Poj Lertchoosakul

"In Mathematics, you don't understand things. You just get used to them." (J. von Neumann)

My homepage has been moved to the following new site:

Poj Lertchoosakul

Deparmental Address:

Institute of Mathematics
Polish Academy of Sciences
ul. Śniadeckich 8
00-656 Warszawa
Poland
Tel: +48 22 522 81 52
E-mail: p.lertchoosakul(at)impan(dot)pl

 


 

Home Address:

ul. Wilcza 69 m 6
00-679 Warszawa
Poland 
Mobile: +48 886 344 577
E-mail: lertchoosakul(at)hotmail(dot)com


Sketched by Kit Nair (9 Oct 2012)

Bibliography

My PhD thesis, under the supervision of Radhakrishnan (Kit) Nair, concentrates on metric number theory in non-Archimedean settings.

From October 2013, I also hold a research fellow working with Michał Rams at IM PAN, Warsaw, Poland. The position is now promoted to a non-tenured assistant professor.

For my CV, click here.

For my work experience, click here

For my mathematical ancestry, click here.

For my mathematical education background, click here.

          

Research Interest

Keywords: Metric Number Theory, Diophantine ApproximationContinued FractionsDynamical Systems, Ergodic TheoryIterated Function Systems, Shrinking Target Properties, Uniform Distribution of SequencesHausdorff 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.

  
  

Related Meetings

Regular Attender
Interesting Upcoming Meetings

* Note that "(-) = not confirmed to attend" and "(Confirmed) = confirmed to attend."
  

Attended Meetings



Publications (available on an appropriate request)

For the preprint/abstract of each paper, see Papers and Talks.

Papers in Preparation and Preprints 

[12] "Distribution functions for subsequences of generalised van der Corput sequences," (with A. Jaššová, R. Nair and M. Weber), in submission.

[11] "The Halton sequence and its discrepancy in a generalized numeration system," (with A. Jaššová and R. Nair), in submission.

[10] "Polynomial actions in positive characteristic II," (with J. Hančl, A. Jaššová, and R. Nair), in submission.

[9] "Quantitative metric theory of continued fractions in positive characteristic," (with R. Nair), in submission. 

2015  

[8] "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.

[7] "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.

[6] "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.

2014  

[0] "On the metric theory of numbers in non-Archimedean settings," Ph.D. Thesis, University of Liverpool (UK), 2014; http://repository.liv.ac.uk/2006661/.

[5] "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.

[4] "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. 

2013 

[3] "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.

[2] "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.

[1] "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. 

2012 

[1] "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. 
  

 

MathSciNet Reviewer

I have become a reviewer for Mathematical Reviews since July 2015. The following are papers under my review:

[5] MR3370709: K. Dajani, C. Kraaikamp and N.D.S. Langeveld, "Continued fraction expansions with variable numerators", Ramanujan J. 37(3):617-639, 2015.

[4] 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.

[3] MR3347994: H. Li, "Effective limit distribution of the Frobenius numbers", Compos. Math. 151(5):898-916, 2015.

[2] 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.

[1] 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.

 

  

 

Poj Lertchoosakul, P. Lertchoosakul, พจน์ เลิศชูสกุล (Born in Chiang Mai, Thailand)
Assistant Professor at IM PAN, Warszawa, Poland