会場

埼玉大学理学部1号館3階 基礎数理演習室 （このページの理学部と書いてある建物が1号館です）

講演者

安藤 加奈 氏 (千葉大学)

タイトル

Multi-point connection problem

アブストラクト

We consider single differential equations on the complex projective line which have one regular singular point and one irregular singular point. For any sector, any fundamental set of solutions near the regular singular point, and any fundamental set of solutions near the irregular singular point on the sector, there is a linear transformation relating the two fundamental sets of solutions. The problem of finding the coefficients of this linear transformation is called the connection problem. By composing these linear transformations, we can analyze the Stokes phenomenon.
We construct a family of functions whose asymptotic expansions match those of a fundamental solution at a regular singular point. These functions are particular solutions of first order nonhomogeneous differential equations that can be derived from the fundamental solutions at the regular singular point and formal solutions at the irregular singular point of the original differential equation. We call these functions the fundamental functions associated with this two point connection problem. The series expansions of the associated fundamental functions are described by systems of difference equations, and the coefficients relating them to the fundamental solutions can be found by a recursive process. This yields a method for calculating the linear relation between the two fundamental sets of solutions.
In this talk, we introduce the Okubo-Kohno method to solve the two point connection problem for linear ordinary differential equations with an irregular singularity of rank one by analyzing the associated fundamental functions. We will also apply this method to the connection problem with more than two singular points.

講演者

Adam Parusinski 氏 (University of Nice Sophia Antipolis)

タイトル

Normal cycle of semi-algebraic sets

アブストラクト

We give an informal introduction to the normal cycle of a semi-algebraic set. The normal cycle is a geometric object, more precisely a Lagrangian variety, that reflects such geometric features as curvatures measures, vanishing topology and stratified Morse Theory. It provides a geometric interpretation of the Stiefel-Whitney characteristic classes of singular semi-algebraic sets