##### Department of Mathematics,

University of California San Diego

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### Algebra Seminar

## Robert Won

#### UCSD

## Z-graded noncommutative projective geometry

##### Abstract:

The first Weyl algebra $A = k\langle x, y \rangle/(xy - yx - 1)$ is $\mathbb{Z}$-graded with deg x = 1 and deg y = -1. Susan Sierra and Paul Smith studied the category of graded modules over A, showing that this category was equivalent to coherent sheaves on a certain quotient stack. In this talk, we investigate the graded module categories over $\mathbb{Z}$-graded rings called generalized Weyl algebras. We construct commutative rings with equivalent graded module categories. In the pre-talk, we will discuss some preliminaries on categories and graded rings before giving an overview of noncommutative projective geometry. Please note: There will be a pre-talk for graduate students from 2:30 - 3:00. The regular talk will begin at 3:00.

Host: Daniel Rogalski

### November 9, 2015

### 2:00 PM

### AP&M 7321

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