Assistant professor

Nicolaus Copernicus University in Toruń
Faculty of Mathematics & Computer Science
ul. Chopina 12/18,  87-100 TORUŃ, POLAND
E-mail address: robert.skiba@mat.umk.pl
Office: room F 304

Scientific interests

  • Qualitative theory of (nonautonomous) ordinary differential equations and difference equations (periodic and homoclinic solutions).
  • Topological methods in nonlinear analysis (topological degree, fixed point index, fixed point theorems, Fredholm theory).
  • Algebraic topology: homology and cohomology theories.
  • Differential inclusions and nonsmooth analysis.
  • Applications of K-theory in analysis.
  • Numerical discretization theory.

Publications

  1. R. Skiba, On the Lefschetz fixed point theorem for multivalued weighted mappings, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 40, 2001, 201-214.
  2. R. Skiba, Topological essentiality for multivalued weighted mappings, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 41, 2002, 131-145.
  3. J. Pejsachowicz, R. Skiba, Fixed point theory of multivalued weighted maps, Handbook of Topological Fixed Point Theory, Springer, Dordrecht, 2005, 217-263.
  4. R. Skiba, Graph-approximation of multivalued weighted maps, Topol. Methods Nonlinear Anal., 29, 2007, 119-161.
  5. R. Skiba, Fixed points of multivalued weighted maps, Lecture Notes in Nonlinear Analysis, vol. 9, Juliusz Schauder Center for Nonlinear Studies,Nicolaus Copernicus University, Toruń 2007, 1-148.
  6. R. Skiba, M. Ślosarski, On a generalization of absolute neighborhood retratcs, Topology and its Applications, 156 (2009) 697-709.
  7. W. Kryszewski, R. Skiba, A cohomological index of Fuller type for set-valued dynamical systems, Nonlinear Analysis, Theory, Methods & Applications, 75 (2012), 684-716.
  8. J. Pejsachowicz, R. Skiba, Global bifurcation of homoclinic trajectories of discrete dynamical systems, Central European Journal of Mathematics, 10(6) 2012, 2088-2109.
  9. J. Pejsachowicz, R. Skiba, Topology and homoclinic trajectories of discrete dynamical systems, Discrete Contin. Dyn. Syst. S, 6(4), 2013, 1077-1094.
  10. R. Skiba, Applications of weighted maps to periodic problems of autonomous differential equations, Topol. Methods Nonlinear Anal., 42(1) 2013, 9-49.
  11. R. Skiba, A cohomological index of Fuller type for parameterized set-valued maps in normed spaces, Central European Journal of Mathematics, 12(8) 2014, 1164-1197.
  12.  R. Skiba, N. WaterstraatThe Index Bundle and Multiparameter Bifurcation for Discrete Dynamical Systems, DCDS-A, 37(11), 2017, 5603-5629 (arXiv:1612.05837).
  13. C. Potzsche, R. Skiba, Global Continuation of Homoclinic Solutions, Zeitschrift fur Analysis und ihre Anwendungen, Volume 37 (2018), 159-187,DOI: 10.4171/ZAA/1608.
  14. C. Potzsche, R. Skiba, A Continuation Principle for Fredholm maps I:Theory and Basics, accepted in Mathematische Nachrichten.
  15. C. Potzsche, R. Skiba, A Continuation Principle for Fredholm maps II: Application to homoclinic solutions, accepted in Mathematische Nachrichten.
  16. R. Skiba,  On (co)homological classes and new homotopical invariants with applications to differential equations (in preperation).
  17. R. Skiba,N. Waterstraat, Fredholm theory of discrete dynamical systems and its applications to bifurcation theory (in preperation).
  18. R. Skiba, A new statement of the Ważewski Theorem for differential equations (in preperation).

