Chris Ciesielski

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Speaker

Chris received his PhD from Warsaw University, Poland in 1985 and was awarded the {\it Kazimierz Kuratowski Prize} from the Polish Mathematical Society and Polish Academy of Sciences in 1986. Shortly thereafter he moved to West Virginia University where he has served as Professor of Mathematics ever since. He has enjoyed a long and productive research career publishing in the areas of real analysis and its applications, foundations of mathematics including set theory, topology, logic and image processing, especially image segmentation. In 1999 he was named recipient of the {\it Benedum Distinguished Scholar Award}.

Special Session

Different levels of smoothness: Restriction, extension, and covering theorems

This sequence of two one-hour talks is based on the expository paper, written with Juan B. Seoane-Sepulveda.

The aim of these talks is to revisit the centuries old discussion on the interrelations between continuous and differentiable functions from [math]{\mathbb R}[/math] to [math]{\mathbb R}[/math], as well as their higher level analogs. The new angle of this presentation is influenced by a series of very recent results in this research area, including 2016-18 articles.

Talk 1

Differentiability versus continuity: Restriction and extension theorems and monstrous examples

Presentation: Talk 1, pdf

Talk 2

Higher level differentiability: Generalized Ulam-Zahorski problem and small coverings by smooth maps

Presentation: Talk 2, pdf