Title of the talk: Some problems from A^1-homotopical methods in Algebraic Geometry

Date ,Time & Venue: 17 July 2025, 11:00 AM, Seminar Hall, Dept. of Mathematics

Abstract: Morel-Voevodsky in the late 90s pioneered the A^1-homotopical point of view which made it possible to apply homotopical techniques from classical topology to algebraic varieties.  Since then these ideas have found interesting applications in Algebra, Algebraic Geometry, Commutative Algebra, and Number Theory. In the last few years, I have focused on problems that arise out of these homotopical methods. I will discuss some of the interesting problems that arise in this area of research. I will highlight some of the work that I have done, describe current work in progress, and also future research plans. 

About the Speaker: Dr. Rakesh Pawar  is currently a Visiting Scientist in Mathematics at HRI, Prayagraj. He works in the area of Algebraic Geometry with special interest in Homotopical methods applied to problems in Algebraic Geometry and Commutative Algebra together with Algebraic cycles, Milnor-Witt K-theory. 

He has been a Postdoc at ENS de Lyon, France, NBHM Postdoctoral Fellow in IISER Pune, IISER Mohali and University of Duisburg-Essen, Essen, Germany. He obtained a Ph. D. in Mathematics in 2017 from TIFR, Mumbai.