# Topology

## Disconnecting the G_2 Moduli Space

## Universal torsion, L^2-invariants, polytopes and the Thurston norm

## Introduction to the Farrell-Jones Conjecture

The Farrell-Jones Conjecture identifies the algebraic K- and L-groups for group rings with certain equivariant homology groups. We will give some details of its formulation, its status and indicate some ideas of proofs for certain classes of groups. We will try to convince the audience about its significance by considering special cases and presenting the surprizing large range of its applications to prominent problems in topology, geometry, and group theory.

## Decision problems, curvature and topology

I shall discuss a range of problems in which groups mediate between topological/geometric constructions and algorithmic problems elsewhere in mathematics, with impact in both directions. I shall begin with a discussion of sphere recognition in different dimensions. I'll explain why there is no algorithm that can determine if a compact homology sphere of dimension 5 or more has a non-trivial finite-sheeted covering. I'll sketch how ideas coming from the study of CAT(0) cube complexes were used by Henry Wilton and me to settle isomorphism problems for profinite groups, and to settle a conjecture in combinatorics concerning the extension problem for sets of partial permutations.

## Khovanov homology

Lecture notes on Khovanov homology.

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## Duality Notes

These are notes for the Duality talk presented as part of the West Coast Algebraic Toplogy Summer School.

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## Verlinde Algebra

Lecture Notes on Verlinde Algebra

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## WCATSS Problem Set 5

This is the third problem of the West Coast Algebraic Topology Summer School (WCATSS)

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## WCATSS Problem Set 4

This is the third problem of the West Coast Algebraic Topology Summer School (WCATSS)

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## WCATSS Problem Set 3

This is the third problem of the West Coast Algebraic Topology Summer School (WCATSS)

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