Speaker:  Alejandro Maris, Cornell University
Title: On the Product of a Building as a Poset of Standard Cosets
Time: 2:30 PM, Monday, May 1st, 2023
Place:  Malott 206

Abstract: This will be an expository lecture on the first concepts of the theory of buildings, which are a type of simplicial complex. We will illustrate these with the example of a building from a vector space, in particular the case when the field we are working over is $\mathbb{F}_2$ and the vector space is three dimensional. In other words, we will be working with the Fano plane and its associated flag complex. One of the many interesting properties of buildings is that they have a product on the faces. The main goal of the lecture is then to try to understand this product, particularly when there is a sufficiently nice action of a group $G$ on the building. In this case, we can represent our building as a certain poset of subsets of the group $G$ and we can then ask how does the product behave with respect to these subsets of $G$. In the lecture we will see what is this behavior when we are dealing with the specific example of the flag complex of the Fano plane and we will then attempt to give a feel at how this result would generalize to all buildings of this type.


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