Japanese Journal of Mathematics
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Itô geometry
Japanese Journal of Mathematics - - 2007
This note provides a very brief outline of the ideas from which Itô’s theory of stochastic integral equations derive. The emphasis on the ideas rather than the technical details required to implement them.
Denominator identities for finite-dimensional Lie superalgebras and Howe duality for compact dual pairs
Japanese Journal of Mathematics - Tập 7 Số 1 - Trang 41-134 - 2012
Geometric structure in smooth dual and local Langlands conjecture
Japanese Journal of Mathematics - Tập 9 - Trang 99-136 - 2014
This expository paper first reviews some basic facts about p-adic fields, reductive p-adic groups, and the local Langlands conjecture. If G is a reductive p-adic group, then the smooth dual of G is the set of equivalence classes of smooth irreducible representations of G. The representations are on vector spaces over the complex numbers. In a canonical way, the smooth dual is the disjoint union of......
Holonomic -modules and positive characteristic
Japanese Journal of Mathematics - Tập 4 - Trang 1-25 - 2009
We discuss a hypothetical correspondence between holonomic
-modules on an algebraic variety X defined over a field of zero characteristic, and certain families of Lagrangian subvarieties in the cotangent bundle to X. The correspondence is based on the reduction to positive characteristic.
Grothendieck spaces: the landscape and perspectives
Japanese Journal of Mathematics - Tập 16 Số 2 - Trang 247-313 - 2021
Right-handed vector fields & the Lorenz attractor
Japanese Journal of Mathematics - Tập 4 - Trang 47-61 - 2009
The main purpose of this paper is to introduce a class of vector fields on the 3-sphere that we call “right-handed”. Roughly speaking, they are characterized by the fact that any two orbits link positively. We give various natural examples and provide some kind of homological characterization. We then describe some of the main dynamical properties of these flows.
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