##### Department of Mathematics,

University of California San Diego

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### Math 209: Number Theory Seminar

## Chris Xu

#### UC San Diego

## Rational points on modular curves via the moduli interpretation

##### Abstract:

In theory, Chabauty-Coleman provides an explicit method to obtain rational points on any curve, so long as its genus exceeds its Mordell-Weil rank. In practice, when applied to modular curves, we often encounter difficulties in finding a suitable plane model, which only worsens as the genus increases. In this talk we describe how to skip this step and instead work directly with the coarse moduli space. This is joint work with Steve Huang and Jun Bo Lau.

### June 6, 2024

### 2:00 PM

APM 6402 and online (see https://www.math.ucsd.edu/~nts

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