This event is a part of the May 12th initiative.
Lecture 1 (9:30 am)
Title: Cyclotomic fields and their role in modern Number theory
Speaker: Radhika Ganapathy (Indian Institute of Science, Bangalore)
Abstract: A cyclotomic extension of the field Q is a finite extension of Q obtained by adjoining a primitive complex n-th root of unity for some n. Such fields enjoy a unique position in Algebraic number theory. On the one hand they enjoy relatively simple and beautiful algebraic properties making them an excellent resource of examples, and on the other hand they are connected to fundamental problems, like Fermat's last theorem. This talk will be on cyclotomic fields, their structural properties, and their connections to other problems in Number theory.
Lecture 2 (11:15 am)
Title: On some notions of convexity in complex analysis
Speaker: Purvi Gupta (Indian Institute of Science, Bangalore)
Abstract: There are several analytic phenomena that set apart multivariable complex analysis from its one-variable counterpart. Some of these give rise to notions of convexity that have not only played a fundamental role in the development of the field, but also continue to be of interest to mathematicians today. In this talk, we will motivate a few such notions with the help of many examples. Through multiple results --- some classical, some new --- we will illustrate how the topology and the geometry of the underlying object determine when and how it can be ‘made’ convex, or in the absence of such flexibility, what can be said about the ‘smallest’ convex set containing it.
About the Speakers:
Radhika Ganapathy is a faculty member in the Department of Mathematics, IISc-Bangalore. She did her schooling in Chennai, obtained a bachelor’s degree in mathematics from Meenakshi College for Women, Chennai and a Masters degree from IIT Madras. She earned a Ph.D. in Mathematics from Purdue University in 2012. After spending 3 years as a postdoctoral fellow at the Institute of Advanced Study, Princeton, and the University of British Columbia, Vancouver, She joined the Mathematics faculty at TIFR - Mumbai, in 2015. She moved to IISc - Bangalore in 2019 and has been here since. Her research interests broadly lie in Representation theory and Number theory. More specifically she work on problems that are part of the Langlands’ program, which encompasses a vast set of conjectures that provide a bridge between objects of analytic nature (automorphic forms) and those of algebraic nature (Galois representations). She also enjoys teaching Mathematics. She began her teaching career at Purdue (as a Ph.D. student) and has taught a variety of undergraduate and graduate Mathematics courses since.
Purvi Gupta is an Assistant Professor at the Indian Institute of Science, Bangalore. She obtained her Ph.D. from the University of Michigan, Ann Arbor, and spent her postdoctoral years at the University of Western Ontario, Canada, and Rutgers University, New Jersey. Her primary area of research is several complex variables, within which she studies convexity properties of real submanifolds, polyhedral approximations of convex-type domains, and holomorphic function spaces with reproducing kernels.
