### Project 09: "Diophantine approximation and combinatorial problems"

*This project is running since 2010.*

Principal investigator: Robert Tichy

Graz University of Technology, Austria.

*Mentor for*: Planitzer; Bazarova, Raseta, Smertnig.

Associated scientist: István Berkes (since 2015)

Graz University of Technology, Austria.

*Mentor for*: Candellero, Iaco, Temmel.

Associated scientist: Christian Elsholtz (2010–2014)

Graz University of Technology, Austria.

He is now principal investigator of project 13.

Associated scientist: Sophie Frisch (since 2010)

Graz University of Technology, Austria.

### DK Students

**Second phase of the doctoral program:****Niclas Technau**(Germany; since May 2015)

*Email*: technau@math.tugraz.at

*Mentors*: Christian Elsholtz, Mario Weitzer.**First phase of the doctoral program:**-
**Fabrizio Barroero**(Italy; October 2010–November 2013)

Personal homepage;*Email*: barroero@math.tugraz.at

*Mentors*: Alfred Geroldinger, Clemens Heuberger.

*PhD Defense*: November 22, 2013.

*Referees*: C. Fuchs (Salzburg), R. Tichy, J. Vaaler (Austin).

*Examiners*: C. Fuchs (Salzburg), R. Tichy.

### Associated Students

**Second phase of the doctoral program:****Mahadi Ddamulira**(Uganda; since November 2017)

*Email*: mddamulira@tugraz.at

*Mentors*: Christian Elsholtz, Christoph Aistleitner**Kwok Chi Chim**(Hongkong; since September 2014)

*Email*: chim@math.tugraz.at

*Mentors*: Gisbert Wüstholz, Christopher Frei.**Adrian Scheerer**(Germany; January 2014–April 2017)

*Email*: scheerer@math.tugraz.at

*Mentors*: Jörg Thuswaldner, Manfred Madritsch.**First phase of the doctoral program:**-
**Christopher Frei**(Austria; October 2009–October 2011)

Personal homepage;*Email*: frei@math.tugraz.at

*Mentors:*Clemens Heuberger, Johannes Wallner.

*PhD Defense*: October 11, 2011.

*Referees*: G. Lettl (KFU Graz), R. Tichy.

*Examiners*: G. Lettl (KFU Graz), R. Tichy. -
**Maria Rita Iacò**(Italy; October 2012–December 2014)

*Email*: iaco@mat.unical.it

*Mentors*: Istvan Berkes, Christian Elsholtz.

*PhD Defense*: December 10, 2014.

*Referees*: L. Colzani (Milano), M. Drmota (Vienna)

*Examiners*: I. Carbone (Calabria), L. Colzani (Milano), M. Drmota (Vienna), R. Tichy. -
**Dijana Kreso**(Croatia; October 2010–March 2014)

Personal homepage;*Email*: kreso@math.tugraz.at

*Mentors:*Christian Elsholtz, Alfred Geroldinger

*PhD Defense*: March 21, 2014.

*Referees*: A. Dujella (Zagreb), C. Fuchs (Salzburg), R. Tichy.

*Examiners*: A. Dujella (Zagreb), R. Tichy.

*PhD Defense*: April 24, 2017.

*Referees*: S. Thonhauser (TU Graz), P. Grabner (TU Graz), J. Thuswaldner (MU Leoben).

*Examiners*: P. Grabner (TU Graz), J. Thuswaldner (MU Leoben).

### Project description (pdf-file)

The research of Tichy is focussed on the following topics: Diophantine equations and approximation, ergodic and dynamic methods in number theory, fractal structures in number theory, combinatorial and additive number theory, algorithms and pseudo-randomness, stochastic methods, discrepancy and uniform distribution modulo 1, numeration systems, sequences and automata, harmonic analysis and exponential sums, multivariate approximation and energy functionals, asymptotic analysis of combinatorial algorithms, counting problems on graphs and applications in computational chemistry, stochastic modelling and simulations in finance and insurance. Tichy is also a member of the SFB project "Quasi Monte Carlo Methods and Applications".