Tata Institute of Fundamental Research, Mumbai
Anish Ghosh is a faculty member in the School of Mathematics at the Tata Institute of Fundamental Research in Mumbai. He received his BSc from St. Xavier’s College, Mumbai in 2001 and his PhD from Brandeis University in 2006. After a brief postdoctoral stint at the University of Texas at Austin, he moved to a faculty position at the University of East Anglia, UK and then, after a few years, to the TIFR. Ghosh works at the interface of ergodic theory, Lie groups, and number theory. He was awarded the NASI-Scopus young Scientist award and his work has been supported generously by several grants from the NSF, the EPSRC and the Royal Society. He is currently supported by a DST Swarnajayanti fellowship. He was elected as a Fellow of the Indian Academy of Sciences in 2018
SESSION 3B: Inaugural lectures by Fellows/Associates
A K Singhvi, Physical Research Laboratory, Ahmedabad
An introduction to some aspects of ergodic theory
The word ‘ergodic’ derived from the Greek, from ergon meaning ‘work’ and hodos meaning ‘way’. It owes its origin as a subject to the work of L Boltzmann on the kinetic theory of gases. Boltzmann coined the term ‘ergodic hypothesis’ to describe chaotic systems that satisfy certain desirable properties, including ‘equidistribution’, namely that the average time the system spends in a phase region is proportional to the volume of the region. Subsequently, ergodic theory developed into a separate branch of mathematics with extensive connections to both the pure and applied sciences. Somewhat surprisingly, ergodic theory has substantial connections to number theory, a subject christened the ‘Queen of Mathematics’ by none other than C F Gauss himself. These connections have been extensively studied recently and have proved to be very fruitful in understanding long standing conjectures in both subjects. In his lecture, the speaker will give an overview of ergodic theory and will also try to explain some of these connections.