An invitation to Singularity Theory

Singularity Theory has grown out of two questions:

• How does a curve ”look locally“ near its non-smooth point?
• How does a function ”look locally“ near its degenerate critical point?

By now this is an active area at the crossroad of Algebraic/Differential Geometry, Algebraic Topology, Commutative Algebra (The immediate applications in high-tech often go under the name ”The Catastrophe Theory“.)

The talk will consist of a few examples, showing how the singular creatures differ from the smooth ones, and how we can study them via Taylor expansions, implicit function theorem, properties of knots, ideals, quotients of rings, etc.

Prerequisites: Geometric Calculus 1/Infi3, Algebraic Structures (Complex Analysis and Introduction to Topology are helpful, but not strictly necessary)

(ההרצאה תינתן בעברית)