Marta Tyran-Kamińska

Marta Tyran-Kamińska
Institute of Mathematics
University of Silesia
Bankowa 14
40-007 Katowice
Poland
E-mail: mtyran@us.edu.pl
New webpage

PhD in Mathematics: 1999 University of Silesia
Habilitation in Mathematics: 2011 University of Silesia
Professor in Natural Sciences: 2020

Research

Research interests: Ergodic Theory, Limit theorems, Markov processes in Physics and Biology

Books:

• (with Michael C. Mackey, Moises Santillan, Eduardo S. Zeron), Simple Mathematical Models of Gene Regulatory Dynamics, Lecture Notes on Mathematical Modelling in the Life Sciences, Springer International Publishing, Cham, 2016. Link to publisher
• (with Ryszard Rudnicki), Piecewise Deterministic Processes in Biological Models, SpringerBriefs in Applied Sciences and Technology, Springer International Publishing, Cham, 2017. Link to publisher

Selected publications:

• Stability of Markov processes nonhomogeneous in time, Annales Polonici Mathematici, 71 (1999) 47-59.
• (with Ryszard Rudnicki and Katarzyna Pichór), Markov semigroups and their applications, in: Dynamics of Dissipation, eds.: P. Garbaczewski, R. Olkiewicz, Lectures Notes in Physics 597, Springer-Verlag, Berlin (2002) 215-238.
• Support overlapping Markov semigroups, Bulletin Polish Acad. Sci. Math. 51 (2003) 419-438.
• An invariance principle for maps with polynomial decay of correlations, Communications in Mathematical Physics 260 (2005) 1-15.
• (with Michael C. Mackey), Deterministic Brownian motion: The effects of perturbing a dynamical system by a chaotic semi-dynamical system, Physics Reports 422 (2006) 167-222.
• (with Michael C. Mackey), Temporal Behavior of the Conditional and Gibbs' Entropies, Journal of Statistical Physics 124 (2006) 1443-1470.
• (with Michael C. Mackey), Central limit theorems for non-invertible measure preserving maps, Colloqium Mathematicum 110 (2008), 167-191.
• (with Michael C. Mackey), Central limit theorem behaviour in the skew tent map, Chaos, Solitons, and Fractals 38 (2008), 789-805.
• (with Michael C. Mackey), Dynamics and density evolution in piecewise deterministic growth processes, Annales Polonici Mathematici 94 (2008), 111-129. pdf file
• Substochastic semigroups and densities of piecewise deterministic Markov processes, Journal of Mathematical Analysis and Applications 357 (2009), 385-402. pdf file
• Ergodic theorems and perturbations of contraction semigroups, Studia Mathematica 195 (2009), 147-155. pdf file
• Weak convergence to Levy stable processes in dynamical systems, Stochastics and Dynamics 10 (2010), 263-289. pdf file
• Convergence to Levy stable processes under some weak dependence conditions, Stochastic Processes and their Applications 120 (2010), 1629-1650. pdf file
• Functional limit theorems for linear processes in the domain of attraction of stable laws, Statistics and Probability Letters 80 (2010), 975-981. pdf file
• (with Michael C. Mackey and Romain Yvinec), Molecular distributions in gene regulatory dynamics Journal of Theoretical Biology 274 (2011), 84-96. Link to: published paper arXiv e-print
• (with Katarzyna Pichór and Ryszard Rudnicki), Stochastic semigroups and their applications to biological models, Demonstratio Mathematica 45 (2012), 463-494. Link to: published paper
• (with Michael C. Mackey and Hans-Otto Walther), The Mathematical Legacy of Andrzej Lasota, Wiadomości Matematyczne 48 (2012), 143-156, in the special issue on the ocassion of 6th European Congress of Mathematics
• (with Michael C. Mackey, Romain Yvinec), Dynamic behavior of stochastic gene expression models in the presence of bursting SIAM Journal on Applied Mathemtaics 73 (2013), no. 5, 1830-1852. Link to: published paper
• Diffusion and deterministic systems, Mathematical Modelling of Natural Phenomena 9 (2014), 32–43. Link to: published paper
• (with Michael C. Mackey, Moises Santillan, Eduardo S. Zeron), The utility of simple mathematical models in understanding gene regulatory dynamics, In Silico Biology 12 (2012-2014), 23-53. Link to: published paper
• (with Ryszard Rudnicki), Piecewise deterministic Markov processes in biological models, in: Semigroup of Operators – Theory and Applications, J. Banasiak et al. (eds.), Springer Proceedings in Mathematics & Statistics 113, (2015), pp. 235-255. Link to published paper and to e-print
• (with Weronika Biedrzycka), Existence of invariant densities for semiflows with jumps, Journal of Mathematical Analysis and Applications 435 (2016), 61-84. Link to published paper and to arXiv e-print
• (with Michael C. Mackey), The limiting dynamics of a bistable molecular switch with and without noise, Journal of Mathematical Biology 73 (2016), 367-395. Link to published paper and to arXiv e-print
• (with Michael C. Mackey and Hans-Otto Walther), Response of an oscillatory differential delay equation to a single stimulus, Journal of Mathematical Biology 74 (2017), 1139-1196. Link to published paper and to arXiv e-print
• (with Weronika Biedrzycka), Self-similar solutions of fragmentation equations revisited, Discrete and Continuous Dynamical Systems - Series B 23 (2018), no. 1, 13-27. Link to published paper and to arXiv e-print
• (with Paweł Klimasara) A model for random fire induced tree-grass coexistence in savannas, Mathematica Applicanda 46 (2018), 87-96. Link to published paper and to arXiv e-print
• (with Mateusz Falfus, Michael C. Mackey), The combined effects of Feller diffusion and transcriptional/translational bursting in simple gene networks, Journal of Mathematical Analysis and Applications 470 (2019), 931-953. Link to published paper and to arXiv e-print
• (with Piotr Gwiżdż) Positive semigroups and perturbations of boundary conditions, Positivity 23 (2019), 921-939. Link to published paper and to arXiv e-print
• (with Piotr Gwiżdż) Densities for piecewise deterministic Markov processes with boundary, Journal of Mathematical Analysis and Applications 479 (2019), 384-425. Link to published paper and to arXiv e-print

