2023/2024
Научно-исследовательский семинар "Введение в исчисление Гудвилли"
Статус:
Дисциплина общефакультетского пула
Кто читает:
Факультет математики
Когда читается:
3, 4 модуль
Охват аудитории:
для всех кампусов НИУ ВШЭ
Преподаватели:
Горинов Алексей Геннадьевич
Язык:
английский
Кредиты:
6
Контактные часы:
72
Course Syllabus
Abstract
"Given a smooth function $f:\mathbb{R}^n\to \mathbb{R}$, one can construct its Taylor series at the origin. The homogeneous components of the series are homogeneous polynomials with coefficients obtained by taking the derivatives of $f$ at $0$. Moreover, under some assumptions on $f, x\in\mathbb{R}^n$ and $k$ the value of the degree $k$ Taylor polynomial at $x$ approximates $f(x)$ reasonably well. Remarkably, under some hypotheses which are not too restrictive, all these statements have analogues for functors from (certain subcategories of) topological spaces to topological spaces. For example, the linear approximation of the functor of embeddings in a given manifold $M$ turns out to be the functor of immersions in $M$.
These phenomena are described by the Goodwillie calculus. Our goal is to understand several examples in some detail with a focus on the embedding functor, and then to discuss the general formalism behind these constructions."