VADOR Events Calendar

Our team is constantly involved in research projects, frequently involving collaboration with international scientists and institutions. Research is carried out in a number of languages, however we present mostly in English.

We frequently host one off lectures on topics relating to variational analysis, dynamics and operations research.  In term-time, we host different speakers at our weekly AKOR seminar.  Seminars take place most Thursdays at 3pm in Sem. R. DB gelb 04.  Once a month, the AKOR seminar will be replaced by the Vienna Seminar on Optimization, opens an external URL in a new window - a joint venture with Radu Bot and Yurii Malitskyi of the University of Vienna

We organise the Viennese Conference on Optimal Control and Dynamic Games, typically every three years.  The next iteration - VC2025 - will take place in July 2025.  For further details on this conference, and its forerunners, please visit the VC2025, opens an external URL in a new window website.

Topics and speakers for all forthcoming events will be posted below.

06. March 2025, 15:00 until 17:00

AKOR Seminar: On the semialgebraic Whitney extension problem

Other

Armin Rainer, TU Wien

In 1934, Whitney raised the question of how one can decide whether a function defined on a closed subset of real n-space is the restriction of a $C^m$ function on real n-space. He gave a characterization in dimension 1. The problem was fully solved by Fefferman in 2006.

In this talk, I will discuss a related conjecture: if a semialgebraic function on a closed subset of real n-space has a $C^m$ extension, then it has a semialgebraic $C^m$ extension. In particular, I will show that the $C^{1,\omega}$ case of the conjecture is true in a uniformly bounded way, for each semialgebraic modulus of continuity $\omega$. 

The proof is based on the existence of semialgebraic Lipschitz selections for certain affine-set valued maps and on a uniform semialgebraic version of Whitney’s extension theorem. This is joint work with Adam Parusinski.

 

Calendar entry

Event location

Sem. R. DB gelb 04
1040 Wien
Wiedner Hauptstraße 8 E105-4

 

Organiser

VADOR
vador@tuwien.ac.at

 

Public

No

 

Entrance fee

No

 

Registration required

No

AKOR Seminar: On the semialgebraic Whitney extension problem

Armin Rainer, TU Wien

In 1934, Whitney raised the question of how one can decide whether a function defined on a closed subset of real n-space is the restriction of a $C^m$ function on real n-space. He gave a characterization in dimension 1. The problem was fully solved by Fefferman in 2006.

In this talk, I will discuss a related conjecture: if a semialgebraic function on a closed subset of real n-space has a $C^m$ extension, then it has a semialgebraic $C^m$ extension. In particular, I will show that the $C^{1,\omega}$ case of the conjecture is true in a uniformly bounded way, for each semialgebraic modulus of continuity $\omega$. 

The proof is based on the existence of semialgebraic Lipschitz selections for certain affine-set valued maps and on a uniform semialgebraic version of Whitney’s extension theorem. This is joint work with Adam Parusinski.