Singularities occur naturally in different parts of mathematics. As examples, we can mention zeros of vector fields, knot theory, matrices with zero determinant, quotient spaces modulo actions of groups acting on manifolds, etc. We will mainly focus on singularities in algebraic and analytic geometry. We will discuss several important techniques (using algebra, algebraic geometry, analysis, topology,…) developed by algebraic geometers to study singularities. Some striking applications like the famous result of Abhyankar-Moh, Suzuki about embeddings of the affine line in the complex plane using the topology of singularities of plane curves will be mentioned.
Date and Time : 10-03-2017 17:00
Venue : Seminar Hall, CSB @ Vithura
Speaker : R.V. Gurjar, IIT Bombay