# Analysis, Geometry and Topology

## Academic Staff

# Main Staff

## Nikolov, Nikolai

### Corresponding Member of BAS, Professor, D.Sc., Chairman of the Scientific Council of IMI, Head of Department AGT, President of the UBM

Several complex variables

## Bazhlekova, Emilia

### Associate Professor, D.Sc., Secretary of Department AGT

Fractional calculus; Fractional differential and integral equations: operator-theoretical approach, qualitative properties of solutions. Convolutional calculus: Duhamel-type representations for nonlocal boundary-value problems.

## Hakkaev, Sevdzhan

### Professor, D.Sc.

Stability of nonlinear waves, nonlinear dispersive equations, inverse scattering theory

## Katzarkov, Ludmil

### Corresponding Member of BAS, Professor, D.Sc.

Differential, algebraic and symplectic geometry, topology and mathematical physics.

## Milousheva, Velichka

### Professor, PhD, Deputy Director of IMI

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.

## Barov, Stoyu

### Associate Professor, PhD

Infinite-dimensional topology, Geometric Tomography/Topology, Geometry of Banach spaces, Convexity, Topological vector spaces, Selection theory.

# Additional Staff

## Apostolov, Vestislav

### Associate Professor, PhD

Complex differential geometry, algebraic geometry, global analysis.

## Davidov, Johann

### Professor, D.Sc., Professor Emeritus

## Gutev, Valentin

### Professor, PhD, Associate Member

Research interests: Set-valued mappings, selections, hyperspaces, absolute extensors and retracts, embedding-like properties, finite-dimensional and infinite-dimensional spaces.

## Ivanov, Stefan

### Academician of BAS, Professor, D.Sc.

## Kassabov, Ognian

### Professor, PhD

Riemannian and almost Hermitian manifolds, theory of submanifolds, differential geometry of surfaces in a 3-dimensional and in a 4-dimensional Euclidean or pseudo-Euclidean space.

## Kiryakova, Virginia

### Professor, D.Sc., Professor Emeritus

Fractional Calculus, Special Functions, Integral Transforms, Differential Equations.

## Kovacheva, Ralitza

### Professor, D.Sc., Associate Member

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.

## Muskarov, Oleg

### Academician, Professor, D.Sc., Professor Emeritus

Several complex variables, Analysis on complex and almost complex manifolds, Complex differential geometry, Twistor theory.

## Paneva-Konovska, Jordanka

### Professor, D.Sc.

Fractional Calculus, Special Functions, Integral Transforms, Differential Equations.

## Petrov, Peter

### Chief Assistant Professor, PhD

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.

## Rangachev, Antoni

### Chief Assistant Professor, PhD

Algebraic geometry and commutative algebra, and their interactions with deformation theory and singularity theory.

## Terzian, Stepan

### Professor, D.Sc., Associate Member

Nonlinear functional analysis, critical points theory, private and ordinary differential equations, differential equations, fractional calculus and differential equations of fractional order.

## Troyanski, Stanimir

### Academician, Professor, D.Sc., Associate Member

Geometry of Banach spaces and related aspects of approximation theory, topology, probability theory, descriptive set and function theory.