##### Department of Mathematics,

University of California San Diego

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### Food For Thought Seminar

## Thomas Grubb

#### UCSD

## Sieving and Smooth Bertini Theorems over Finite Fields

##### Abstract:

Loosely defined, a sieve is a mathematical technique for finding the rate of growth of a set of objects with a quantifiable (and hopefully small) error term. Sieve techniques have wide applications in number theory and combinatorics. We will first present the idea behind sieving and present a toy example of calculating the probability that an integer is squarefree. Then we will discuss Poonenâ€™s recently developed algebro-geometric sieve, which allows one to compute the probability that a hypersurface intersects smoothly with a given projective variety X over a finite field.

### October 16, 2018

### 1:00 PM

### AP&M 7321

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