About the lecturer: Apoorva Khare is a professor of mathematics at the Indian Institute of Science in Bengaluru, where he has been a faculty member since 2017. Previously, he held academic appointments as a Research Associate at Stanford University (2011–2017), a Lecturer at Yale University (2009–2011), and a Visiting Assistant Professor at the University of California at Riverside (2006–2009), alongside numerous short academic visits to institutions worldwide. Professor Khare completed his Ph.D. at the University of Chicago in 2006 under the supervision of Victor Ginzburg. His distinguished research career is recognized by numerous prestigious awards, including the Shanti Swarup Bhatnagar Prize and his election as a Fellow of the Indian Academy of Sciences in 2023. Professor Khare's scholarly contributions include publications in some of the top mathematical journals as well as co-authoring the book “Beautiful, Simple, Exact, Crazy: Mathematics in the Real World” (with Anna Lachowska). His research also deeply explores representation theory and algebraic combinatorics, with significant contributions involving complex semi-simple Lie algebras, Category O, Kazhdan-Lusztig polynomials, and symmetric function identities. More recently, he has focused on matrix analysis and positivity, specifically studying entrywise positivity preservers and totally positive kernels. Beyond his research, he actively serves the global mathematical community in various editorial roles, alongside mentoring several Ph.D. students and postdoctoral researchers.