## EVENT DETAILS AND ABSTRACT

**Colloquium**
**Title:** Telescopes, exotic spheres, and p-adic cohomology theories

**Speaker:** Jeremy Hahn

**Speaker Info:** MIT

**Brief Description:**

**Special Note**:

**Abstract:**

A smooth, oriented n-manifold is called a homotopy sphere if it is homeomorphic, but not necessarily diffeomorphic, to the standard n-sphere. In dimensions n>4, one often studies the group $\Theta_n$ of homotopy spheres up to orientation-preserving diffeomorphism, with group operation given by connected sum. I will introduce the telescope conjecture in stable homotopy theory, and explain how its failure gives new lower bounds on the complexity of $\Theta_n$. To disprove the telescope conjecture, we construct invariants capable of distinguishing many diffeomorphism classes of exotic spheres: interestingly, key finiteness properties of these invariants are proved using modern advances in algebraic K-theory, cyclotomic spectra, and prismatic/syntomic cohomology.

**Date:** Wednesday, October 18, 2023

**Time:** 4:00pm

**Where:** Lunt 105

**Contact Person:** Bao Le Hung

**Contact email:** lhvietbao@gmail.com

**Contact Phone:**

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