SaLam! 

I am Marzieh; I am a postdoctoral researcher at Max Planck Institute for Mathematics in the Sciences and ScaDS AI Institute in Leipzig, Germany where  I work in the group of Prof. Sayan Mukherjee. I got my Ph.D.  under the supervision of Prof. Dr.  Jürgen Jost on "Topological and Geometric Methods with a View Towards Data Analysis".

I have a broad range of interests in both theoretical and applied mathematics; what attracts me the most is not specific subjects and directions but the profound and beautiful connections between them and in particular connections between Geometry, Topology, Spectral Analysis, and Stochastic processes. Simultaneously I like to explore and learn more about the applications of these areas in data science and machine learning.  

My Main Research Interests are: 

• Discrete Hodge Laplacian and its applications in clustering, semi-supervised learning, and dimension reduction

• (Morse-Floer-Conley) Homology theories in smooth and combinatorial settings and their applications in shape analysis and image processing.

• Geometry and Topology of (directed) Hypergraphs and Simplicial Complexes

• Generalized (Discrete) curvature notions, such as Ollivier-Ricci, and their applications in complex network analysis

• Discrete Optimal Transport and its applications in different domains

• Stochastic process on discrete structures and their applications in data analysis and machine learning