##### Department of Mathematics,

University of California San Diego

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### Math 208: Seminar in Algebraic Geometry

## Dr. Valery Lunts

#### Indiana University

## Vector field on the plane

##### Abstract:

Given a vector field on a complex plane C^2 with polynomial coefficients one would like to know if all the integral curves of this vector field are algebraic. The problem seems to be very difficult. I will discuss an approach to this problem using the reduction to characteristic p, which produces a conjectural answer. Also I will explain the relation with the famous Grothendieck-Katz p-curvature conjecture. Probably the main beauty of the subject is its completely elementary nature, which makes it accessible to a first year student.

Host: James McKernan

### February 23, 2024

### 4:00 PM

APM 7321

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