Colloquium Lectures

Tangency varieties and application
Báo cáo viên: PGS TS Phạm Tiến Sơn (Trường ĐH Đà Lạt)

Thời gian: 9h30, Thứ 6, ngày 14 tháng 8 năm 2020

Địa điểm: Hội trường tầng 3, Nhà A5, Viện Toán học

Tóm tắt: Let $f colon mathbb{R}^n to mathbb{R}$ be a continuous function definable in a polynomially bounded o-minimal structure (e.g., semialgebraic or globally subanalytic functions). By the tangency variety of $f$ we mean the set of all points $x in mathbb{R}^n$ such that the level set $f^{-1}(f(x))$ is tangent to the sphere in $mathbb{R}^n$ centered at the origin with radius $|x|.$ In this talk we show that the tangency variety of $f$ contains many useful information (local and at infinity) of $f.$

For example, there exist some relationships between tangency values and bifurcation values at infinity of $f$ as well as, values at which $f$ does not satisfy the (weak) Palais--Smale condition. In particular, some applications of tangency varieties in semi-algebraic optimization are presented.