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Arcs in algebraic varieties


Title : Arcs in algebraic varieties.
Speaker : Prof. Arvind Nair, TIFR Mumbai.
Date : 09/02/2022, 05:30 PM , Online Mode.

About the speaker:

Prof. Arvind Nair is an eminent Mathematician from TIFR Mumbai, working in fundamental areas of Mathematics, namely, Representation theory, Automorphic forms, and Algebraic Geometry. Prof. Nair completed his PhD from Michigan University in 1996. Since then, he has been a permanent faculty at School of Mathematics at TIFR Mumbai. Prof. Nair is also a regular visitor to the prestigious “Institute of Advanced Studies” at University of Princeton.

Title of the Talk:  Arcs in algebraic varieties


An algebraic variety is, roughly speaking, the set of solutions of a system of polynomial equations.  The arc space of a variety (introduced by John Nash around 1968) gives a new perspective on some aspects of the geometry of algebraic varieties.  I will try to give an idea of why we are interested in arc spaces and how they are useful.  I will try to illustrate things with simple examples in 2 and 3 dimensions, for which we will use calculus in at most three variables.