Department of Computational and Data Sciences
Department Seminar
Speaker : Prof. Swadesh Kumar Sahoo
Title : “Areas of Regions and Open Problems”
Date & Time: November 28th, 2025 (Friday), 11:00 AM
Venue : # 102, CDS Seminar Hall
ABSTRACT
This talk studies the areas of image regions produced by certain complex functions and related open problems. It focuses on analytic functions defined on the unit disk that are one-to-one and normalized in a standard way, and it uses an integral quantity that measures the area of the region obtained by mapping a disk under such a function. The main aim is to understand the area when the function is modified by dividing the variable by the function value, within well-known families of functions that have specific geometric behavior. The work includes a conjecture proposed by Yamashita in nineteen ninety, later solved in two thousand thirteen, and also revisits the famous Bieberbach conjecture about bounds on coefficients of univalent functions, which was proved by Louis de Branges after about seventy years. Some of the associated open problems and challenges will alsobe highlighted.
BIO: Dr. Swadesh Kumar Sahoo is a Professor in the Department of Mathematics at the Indian Institute of Technology (IIT) Indore, specializing in Complex Variables and Hyperbolic Geometry. He joined IIT Indore in 2010. Prof. Sahoo has established himself as a distinguished researcher through his excellent publications in leading international journals including Journal of Mathematical Analysis and Applications, Computational Methods and Function Theory, Acta Mathematica Hungarica, Bulletin of the Malaysian Mathematical Sciences Society, Mediterranean Journal of Mathematics, and Results in Mathematics IIT Indore. His significant research contributions include work on successive coefficients for spirallike functions, Bohr inequalities for integral operators, radius of convexity problems, Hornich operations on functions of bounded boundary rotations, and geometric properties of conformal mappings and hyperbolic metrics. His scholarly impact is reflected in extensive citations within the academic community, and he serves as Technical Editor for The Journal of Analysis (Springer) while maintaining active involvement in organizing international conferences and advancing mathematical research excellence at IIT Indore.
Host Faculty: Dr. Ratikanta Behera
ALL ARE WELCOME
