## Expository Papers

Here are a few of the expository papers I've written. Most of them I made for my own benefit, so they may very well have mistakes.

Flatness I wrote up everything I wanted to remember about flatness here. It's basically a copy of a chapter from Eisenbud, with a few remarks mixed in. |
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Buildings I wrote this introductory paper on buildings a few years ago. It is a reworking of the books by Ronan and Brown, although a few of the theorems and proofs are my own ideas. |

Here are outlines for some old talks. These also weren't intended for general consumption, so I make no claims to accuracy.

Intro to the MMP This is a talk I gave at the MMP seminar at MIT. It contains the basic background necessary for understanding the steps of the MMP. The goal was to prepare people to study Hacon and McKernan's paper "On the Existence of Flips". |
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Fujita Approximations This is a talk I gave at STAGE in 2008. The goal was to understand Takagi's proof of Fujita Approximation in arbitrary characteristic. |
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Rationally Connected Threefolds and
Symplectic Invariants This talk I gave at BAGS in 2008. It is an attempt to understand Voisin's paper on whether rational connectedness is a symplectic invariant for threefolds. |