Department of Analysis, Geometry and Topology was founded in 2016 as a result of merging three departments: of Functional Analysis, Nonlinear Mathematical Analysis, and Mathematical modelling of self-organization phenomena. Since 2022 the Head of the Department is PhD, Senior researcher Chernega Iryna.
The main research fields of the Department of analysis, geometry and topology are:
- The theory of polynomial and analytic mappings on Banach spaces;
- Spectral theory of unbounded operators and locally convex algebras;
- Differential-geometric, topological and algebraic structures associated with nonlinear dynamical systems on finite-dimensional and functional manifolds;
- Geometry of momentum mapping, geometry of symplectic, Kahler, hyperkahler, spinor and Poisson manifolds;
- Geometric, topological and combinatorial theory of graphs.
The results obtained within the research projects of the department were the basis for 10 doctoral theses and 34 PhD thesis , 7 monographs and many articles in leading national and foreign scientific journals.
Doctoral theses
- Pankov O.A. "Almost periodic solutions of nonlinear differential operator equations", 1988; speciality - 01.01.02 - differential equations.
- Ivashkovych S.M. "Extension of holomorphic and meromorphic maps into complex manifolds", 1993; speciality - 01.01.01 - mathematical analysis.
- Lopushansky O.V. "Semilimited and limited operators in spectral theory of locally convex algebras", 1994; speciality - 01.01.01 - mathematical analysis.
- Bobryk R.V. "Dynamical systems under rapidly changing random disturbances," 1994; speciality - 01.01.05 - Theory of Probability and Mathematical Statistics.
- Zagorodnyuk A.V. "Spaces and algebras of polynomial and analytic maps in infinite-dimensional Banach spaces", 2006; speciality - 01.01.01 - mathematical analysis.
- Plachta L.P. Knots invariants and surfaces in 3-dimensional space", 2008; speciality - 01.01.04 - geometry and topology.
Books
- Гахов Ф.Д., Черский Ю.И. Уравнения типа свертки. - М.: Наука, 1978 - 296.
- Панков А.А. Ограниченные и почти периодические решения нелинейных дифференциально операторных уравнений. - К.: Наукова думка, 1985 -184 с.
- Сироїд І.П. Комплекснозначний метод оберненої задачі розсіяння і дослідження несамоспряжених пар Лакса для системи кортевега-де Фріза. – Львів: Інститут прикладних проблем механіки і математики ім. Я.С. Підстригача НАН України, 2005. – 191 с.
- Prykarpatsky A.K., Mykytiuk I.V. “Algebraic aspects of integrability of nonlinear dynamical systems on manifolds”, Kiev, Naukova dumka, 1991, 287 p.
- Prykarpatsky A.K., Mykytiuk I.V. "Algebraic integrability of nonlinear dynamical systems on manifolds. Classical and quantum aspects". Math. and its Appl. V.443, Dordrecht, Boston, London, Kluwer Academic Publishers, 1998, 554 p.
- Hentosh O., Prytula M., Prykarpatsky A. Differential-geometric and Lie-algebraic foundations of investigating nonlinear dynamical systems on functional manifolds, Lviv, Ivan Franko Lviv National University Publishing, 2006, 408 p.
- Gadea Pedro M., Munoz Masque Jaime, Mykytyuk Ihor V. “Analysis and Algebra on Differentiable Manifolds”, Springer, A Workbook for Students and Teachers, Series: Problem Books in Mathematics, 2nd ed. 2013, 2013, XXV, 613 p. 68 illus., 38 in color.