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Friday, February 2, 2018

**Abstract:** I will discuss the paper "A Vietoris-Smale mapping theorem for the homotopy of hyperdefinable sets" by Alessandro Achille and Alessandro Berarducci [arXiv]. In this paper, they compare the definable homotopy groups of a space $X$ definable in an o-minimal structure (denoted $\pi_n(X)^\mathrm{def}$) with the (usual) homotopy groups of the quotient $X/E$, where $E$ is a certain kind of type-definable equivalence relation on $X$. Under certain assumptions, these groups are actually isomorphic. These types of quotients were first studied by Pillay in the case that $X$ is actually a definable group. This is the first talk that I will give on this paper.

Friday, February 9, 2018

Friday, February 16, 2018

Friday, February 23, 2018

Friday, March 2, 2018

Friday, March 9, 2018

Friday, March 16, 2018

Friday, March 30, 2018

Friday, April 6, 2018

Tuesday, April 10, 2018

Friday, April 20, 2018

Friday, October 12, 2018