by the authors due to an error in the main theorem.
An expository article on Turaev surfaces written for "A Concise Encyclopedia of Knot Theory," to appear.
This paper has been withdrawn due to an error in the proof of Theorem 5.3.
This paper has been withdrawn by the author due to a mistake.
This comment about the article "Hamiltonian for the Zeros of the Riemann Zeta Function", by C. M. Bender, D. C. Brody, and M. P. M\"uller, published recently in Phys. Rev. Lett. (Phys. Rev. Lett., 118, 130201, (2017)) gives arguments…
Here I discuss the major pitfalls and the most severe mistakes of the above mentioned paper. The thorough analysis shows that despite all the claims the present work has nothing to do with the thermalization process in relativistic heavy…
This is the draft of lecture notes for Phd students in Sichuan University. In this notes we expand Li-Ruan's paper with much more detailed explanations and calculations.