Curriculum vitae

EDUCATIONAL BACKGROUND:

  •     Master of Mathematics (master thesis: “The Lefschetz fixed point Theorem and topological essentiality for multivalued weighted maps”), Nicolaus Copernicus University in Toruń, 2001, Poland.
  •     Doctor of Mathematics (dissertation: “Fixed points of multivalued weighted maps”), Nicolaus Copernicus University in Toruń, 2006, Poland.

EMPLOYMENT HISTORY:

  •     2005-2006: Assistant, Nicolaus Copernicus University in Toruń, Faculty of Mathematics and Computer Science.
  •     2006- : Assistant Professor (Adiunkt), Nicolaus Copernicus University in Toruń, Faculty of Mathematics and Computer Science, Toruń, Poland.

HONORS AND AWARDS:

  • Scholarship of the Minister of Science and High Education, 1999/2000.
  • Scholarship of the Minister of Science and High Education, 200/2001.
  • The best student of the Faculty of Mathematics and Computer Science from the Nicolaus Copernicus University in Toruń, 1999/2000.
  • The best graduate of the Faculty of Mathematics and Computer Science from the Nicolaus Copernicus University in Toruń, 2000/2001.
  • Award of the Rector of the Nicolaus Copernicus University in Toruń, 2007.
  • Award of the Rector of  the Nicolaus Copernicus University in Toruń, 2015.
  • Medal of the National Education Commission, 2018.
  • Award of the Rector of  the Nicolaus Copernicus University in Toruń, 2019.

SCIENTIFIC GRANTS:

  • 2003-2006: Participation in grant of State Committee for Scientific Research, KBN 2 P03A 015 25, “Topological fixed point theory and its applications in nonlinear analysis”.
  • 2007: Grant of Nicolaus Copernicus University, “Numerical methods in the study of homotopical invariants for weighted maps”.
  • 2009-2012: Participation in grant of Ministry of Science and Higher Education, MNiSW N N201 395137, “Topological invariants in nonlinear analysis”.
  • 2014-2017: Participation in grant of National Science Center (Poland), NCN 2013/09/B/ST1/01963, “Dynamics of nonlinear evolutionary equations - topological approach”.
  • 2017-2018: Grant of National Science Center (Poland), NCN DEC-2017/01/X/ST1/00889, “Continuations and global bifurcations of homoclinic trajectories for nonlinear problems”.

SELECTED RESEARCH TALKS:

