Abstract:
For each d>=2, the mapping class group for plane curves of degree d will be defined and it is proved that there exists uniquely the Meyer function on this group. In the case of d=4, using our Meyer function, we can define the local signature for 4-dimensional fiber spaces whose general fibers are non-hyperelliptic compact Riemann surfaces of genus 3. Some computations of our local signature will be given.

Abstract:
We present a formula expressing Earle's twisted 1-cocycle on the mapping class group of a closed oriented surface of genus >=2 relative to a fixed base point, with coefficients in the first homology group of the surface. For this purpose we compare it with Morita's twisted 1-cocycle which is combinatorial. The key is the computation of these cocycles on a particular element of the mapping class group, which is topologically a hyperelliptic involution.

Abstract:
The notion of a symplectic expansion directly relates the topology of a surface to formal symplectic geometry. We give a method to construct a symplectic expansion by solving a recurrence formula given in terms of the Baker-Campbell-Hausdorff series.

Abstract:
A complete description of the global monodromy of a Lefschetz fibration arising from the Fermat surface of degree 4 is given. As a by-product we get a positive relation among right hand Dehn twists in the mapping class group of a closed orientable surface of genus 3.

Abstract:
We introduce an invariant for trivalent fatgraph spines of a once bordered surface, which takes values in the first homology of the surface. This invariant is the secondary object coming from two 1-cocycles on the dual fatgraph complex, one introduced by Morita and Penner in 2008, and the other by Penner, Turaev, and the author in 2013. We present an explicit formula for this invariant and investigate its properties. We also show that the mod 2 reduction of the invariant is the difference of naturally defined two spin structures on the surface.

Abstract:
We study a secondary invariant, called the Meyer function, on the fundamental group of the complement of the dual variety of a smooth projective variety. This invariant have played an important role when studying the local signatures of fibered 4-manifolds from topological point of view. As an application of our study, we define a local signature for generic non-hyperelliptic fibrations of genus 4 and 5 and compute some examples.

Abstract:
For any unoriented loop on a compact connected oriented surface with one boundary component, the generalized Dehn twist along the loop is defined as an automorphism of the completed group ring of the fundamental group of the surface. If the loop is simple, this is the usual right handed Dehn twist, in particular realized as a mapping class of the surface. We investigate the case when the loop has a single transverse double point, and show that in this case the generalized Dehn twist is not realized as a mapping class.

Abstract:
Multilateral Nuclear Approaches (MNAs) is a concept of international and/or multilateral control of nuclear material and/or nuclear fuel cycle facilities. It is a strategy for contributing to and promoting the sustainability of nuclear energy while enhancing nuclear nonproliferation, by ensuring nuclear fuel supplies and fuel cycle services, and risk control and reducing risk regarding nuclear safety. In order to establish such a MNA, the authors draw out 12 features of the MNA by analyzing various past and current MNA proposals, together with the current environment surrounding nuclear energy use. Those proposals are: (A) nuclear nonproliferation, (B) assurance of supply of nuclear material and fuel cycle services, (C) access to technologies, (D) multilateral involvement, (E) siting—choice of host state, (F) legal aspects, (G) political and public acceptance, (H) economics, (I) nuclear safety, (J) nuclear liability, (K) transportation, and (L) geopolitics. These proposals are also expected to serve as a guidepost and evaluation criteria of MNA.

Abstract:
One of primary challenges for ensuring effective and efficient functions of the multilateral nuclear approaches (MNA) to nuclear fuel cycle facilities is harmonization between a MNA framework and existing nuclear cooperation agreements (NCA). A method to achieve such harmonization is to construct a MNA framework with robust non-proliferation characteristics, in order to obtain supplier states’, especially the US’s prior consents for non-supplier states’ certain activities including spent fuel reprocessing, plutonium storages and retransfers of plutonium originated in NCAs. Such robust characteristics can be accomplished by MNA member states’ compliances with International Atomic Energy Agency (IAEA) Safeguards, regional safeguards agreements, international conventions, guidelines and recommendations on nuclear non-proliferation, nuclear security, safety, and export control. Those provisions are to be incorporated into an MNA founding agreement, as requirements to be MNA members in relation to NCAs. Furthermore, if an MNA facility is, (1) owned and operated jointly by all MNA member states, (2) able to conclude bilateral NCAs with non-MNA/supplier states as a single legal entity representing its all member states like an international organization, and (3) able to obtain necessary prior consents, stable, smooth, and timely supplies of nuclear fuel and services can be assured among MNA member states. In this paper, the authors will set out a general MNA framework and then apply it to a specific example of Europe Atomic Energy Community (EURATOM) and then consider its applicability to the Asian region, where an establishment of an MNA framework is expected to be explored.