In this talk, we shall discuss the Chebyshev center problem, often called the problem of best simultaneous approximation, in Banach spaces. The problem involves finding a closed ball of the smallest radius containing a given closed and bounded subset of the space. We will discuss some examples of Banach spaces with this property. We will relate this notion to other existing geometric notions in Banach spaces. Towards the end, we will discuss some new results in this direction.
Dr. Syamantak Das obtained his Master’s degree in Mathematics from the Indian Institute of Technology (IIT) Patna, followed by a Ph.D. from IIT Hyderabad. His research interests are primarily in Banach Space Theory, with a particular focus on the geometry of Banach spaces. He is currently a visiting researcher at IIT Madras.