1. Marina Franca (Italy), 1-5.09.2003, “Mathematical Foundation of Turbolent Viscous Flows”, Centro Internazionale Matematico Estivo, workshop.
2. Cetraro (Italy), 19-29.06.2004, “Nonlinear and Optimal Control Theory”, Centro Internazionale Matematico Estivo, workshop.
3. Będlewo (Poland), Banach Center of the Institute of Mathematics of the Polish Academy of Sciences, 26-30.06.2006, Jean Leray Centennial Conference, Topological Methods in Nonlinear Problems, talk: “Graph-approximation of multivalued weighted maps”.
4. Będlewo (Poland), Banach Center of the Institute of Mathematics of the Polish Academy of Sciences, 22-28.07.2007, Topological Theory of Fixed and Periodic Points TTFPP, talk: “Fixed points of multivalued weighted maps”.
5. Toruń (Poland), Nicolaus Copernicus University in Toruń, 10-14.09,2007, Fifth Symposium on Nonlinear Analysis, talk: “On the Lefschetz fixed point theorem for multivalued weighted carriers”.
6. Hannover (Germany), 1-5.09.2008, Leibniz Universität, Summer School Functional Analytic Methods in Partial Differential Equations, workshop.
7. Brno (Czech Republic), 20–24.06.2009, Masaryk University, Conference on Differential Equations and Their Applications (EQUADIFF 12), talk: “A cohomological index of Fuller type for dynamical systems”.
8. Dresden (Germany), 25-28.05.2010, The 8th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Dresden University of Technology, talk: “The Fuller index and Bifurcation points”.
9. Będlewo (Poland), Banach Center of the Institute of Mathematics of the Polish Academy of Sciences, 24-30.06.2012, Dynamics, Topology and Computations DyToComp12, poster: “Global bifurcation of homoclinic trajectories of discrete dynamical systems”.
10. Białystok (Poland), 21-26.07.2013, PODE 2013, Progress on Difference equations, talk: “Homoclinic trajectories of discrete dynamical systems”.
11. Madrid (Spain), 7-11.07.2014, The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications, talk: “Cohomological index of Fuller type and its applications”.
12. Poznań (Poland), 17-20.09.2014, Joint Meeting of the German Mathematical Society (DMV) and the Polish Mathematical Society (PTM), talk: “Homoclinic trajectories of discrete dynamical systems”.
13. Szeged (Hungary), 30.06-05.07.2015, 10th Colloquium on the Qualitative Theory of Differential Equations.
14. Berlin (Germany), Free University of Berlin, “Patterns of Dynamics”, 25-29.07.2016, talk: “Homotopy invariants in bifurcation theory for dynamical systems”.
15. Mogilev (Belarus), the Belarusian-Russian University, International scientific and practical seminar of the team supervisors: 23.02.2017, talk: ”A topological degree of Fuller type for periodic orbits”.
16. Amadora (Portugal), 05-09.06.2017, International Conference on Diferential & Diference Equations and Applications, talk: “Homoclinic solutions for discrete dynamical systems”.
17. Klagenfurt (Austria), The Alpen-Adria-Universität Klagenfurt, Institut fur Mathematik, 1-8.10.2017, talk: “Periodic solutions of differential equations without uniqueness”, research visit.
18. Klagenfurt (Austria), The Alpen-Adria Universitat Klagenfurt, Institut fur Mathematik, 04-19.09.2018, , research visit.
19. Canterbury (United Kingdom), University of Kent, School of Mathematics, Statistics & Actuarial Science, 05-14.06.2018, research visit.
20. Halle (Germany), Martin-Luther-Universitat Halle-Wittenberg, Faculty of Natural Sciences II - Chemistry, Physics and Mathematics, 02-10.06.2019, talk: ”Periodic solutions of differential equations without uniqueness”, research visit.
21. AGH University of Science and Technology, Kraków (Poland), "Dynamics, Equations and Applications", 16-20.09.2019 r., talk: "A Continuation Principle for Fredholm maps and its application to differential equations".

 

PROFESSIONAL ACTIVITY:

  • Member of the Organizing Committee, Conference: V Symposium on Nonlinear Analysis, 10-14.09.2007, Nicolaus Copernicus University in Toruń, Poland.
  • Member of the Organizing Committee, Conference: VI Symposium on Nonlinear Analysis, 7-9.09.2011, Nicolaus Copernicus University in Toruń, Poland.
  • Member of the Organizing Committee, Conference: East - West Conference on Mathematics Education, 04–08.08.2014, Warsaw, Poland.
  • Member of the Organizing Committee, Conference: VII Symposium on Nonlinear Analysis, 14-18.09.2015, Nicolaus Copernicus University in Toruń, Poland.
  • Member of the Organizing Committee, Conference: East West Conference on Mathematics Education 2015, 29.06-3.07.2015, Warsaw, Poland.
  • Organizer, International Mathematics Competition for Students: Mirror of the William Lowell Putnam Mathematical Competition, Nicolaus Copernicus University in Toruń, 2014, 2015, 2016, 2017, 2018, Toruń, Poland.
  • Member of the Organizing Committee, Conference: East - West Conference on Mathematics Education EWCOME 2017, 24-26.07.2017, Warsaw, Poland.
  • Member of the Organizing Committee, Conference: East - West Conference on Mathematics Education EWCOME 2018, 22-23.09.2018, Warsaw, Poland.
  • Member of the Organizing Committee, Conference: “Special Workshop on Nonlinear Analysis, Juliusz Schauder Medal Awarding Ceremony, Toruń, 21-23.05.2018”, Toruń, Poland.