The department's main fields of research include the development of efficient quasi-Monte Carlo methods to support numerical integration and approximation of functions as well as mathematical simulation in various fields of applications, particularly in the field of mathematical finance.

Quasi-Monte Carlo methods rely on - sometimes high-dimensional - point sets and sequences with particular distribution properties which are generated and analyzed with the help of number theoretical algorithms. The efficient generation and analysis of such point sets, but also the analysis of the resulting algorithms (complexity theory) are at the main focus of the department's research activity.

Other core areas include:

• developing and analyzing stochastic methods in the area of mathematical finance
• efficient use of (quasi-) Monte Carlo methods in finance
• analyzing derivative financial instruments and trading strategies

G. Larcher and F. Pillichshammer were speaker and co-speaker of the Austrian Science Fund-Special Research Area "Quasi-Monte Carlo Methods: Theory and Application", the project duration was from February 2014 to January 2023.