Research

My research follows two different directions. I am interested in the emerging field of topological data analysis and persistent homology which is a very active subfield of algebraic topology. Apart from that I am interested in applied questions related to uniform distribution of point sets, pseudorandomness and quasi-Monte Carlo integration.


I am interested in the very basic question of how to distribute points in a uniform manner in squares, on spheres or on more complicated shapes. Apart from that I enjoy to work on interdisciplinary projects with other scientists (such as biologists) in which the aim is to get geometric information about real world objects from digital images.




Publications in peer reviewed journals


            J21.       On the intriguing search for good permutations. Survey article dedicated to Henri Faure. To appear, Unif. Distr. Theor. arXiv

            J20.       (with U. Bauer) Persistent Betti numbers of random Cech complexes. Submitted. arXiv

            J19.       (with D. Vartziotis) On the symmetry of finite sums of exponentials. To appear, Elemente der Mathematik.

            J18.       (with S. Steinerberger) Heating a room with number theory. To appear, Mathematics Magazine. 

            J17.       (with M. Rachh, S. Steinerberger) Optimal Jittered Sampling for two points in the unit square. Stat. & Prob. Letters (132) 2018, 55-61. arXiv

 

            J16.       (with A. Topuzoglu) On the discrepancy of two families of permuted van der Corput Sequences. Unif. Distr. Theor. (13) 2018, no. 1, 47-64. journal

 

            J15.       (with Ch. Aistleitner, T. Lachmann) Pair correlations and equidistribution. J. Number Theory (182) 2018, 206-220. arXiv

 

            J14.       Lattices Modulo N with long shortest distances. Elemente der Mathematik (72) 2017, 111-121.

 

            J13.       (with Ch. Aistleitner, R.F. Tichy, A.M. Svane) On functions of bounded variation. Math. Proc. Cambridge Philos. Soc. (162) 2017, 405-418. arXiv

 

            J12.       Bounds for the traveling salesman paths of two-dimensional modular lattices. Journal of Combinatorial Optimization(33) 2017, 1378-1394. arXiv

 

            J11      An accurate heuristic for a problem of Shparlinski. Experimental Mathematics (26) 2017, 72-76.

 

            J10.        (with S. Steinerberger) On the discrepancy of jittered sampling. Journal of Complexity (33) 2016, 199-216. arXiv

 

            J9.        (with H. Edelsbrunner) Approximation and convergence of intrinsic volumes. Advances in Mathematics (287) 2016, 674-703. preprint

 

            J8.        Uniformly distributed sequences in the orthogonal group and on the Grassmannian manifold. To appear, Math. Comput. Simulation. arXiv


            J7.         (with A.M. Svane) A Koksma-Hlawka inequality for general discrepancy systems. Journal of Complexity (31) 2015, 773-797.

 

            J6.         (with S. Steinerberger) Local Extrema in quantum chaos. Physics Letters A (379) 2015535-541. arXiv

 

            J5.         (with H. Edelsbrunner) Stable length estimates of tube-like shapes. J. Math. Imaging Vis. (50) 2014, 164-177. preprint

 

            J4.         Weak multipliers for generalized van der Corput sequences. J. de Théor. Nombres Bordeaux (24) 2012, no 3, 729-749.

 

            J3.         Elementary solutions of the Bernstein problem on two intervals. J. of Mathematical Physics, Analysis, Geometry (8) 2012, no 1, 63-78.

 

            J2.         (with W. Ch. Schmid) A lower bound for the diaphony of generalised van der Corput sequences in arbitrary base b. Unif. Distrib. Theory (6) 2011, no 2, 31-46.

 

            J1.         (with W. Ch. Schmid) A good permutation for one-dimensional diaphony. Monte Carlo Methods Appl.(16) 2010, 307-322.



Publications in conference proceedings


        C3.         (with A. Topuzoglu) Permutations of finite fields and uniform distribution modulo 1. 

                       Algebraic Curves and Finite Fields,edited by H. Niederreiter, A. Ostafe, D. Panario and A. Winterhof,Radon Series on Applied and Computational Mathematics16 (2014), 145-160.


        C2.         Van der Corput Sequences and Linear Permutations.

                       Electronic Notes in Discrete Mathematics (43) 2013, 43-50. (Abstract for Erdös Centennial)


        C1.         (with W. Ch. Schmid) On the Asymptotics of a Lower Bound for the Diaphony of Generalized van der Corput Sequences. 

                       Monte Carlo Methods and Applications, Proceedings of the 8th IMACS Seminar on Monte Carlo Methods, Borovets 2011, edited by K. Sabelfeld and I. Dimov (2012), Chapter 18, 163-169.



Theses

        T2.         On the approximation of intrinsic volumes. PhD thesis, IST Austria, 2015.

 

        T1.         Discrepancy of generalised van der Corput sequences. MSc thesis, University of  Salzburg, 2011.



Non Scientific Publications


        N3.         Löcher in der Mathematik. Invited article for the proceedings of the Gesprächswoche 2017 of Forum St. Stephan.

 

        N2.         Instant Insanity und andere wahnsinnig schwere Probleme. Contributed article for the proceedings of the Proscientia Summer Academy 2014, Mariazell, Austria.

 

        N1.         Revolutionen in der Mathematik. Contributed article for the proceedings of the Proscientia Summer Academy 2013, Szombathely, Hungary.


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