Analysis, Geometry and Topology
Academic Staff
Main Staff
Several complex variables Lie theory, reductive and semisimple Lie groups, linear representations and actions on manifolds. Geometry of flag varieties. Geometric Invariant Theory. Differential, algebraic and symplectic geometry, topology and mathematical physics. Stability of nonlinear waves, nonlinear dispersive equations, inverse scattering theory Fractional calculus; Fractional differential and integral equations: operator-theoretical approach, qualitative properties of solutions. Convolutional calculus: Duhamel-type representations for nonlocal boundary-value problems. Differential geometry of Riemannian manifolds, differential geometry of surfaces and hypersurfaces in Euclidean or Minkowski spaces, local theory of surfaces in pseudo-Euclidean spaces with neutral metric. Differential Geometry and its connections to Algebraic Geometry, Complex Analysis and Theoretical Physics Infinite-dimensional topology, Geometric Tomography/Topology, Geometry of Banach spaces, Convexity, Topological vector spaces, Selection theory.
Nikolov, Nikolai
Corresponding Member of BAS, Professor, D.Sc., Chairman of the Scientific Council of IMI, Head of Department AGT, Vice President of the UBM
Tsanov, Valdemar
Associate Professor, PhD, Secretary of Department AGT
Katzarkov, Ludmil
Corresponding Member of BAS, Professor, D.Sc.
Hakkaev, Sevdzhan
Professor, D.Sc.
Bazhlekova, Emilia
Professor, D.Sc.
Milousheva, Velichka
Professor, PhD, Deputy Director of IMI
Grantcharov, Gueo
Professor, PhD
Barov, Stoyu
Associate Professor, PhD
Shkolnikov, Mihail
Associate Professor, PhD
Additional Staff
Complex differential geometry, algebraic geometry, global analysis. Research interests: Set-valued mappings, selections, hyperspaces, absolute extensors and retracts, embedding-like properties, finite-dimensional and infinite-dimensional spaces. Fractional Calculus, Special Functions, Integral Transforms, Differential Equations. Approximations by rational functions in the complex plane: Pade approximation, best rational approximation, orthogonal polynomials, rate of approximation; complex analysis, potential theory, numerical analysis, mathematical modelling. Several complex variables, Analysis on complex and almost complex manifolds, Complex differential geometry, Twistor theory. Fractional Calculus, Special Functions, Integral Transforms, Differential Equations. My research has been in the area of arc and jet schemes, motivic integration, and their applications to singularities, such as Nash problem. Also, I am working in topology of complements of algebraic sets, including generalizations of Zariski - van Kampen theorem for higher homotopy groups, and hyperplane arrangements. Recently started my interest in applications of singularities of differentiable maps to medical imaging. Algebraic geometry and commutative algebra, and their interactions with deformation theory and singularity theory. Nonlinear functional analysis, critical points theory, private and ordinary differential equations, differential equations, fractional calculus and differential equations of fractional order. Geometry of Banach spaces and related aspects of approximation theory, topology, probability theory, descriptive set and function theory.
Apostolov, Vestislav
Associate Professor, PhD
Davidov, Johann
Professor, D.Sc., Professor Emeritus
Gutev, Valentin
Professor, PhD, Associate Member
Ivanov, Stefan
Academician of BAS, Professor, D.Sc.
Kiryakova, Virginia
Professor, D.Sc., Professor Emeritus
Kovacheva, Ralitza
Professor, D.Sc., Associate Member
Muskarov, Oleg
Academician, Professor, D.Sc., Professor Emeritus
Paneva-Konovska, Jordanka
Professor, D.Sc., Associate Member
Petrov, Peter
Chief Assistant Professor, PhD
Rangachev, Antoni
Chief Assistant Professor, PhD
Terzian, Stepan
Professor, D.Sc., Associate Member
Troyanski, Stanimir
Academician, Professor, D.Sc., Associate Member