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What's Happening in Fine Hall

EllipticÌýcurvesÌýare fundamental and well-studied objects in arithmetic geometry. However, much is still not known about many simple-sounding properties, such as the expected number of rational or integral points on a "random"ÌýellipticÌýcurve. We will briefly discuss some conjectures and theorems related to these problems. In particular, we will show why the second moment (and the average) for the number ofÌýintegralÌýpointsÌýonÌýellipticÌýcurvesÌýover a number field is bounded (joint work withÌýLevent Alpöge).

This talk will be suitable for a general mathematical audience.Ìý