Some preprints are at arXiv. Link to search results

Meetings

• XXV Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie Jadwisin, Poland, September 16-20, 2019
• Jubileuszowy Zjazd Matematyków Polskich w stulecie PTM Kraków, Poland, September 3-7, 2019
• BIOMATH Będlewo, Poland, June 16-20, 2019
• Semigroups of Operators: Theory and Applications Kazimierz Dolny, Poland, September 30 - October 5, 2018
• UMI-SIMAI-PTM Joint Meeting Wrocław, Poland, September 17-20, 2018
• XXIV Krajowa Konferencja Zastosowań Matematyki w Biologii i Medycynie Zakopane-Kościelisko, Poland, September 3-7, 2018
• LVIII Szkoła Matematyki Poglądowej Wola Ducka, Poland, August 23-28, 2018
• XV Konferencja z Probabilistyki Będlewo, Poland, May 21-25, 2018
• Simons Semester on Mathematical Biology Banach Center, Warsaw, 1 December 2017 - 31 March 2018
• From individual based models to structured population level description Będlewo, Poland, March 12-16, 2018
• Information transmission in biological systems Będlewo, Poland, March 5-9, 2018
• BioPhysMath Warsaw, December 7-9, 2017
• NHOC2017 Porto, Portugal, July 3-5, 2017
• Śladami kobiet w matematyce: w stulecie urodzin profesor Heleny Rasiowej Rzeszów, Poland, June 22-24, 2017
• PDMPs, Theory and applications Seillac, France, May 29-June 2, 2017
• BioFizMat6 Warsaw, Poland, May 26-27, 2017
• BioFizMat5 Warsaw, Poland, December 8-9, 2016
• 7th Forum of Polish Mathematicians Olsztyn, Poland, September 12-17, 2016
• Dynamical Systems and Applications, Łódź, Poland, June 16-18,2016
• Statistical properties of dynamical systems Workshop at the Erwin Schrödinger Institute, Vienna, May 9-13, 2016
• Evolution equations: theory and applications Besancon, France, March 23-2, 2015
• ECMTB 2014 9th European Conference on Mathematical and Theoretical Biology, Gothenburg, June 15-19, 2014
• In honour of Michael Mackey's 70th birthday Lyon, France, June 3-6, 2013
• Thematic program: Mathematical Biology Lyon, France, March 4 - June 14, 2013
• Mini-symposium How mathematics illuminates biology at 6th European Congress of Mathematics Kraków, July 2-7, 2012
• Workshop on Infinite Ergodic Theory University of Surrey, UK, 28 May to 1 June 2012
• ECMTB 2011 8th European Conference on Mathematical and Theoretical Biology, and Annual Meeting of The Society for Mathematical Biology, Kraków, June 28-July 2, 2011
• XI Konferencjaz Probabilistyki Będlewo, Poland, May 24-28, 2010
• Workshop on Limit Theorems Prague, August 3 - 6, 2009
• Ergodic Theory - Limit Theorems and Dimensions Workshop at the Erwin Schrödinger Institute, Vienna, December 17-21, 2007
• Workshop Deconstructing Biochemical Networks Centre de Recherche Mathematiques, Universite de Montreal, Montreal, Canada, September 24-28, 2007
• 9th Rencontres Mathematiques de Rouen Ergodic Theory and Limit Theorems Rouen, France, June 11-14, 2007
• London Mathematical Society Durham Symposium: Dynamical Systems and Statistical Mechanics University of Durham, UK, July 3-13, 2006
• International Centre for Mathematical Sciences, Workshop on Probabilistic Limit Laws for Dynamical Systems Edinburgh, UK, June 13-17, 2005

Teaching

Spring 2018/2019
Functional Analysis for Markov Processes
Elements of Statistics A
Office hours: see here

Winter 2018/2019
Introducion to Computer Science - access requires a user and password

Year 2017/2018
Assistant Professor at Institute of Mathematics Polish Academy of Sciences

Spring 2016/2017
Piecewise deterministic processes

Winter 2016/2017
Biomathematics

Spring 2015/2016
Piecewise deterministic processes

Winter 2015/2016
Dynamical System
Biomathematics

Spring 2014/2015
Biomathematics

Winter 2014/2015
Dynamical System
Piecewise deterministic processes
Biomathematics

Spring 2013/2014
Biomathematics

Winter 2013/2014
Dynamical Systems
Piecewise deterministic processes
Biomathematics

Spring 2012/2013
Dynamical Systems
Biomathematics
Risk in Insurance

Winter 2012/2013
Biomathematics
Deterministic Chaos and Randomness

Spring 2011/2012
Probability Theory
Dynamical Systems
Risk in Insurance

Winter 2010/2011
Probability Theory
Stochastic Processes

Winter 2009/2010
Stochastic Processes
Risk and Insurance

Spring 2007/2008
Mathematical Statistics

Winter 2007/2008
Assistant Professor at Institute of Mathematics Polish Academy of Sciences

Spring 2006/2007
Probability Theory
Computer Science