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Infinitesimals

Kobi Kremnitzer

Date Icon Week 5, Tuesday 14 February HT 2012
Time Icon 8:15pm

After the work of Cauchy and Weierstrass on the foundations of analysis it seemed like infinitesimals are unnecessary incoherent entities. Infinitesimals have survived and flourished in algebra, algebraic geometry and model theory, even after the brutal attack on them by analysts. I will discuss synthetic differential geometry. This is an approach to analysis and geometry that does not use epsilon and delta, but infinitesimals instead. Many theorems from first year analysis have one line proofs in this language. This approach is now finding many applications in geometry and mathematical physics.