The Ramanujan Tau Function
Bio
#Prof. M. Ram Murty obtained his PhD from Massachusetts Institute of Technology (MIT) in 1980 and then was a member of the Institute for Advanced Study (IAS, Princeton) and Tata Institute of Fundamental Research (TIFR) during 1980-82. He currently holds the Queen's Research Chair at Queen's University in Kingston, Ontario, Canada. In 2008, he was elected as Fellow of the Indian National Science Academy (INSA) and in 2013 was awarded the Simons Fellowship. He has written more than 250 research papers and more than a dozen books including one on Indian philosophy. He is also an adjunct professor at several Indian institutions including TIFR, IMSc, HRI, CMI, IIT (Bombay) and IISER (Bhopal). He specializes in number theory.
In the lecture, I will survey the famous Ramanujan Tau function. I will highlight how his three conjectures regarding this function motivated the growth of the theory of modular forms, as well as their intimate connection to algebraic geometry and the Langlands program. I will discuss some recent developments and indicate open problems. The talk will be accessible to a general mathematical audience.
