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.

12. December 2024, 15:00 until 17:00

AKOR Seminar: On the regularity of the solution map for polynomials

Seminar

Armin Rainer, VADOR, TU Wien

How do the roots of a monic polynomial whose coefficients depend smoothly on parameters depend on those parameters? This question plays an important role in many areas, e.g., PDEs, perturbation theory of linear operators, and local smooth analysis.   The subject, which started with Rellich’s work in the 1930s, enjoyed sustained interest through time that intensified in the last two decades, bringing some definitive optimal results. In particular, if the coefficients are of class $C^{d-1,1}$, where $d$ is the degree  of the polynomial, then any continuous root is of Sobolev class $W^{1,q}$, for each $1 \le q < d/(d-1)$. In this talk, I will discuss this optimal result and recent work  investigating the continuity of the solution map “coefficients-to-roots”. 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 regularity of the solution map for polynomials

Armin Rainer, VADOR, TU Wien

How do the roots of a monic polynomial whose coefficients depend smoothly on parameters depend on those parameters? This question plays an important role in many areas, e.g., PDEs, perturbation theory of linear operators, and local smooth analysis.   The subject, which started with Rellich’s work in the 1930s, enjoyed sustained interest through time that intensified in the last two decades, bringing some definitive optimal results. In particular, if the coefficients are of class $C^{d-1,1}$, where $d$ is the degree  of the polynomial, then any continuous root is of Sobolev class $W^{1,q}$, for each $1 \le q < d/(d-1)$. In this talk, I will discuss this optimal result and recent work  investigating the continuity of the solution map “coefficients-to-roots”. Joint work with Adam Parusinski