会場

数学研究室1（埼玉大学理工学研究科棟5階）

講演者

Goulwen Fichou (University of Rennes)

タイトル

Motivic Milnor fibre and logarithmic geometry

アブストラクト

We provide a description of the motivic and topological Milnor fibre of a regular function with only normal crossing singularities using logarithmic geometry. This approach resembles the description of the geometry monodromy using real oriented blowing-up given by Norbert A’Campo in 1975. Joint work with Jean-Baptiste Campesato and Adam Parusinski.

講演者

Masaaki Umehara (Institute of Science Tokyo)

タイトル

Explicit analytic functions defining the images of wave front singularities

アブストラクト

We present explicit real-analytic functions whose zero sets characterize the images of the standard maps of wave-front singularities. These functions provide realizations of the “main-analytic sets” introduced  by Ishikawa–Koike–Shiota (1984).

More concretely, a subset of Euclidean space is called a “global main-analytic set” if it can be described, up to a set of smaller Hausdorff dimension, as part of the zero set of a single real-analytic function, referred to as its “main-analytic function”.

In this talk, we propose a general framework for constructing such main-analytic functions by a new method based on explicit computations of resultants. In particular, we obtain new formulas for the main-analytic functions associated with the standard maps of wave-front singularities of types A, D, and E. I will also explain why these constructions are of interest.