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Arhiv - Obvestila DOKTORSKI ŠTUDIJ

Zbrano dne 14.03.2019 ob 12:53


Število vseh obvestil: 1

1. obvestilo: 04.02.2019 - Mathematical Research Seminar



Mathematical Research Seminar
Datum: 04.02.2019

Students are kindly invited to participate to the Mathematical Research Seminar tomorrow, Tuesday 5th February at 10:00.


Lecturer: Tadeusz Januszkiewicz (Polish Academy of Sciences, Poland)
Title: On k-regular maps
Date and time: Tuesday, 5th February 2019. (10:00-11:00)
Location: FAMNIT-MP1

Abstract:
The concept of k-regular maps was introduced into topology by Karol Borsuk in 1950'. Long before it was investigated in interpolation and approximation theory by (among others) Chebyshev and Kolmogorov, and had distinctly applied mathematics flavor.
A continuous map f: X\to V, from a topological space to a vector space is k-regular of for any k distinct points in X their images are linearly independent.

Example:
If f:X\to V is an embedding, then the map F: X\to R\oplus V, defned by F(x)=(1,f(x)) is 2-regular.

In analogy to theory of embeddings, one of central problems in the study of k-regular maps is (given k, X)  to construct a k-regular map of X into space V of minimal possible dimension. Unlike for embeddings, this is interesting already for X=R^d I will discuss  lower bounds (obstructions) to the existence to the existence of k-regular maps (this involves some algebraic topology of configuration spaces, following work of many people, most recent being Blagojevic, Cohen, Lueck and Ziegler) and upper bounds (constructions) (this involves some algebraic geometry of secant varieties and  Hilbert schemes, following the work of Buczynski, Januszkiewicz, Jelisiejew and Michalek).
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