Complex Analysis with a focus on Geometric Function Theory, including univalent and multivalent functions, logarithmic coefficients, special functions, q-theory, and harmonic univalent functions.

Dr. Navneet Lal Sharma is an Assistant Professor in the Department of Mathematics at Gati Shakti Vishwavidyalaya (GSV), Vadodara, a Central University under the Ministry of Railways, Government of India, where he has been serving since August 2022. He also holds the responsibility of Programme Coordinator for B.Tech First Year (All Branches). Dr. Sharma earned his Ph.D. in Mathematics from Indian Institute of Technology (IIT) Indore, with specialization in Complex Analysis and Geometric Function Theory, supported by the NBHM PhD Fellowship. He has nearly eight and a half years of combined teaching and research experience, including postdoctoral research at premier institutions such as ISI Chennai, IIT Madras, IIT Kharagpur, and as a Visiting Scientist at Universiti Sains Malaysia under the prestigious SERB–SIRE International Research Fellowship. His research focuses on univalent and multivalent function theory, logarithmic coefficients, special functions, q-theory, and harmonic univalent functions. Dr. Sharma has published extensively in reputed SCI/Scopus-indexed international journals and has received several competitive fellowships and research grants, including a SERB Core Research Grant worth approximately ?21 lakhs. He has delivered numerous invited and contributed talks at national and international conferences and has actively contributed to academic leadership through organizing workshops, seminars, and student induction programs. Passionate about teaching, he has taught a wide range of undergraduate, postgraduate, and doctoral-level mathematics courses and is actively involved in research supervision and academic mentoring. Reference: Univalent Functions and Its Applications Let A denote the family of all functions f that are an alytic in the unit disk D := {z ∈ C : |z| < 1} and normalized so that f(0) = 0, f′ (0) = 1. Clearly, a function f ∈ A has the Taylor series expansion of the form f(z) = z + P n ∞ =2 anz n . Denote by S the family consisting of functions f ∈ A that are univalent in D. In this talk, I will discuss the properties of the class S like: coefficient bounds, Growth & Distortion theorems. Also, I will discuss the geometric subclasses of S like: starlike, convex and close-to-convex with their properties. This talk is based on the following books: 1. P. Duren, Univalent functions (Grundlehren der mathematischen Wissenschaften 259, New York, Berlin, Heidelberg, Tokyo), Springer Verlag, 1983. 2. A. W. Goodman, Univalent functions, Vols. 1-2, Mariner, Tampa, Florida, 1983. 3. Ch. Pommerenke, Univalent functions, Vandenhoeck and Ruprecht, G¨ottingen, 1975.