IISER, Pune

Haripada Sau is currently an Assistant Professor at IISER Pune and works in Hilbert space operator theory. His expertise revolves around the rational dilation problem, which originated from the pioneering works of Sz.-Nagy, Ando, and Arveson around the mid-20th century. His current research focuses on a variant of the rational dilation problem constrained to certain affine varieties. He holds a PhD from the Indian Institute of Science under the supervision of Prof. Tirthankar Bhattacharyya. He has done postdoctoral research at IIT Bombay, Virginia Tech, IIT Guwahati, and the TIFR Centre for Applicable Mathematics. Selected as Associate in 2023.

SESSION 3B - Lectures by Fellows/Associates

Praveen Chaddah, Gurugram

A constrained Ando dilation problem

Ando 's inequality and its remarkable improvements, first for certain matrices and then for certain operators, motivate us to ask a question that can be seen as a constrained Ando dilation problem. The statement involves a class of two-variable polynomials with a geometric condition on its zero sets, called the toral polynomials. If a pair of commuting operators is annihilated by a toral polynomial, then the pair is called a toral pair. "Does every toral pair of commuting contractions dilate to a toral pair of commuting isometries?" We shall see why one may want to find an answer to this question in this talk.