##### Department of Mathematics,

University of California San Diego

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### RTG - Graduate Colloquium

## Alex Mathers - Ph.D. student

#### UC San Diego

## The Direct Summand Conjecture

##### Abstract:

The direct summand conjecture, part of the homological conjectures in commutative algebra, was first proposed by Mel Hochster in 1973. The conjecture is easily proven when the given ring contains a field, but the ``mixed characteristic'' case seemed, for the most part, impenetrable. In 2016 Yves Andre announced a proof of the conjecture which utilizes the theory of perfectoid spaces. We will attempt to give a (somewhat) detailed proof of the DSC in a simplified scenario, and then give a general idea of the methods used to prove the theorem in the general case.

### November 3, 2020

### 4:00 PM

### Contact fmcglade@ucsd.edu for zoom info

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