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After quickly recalling what is the Euler characteristic and what is homology and after briefly describing the Jones polynomial, I will move on to describe in simple terms Khovanov's novel "Categorification of the Jones Polynomial", which is to the Jones polynomial as homology is to the Euler characteristic. Namely, it is much more interesting.

My talk will be similar to a talk I gave at the Topology and Geometry seminar last November (see here); it will be based on the same paper and will mostly follow the same handout. The only new material will be on the back side of the handout, which will be printed with a list of reasons for why is categorification interestings.