Quantitative bounds on the topology of semi-algebraic and definable sets
By Saugata Basu
Appears in collection : Model Theory and Combinatorics
I will survey some old and new results on bounding the topology of semi-algebraic and definable sets in terms of various parameters of their defining formulas, and indicate how some of these results impact problems of discrete geometry over the reals. If time permits I will pose some open questions as well.