会場

埼玉大学 大学院理工学研究科棟5階 数学研究室1 （このページの15番の建物）

Tea and coffee

講演者

須山慶太, Keita Suyama（埼玉大学）

タイトル

Local Duality and Eisenbud-Levine Theorem

アブストラクト

We introduce local duality for formal power series ring based on residue pairing. We apply this duality to Eisenbud-Levine theorem for mapping degree of finite real map germs. This allows us an algorithmic study on mapping degree of given map germ.

講演者

李強, Qiang Li（東北師範大学，埼玉大学）

タイトル

The (m,k)-bifurcation models on specific domains and application

アブストラクト

In this talk, we will introduce the (m,k)-bifurcation model for nonlinear elliptic partial differential equation. We will show how our models work on rectangle and square. By these (m,k)-bifurcation model, the variations of the bifurcation at the first few eigenvalues, and the asymptotic behavior of the bifurcation branches rely on the domain of partial differential equations, are shown.

講演者

池祐一, Yuichi Ike（東京大学）

タイトル

Hyperbolic localization and Lefschetz fixed point formulas for higher-dimensional fixed point sets

アブストラクト

We consider Lefschetz fixed point formulas for constructible sheaves with higher-dimensional fixed point sets. In this talk, we give an explicit formula of the local contributions from them by using some constructible functions associated with hyperbolic localizations. This is a joint work with Yutaka Matsui and Kiyoshi Takeuchi.

講演者

Cristina Valle（首都大学）

タイトル

Blow-analytic equivalence of curves on quadratic cones

アブストラクト

We investigate blow-analytic equivalence of curve germs embedded in real surfaces with an isolated singularity. For simplicity, we fix the ambient surface to be a quadratic cone. Then we can establish a relationship between the classification of curves in the cone and the (already known) case of curve singularities in a smooth surface. After recalling some topological and combinatorial invariants, we explicitly classify unibranched and bibranched curves embedded in a cone up to blow-analytic homeomorphism.

Seminar dinner