Schedule:

We are meeting in BA6180 from September 10 to December 3.

**About:**

- I will try to cover the backbone from chapters 2 to 6 of the main book. If possible I will talk about chapter 7, but I am not sure we will be able to talk too much about.

**Bibliography:**

[1] *Buildings.* Peter Abramenko, Kenneth S. Brown. Springer, Graduate Texts in Mathematics, Vol. 248

**Logbook:**

Date | What did we do? | Notes |

September 10 | We talked about properties of pairs (W, S). We defined the deletion, exchange and foldingconditions and discussed parabolic subgroups.[1] Sections 2.3.1 and 2.3.2.See also [1] section 1.5 | N/A |

September 17 | We introduced the action and the coxeter conditions and defined Coxeter Group. We defined what the associated Coxeter Complex is and saw an example of it.[1] Section 2.1, 2.3.3, 2.4, 3.1See section 2.2 to see examples. | |

September 24 | We finished the topics in the notes of previous time: we proved the properties of the Coxeter Complex, [1] Theorem 3.5. We also defined the components associated to an automorphism and discussed why they satisfy the conditions they do: [1] Lemma 3.31.[1] Section 3.1, 3.3.1Our discussion about the reason why the complex is thin was confusing. Here is a written explicit proof: THIN. | |

October 1 | ||

October 8 | ||

October 15 | ||

October 22 | ||

October 29 | ||

November 5 | ||

November 12 | ||

November 19 | ||

November 26 | ||

December 3 |

**Notes:**

- The book [1], for U of T students, can be obtained as a MyCopy book in springer through the UofT libraries.
**Chapter 1**of [1] covers finite reflection groups, which are the objects we are trying to generalize to build coxeter systems. From them we will build buildings. It is very instructive to review this chapter as we progress and see how it is done in the case of finite W.

**Alternative References:**

# | Reference: |

1 | An application of the bulding to orbital integralsJonathan D. Rogawski |

2 | Twin Buildings and Application to S-Arithmetic GroupsPeter Abramenko |

3 | Buildings and their applications in Geometry and TopologyLizhen Ji |