Institute of Mathematics
ul. Wilcza 69 m 6
My PhD thesis, under the supervision of Radhakrishnan (Kit) Nair, concentrates on metric number theory in non-Archimedean settings.
For my CV, click here.
For my work experience, click here.
For my mathematical ancestry, click here.
For my mathematical education background, click here.
Keywords: Metric Number Theory, Diophantine Approximation, Continued Fractions, Dynamical Systems, Ergodic Theory, Iterated Function Systems, Shrinking Target Properties, Uniform Distribution of Sequences, Hausdorff Dimension, Fractal Geometry, Generalized Numeration System, Pisot Beta-Expansion, Tiling Dynamical Systems, Non-Archimedean Spaces, a-Adic Integers, p-Adic Numbers, and Formal Laurent Series over a Finite Field
My recent research has focused on the metrical theory of numbers in non-Archimedean settings. This is a branch of number theory that studies and characterizes sets of numbers, which occur in a locally compact topological field endowed with a non-Archimedean absolute value. This is done from a probabilistic or measure-theoretic point of view. The central theme of this theory is to determine whether a given arithmetic property holds everywhere except on an exceptional set of measure zero. Also, the metric theory of numbers includes the study of the complexity of those exceptional sets in terms of Hausdorff dimension. Nowadays, the theory is deeply intertwined with measure theory, ergodic theory, dynamical systems, fractal geometry and other areas of mathematics. My research emphasized the study of non-Archimedean settings, such as the a-adic integers, the p-adic numbers and the formal Laurent series over a finite field, which possess different geometric nature from the classical real numbers. It also aimed to make contributions to various fields, including subsequence ergodic theory, continued fractions, Diophantine approximation and uniform distribution theory, of the non-standard metric number theory.
Currently, I am venturing further afield to extend the lines of research, e.g. fractals and iterated function systems, metric Diophantine approximation and shrinking target properties, ergodic theory and analytic number theory, and self-inducing systems and Pisot numbers.
* Note that "(-) = not confirmed to attend" and "(Confirmed) = confirmed to attend."
For the preprint/abstract of each paper, see Papers and Talks.
Papers in Preparation and Preprints
 "Distribution functions for subsequences of generalised van der Corput sequences," (with A. Jaššová, R. Nair and M. Weber), in submission.
 "The Halton sequence and its discrepancy in a generalized numeration system," (with A. Jaššová and R. Nair), in submission.
 "Polynomial actions in positive characteristic II," (with J. Hančl, A. Jaššová, and R. Nair), in submission.
 "Quantitative metric theory of continued fractions in positive characteristic," (with R. Nair), in submission.
 "On the quantitative metric theory of continued fractions," (with J. Hančl, A. Jaššová, and R. Nair), to appear in Proc. Indian Acad. Sci. Math. Sci.
 "On variants of the Halton sequence," (with A. Jaššová and R. Nair), to appear in Monatsh. Math.; first published online 26 July 2015 at http://dx.doi.org/10.1007/s00605-015-0794-8.
 "On recurrence in positive characteristic," (with A. Jaššová, S. Kristensen, and R. Nair), Indag. Math. (N.S.), 26(2):346-354, 2015; http://dx.doi.org/10.1016/j.indag.2014.11.003.
 "On the metric theory of numbers in non-Archimedean settings," Ph.D. Thesis, University of Liverpool (UK), 2014; http://repository.liv.ac.uk/2006661/.
 "On the metric theory of continued fractions in positive characteristic," (with R. Nair), Mathematika, 60(2):307-320, 2014; http://dx.doi.org/10.1112/S0025579314000114.
 "On the complexity of the Liouville numbers in positive characteristic," (with R. Nair), Q.J. Math., 65(2):439-457, 2014; http://dx.doi.org/10.1093/qmath/hat019.
 "Distribution functions for subsequences of the van der Corput sequence," (with R. Nair), Indag. Math. (N.S.), 24(3):593-601, 2013; http://dx.doi.org/10.1016/j.indag.2013.03.006.
 "On the metric theory of p-adic continued fractions," (with J. Hančl, A. Jaššová, and R. Nair), Indag. Math. (N.S.), 24(1):42-56, 2013; http://dx.doi.org/10.1016/j.indag.2012.06.004.
 "Polynomial actions in positive characteristic," (with J. Hančl, A. Jaššová, and R. Nair), Proc. Steklov Inst. Math., 280(suppl.2):37-42, 2013; http://dx.doi.org/10.1134/S0081543813030048.
 "Polynomial actions in positive characteristic," (with J. Hančl, A. Jaššová, and R. Nair), Mathematics and Informatics, 1, Dedicated to 75th Anniversary of Anatolii Alekseevich Karatsuba, Sovrem. Probl. Mat., 16, Steklov Math. Inst., RAS, Moscow, 45-51, 2012; http://dx.doi.org/10.4213/spm33.
I have become a reviewer for Mathematical Reviews since July 2015. The following are papers under my review:
 MR3370709: K. Dajani, C. Kraaikamp and N.D.S. Langeveld, "Continued fraction expansions with variable numerators", Ramanujan J. 37(3):617-639, 2015.
 MR3330565: H. Kaneko, "Applications of numerical systems to transcendental number theory", Numeration and Substitution 175-186, 2012, RIMS Kôkyûroku Bessatsu, B46, Res. Inst. Math. Sci. (RIMS), Kyoto, 2014.
 MR3347994: H. Li, "Effective limit distribution of the Frobenius numbers", Compos. Math. 151(5):898-916, 2015.
 MR3346478: L. Shen and T. Zhong, "How the parameter ɛ influence the growth rates of the partial quotients in GCFɛ expansions," J. Korean Math. Soc. 52(3):637-647, 2015.
 MR3343454: H. Inoue and K. Naito, "Entropy and recurrent dimensions of discrete dynamical systems given by p-adic expansions," p-Adic Numbers Ultrametric Anal. Appl. 7(2):157-167, 2015.