Singularities of differentiable maps and Thom polynomials

セミナー iTHEMS数学セミナー
日時
2026年5月22日(金)15:00 - 17:30 (JST)
講演者
  • 田邊 真郷 (理化学研究所 数理創造研究センター (iTHEMS) 数理基礎部門 基礎科学特別研究員)
会場
言語
英語
ホスト
Zhe Wang

Singularities are locations where something is exceptional. In particular, singularities of differentiable maps are mathematical concepts corresponding to stationary points of functions and apparent contours of surfaces under projection onto the retina. These are unavoidable in general, but important to study the shape of spaces and behavior of maps. The theory for them was initiated by R. Thom in 1950's, and have been deeply studied by many researchers.

In this talk, I would like to ...

  • show guiding examples of singularities to make you familiar with them;
  • share basic motivation of singularity theory of differentiable maps;
  • introduce Thom polynomials, a tool to build a bridge between counting singularities and topological invariants of spaces and maps.

If time permits, I would also like to talk about a relative version of Thom polynomials, which is my recent interest.

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