ADAM BOBROWSKI

Stopień, tytuł naukowy, stanowisko

doktor habilitowany, profesor Politechniki Lubelskiej, kierownik katedry

Nr telefonu w miejscu zatrudnienia

52 42 599, 53 81 364

Adres poczty elektronicznej

a.bobrowski@pollub.pl, adambob@antenor.pol.lublin.pl

Specjalność naukowa

analiza funkcjonalna, zastosowania matematyki

Zakres prowadzonych badań naukowych

Modele matematyczne w genetyce

Inne  dane

 

 

My background is in functional analysis and stochastic processes. My interests in these fields were shaped by professors Tadeusz Leżanski and Andrzej Lasota. After graduation from Maria Curie Skłodowska University (with distinction), I had a privilege to study semigroup theory under professor Jan Kisyński, who also was my PhD advisor. My interest in problems of convergence of semigroups of operators and generalizations of the Hille-Yosida theorem to non-densely defined operators (a theory involving integrated and regularized semigroups, and inverting of the Laplace transform for vector-valued functions) have grown out of my collaboration with him. In 1997 I moved to Houston, TX where I was affiliated with Rice University, University of Texas (Medical Center) and University of Houston. It is there that I became interested in problems of mathematical modeling in biology (seminar). In particular, I worked with professors Marek Kimmel and Ranajit Chakraborty, on models involving genetic drift or, viewed backwards, Kingman's coalescence (M. Moehle's page). In 2002 I returned to Lublin, Poland and to Technical University I have been affiliated with since 1988.
I am still active in both fields of research mentioned above, though I tend to spend more time studying the later subject. I am a co-chair of  Applications of Mathematics group of researchers from Maria Curie - Sklodowska University, Lublin and Lublin University of Technology.

Personal data: I have a wife, Beata and two sons Radek (picture with our dog, named Gooseberry) and Marek .

Publications in Pure Mathematics:

  1. Bobrowski, A. (1992), ``Some Remarks on the Two- dimensional Dirac Equation'', Semigroup Forum Vol. 45, 77-91.
  2. Bobrowski, A. (1993), ``Computing the Distribution of the Poisson-Kac Process", Annales UMCS Vol. XLVII, 1 Sec. A, 1-17.
  3. Bobrowski, A. (1994), ``Degenerate Convergence of Semigroups", Semigroup Forum. Vol. 49, 303-327.
  4. Bobrowski, A. (1994), ``Integrated Semigroups and the Trotter - Kato Theorem", Bull. Polish Acad. Sci. Vol. 41, No 4, 297 - 303.
  5. Bobrowski, A. (1995), ``Examples of a Pointwise Convergence of Semigroups", Annales UMCS Vol. XLIX, Sec. A, 15-33.
  6. Bobrowski, A. (1996), ``Generalized Telegraph Equation and the Sova-Kurtz Version of the Trotter-Kato Theorem", Ann. Polon. Math.Vol. LXIV.1, 37 - 45.
  7. Bobrowski, A. (1997), ``On the Generation of Non-continuous Semigroups", Semigroup Forum Vol. 54, 237-252.
  8. Bobrowski, A. (1997), ``On the Yosida Approximation and the Widder - Arendt Theorem'', Studia Mathematica 124(3), 281-290.
  9. Bobrowski, A. (1997), ``The Widder-Arendt Theorem on Inverting of The Laplace Transform and Its Relationship With The Theory of Semigroups of Operators'', Methods Funct. Anal. Topology, Vol.3, No.4, 1-39.
  10. Bobrowski, A. (1998), ``On Approximation of (1.A) Semigroups by Discrete Semigroups'', Bull. Polish Acad. Sci. Vol
    46 No 2, 142-154.
  11. Bobrowski, A. (1998), ``A Note on Convergence of Semigroups'', Ann. Polon. Math. Vol LXIX.2, 107-127.
  12. Bobrowski, A., (2001) ``Notes on the Algebraic Version of the Hille - Yosida - Phillips - Miyadera Theorem'', Houston J. of Mathematics, Vol 27, No 1, 75-95.
  13. Bobrowski, A., (2001) ``Inversion of the Laplace Transform and Generation of Abel Summable Semigroups'', J. Funct. Anal., Vol 186, No 1, 1-24.
  14. Bobrowski, A. and Kubalińska, M., (2006), ``On a Functional Equation with Derivative and Symmetrization”, Ann. Polon. Math. 89.1, 13-24.

 

Publications in Applied Mathematics

  1. Bobrowski, A., Kimmel, M., (1999), ``Asymptotic Behaviour of a Semigroup Related to Branching Random Walk Models of DNA Repeats'', J. Biol. Systems Vol 7 No 1, 33-43.
  2. Świerniak, A., Polański, A., Kimmel, M., Bobrowski, A., \'Smieja, J. (1999) ``Qualitative Analysis of Controlled Drug Resistance Model - Inverse Laplace and Semigroup Approach", Control and Cybernetics Vol 27 No 1, 61-73.
  3. Bobrowski, A., Kimmel, M., (1999) ``Dynamics of the Life History of a DNA-repeat Sequence", Archives of Control Sciences, Vol 9 (XLV), No 1-2, 57-67.
  4. Bobrowski, A., Kimmel, M., Chakraborty, R., Arino, O., (2001) ``A Semigroup Representation and Asymptotic Behavior of The Fisher-Wright-Moran Coalescent", Chapter 8 in ``Handbook of Statistics 19: Stochastic Processes: Theory and Methods'', C.R. Rao and D.N. Shanbhag, eds., Elsevier Science, Amsterdam.
  5. Bobrowski, A., Wang, N., Kimmel, M., Chakraborty, R. (2002), ``Nonhomogeneous Infinite Sites Model under Demographic Change: Mathematical Description and Asymptotic Behavior of Pairwise Distributions," Mathematical Biosciences 175, 83-115.
  6. Polański, A., Bobrowski, A. and Kimmel, M., (2003) ``A Note on Distributions of Times to Coalescence, Under Time - Dependent Population Size". Theoretical Population Biology Vol 63, No. 1, 33 - 40.
  7. Bobrowski, A., Kimmel, M., (2003) ``A Random Evolution Related to a Fisher - Wright - Moran Model With Mutation, Recombination and Drift". Mathematical Methods in the Applied Sciences 26, 1587-1599.
  8. Bobrowski, A., ``Quasi-stationary Distributions of a Pair of Markov Chains Related to Time Evolution of a DNA Locus.'' Adv. Appl. Prob 36, (2004), 57-77.
  9. Bobrowski, A., Kimmel, M., ``Asymptotic behavior of joint distributions of characteristics of a pair of randomly chosen individuals in discrete - time Fisher - Wright models with mutations and drift", Theoretical Population Biology 66(4), 355-367. 

To appear soon:

  1. Bobrowski, A. (2006), ``Degenerate Convergence of Semigroups Related to a Model of Stochastic Gene Expression,” to appear in Semigroup Forum.
  2. Bobrowski, A. (2006), ``On Limitations and Insufficiency of the Trotter-Kato Theorem”, to appear in Semigroup Forum.

 

 

Books:

1. Translation of J.F.C Kingman's ``Poisson Processes" into Polish, Wydawnictwo PWN: Warsaw 2001.

2. “Functional Analysis for Probability and Stochastic Processes”, Cambridge University Press, 2005.

 

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A simple simulation of interplay of genetic drift and mutations. A model due to J.F.C Kingman, the program written by P. Wlaz.