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Some moduli spaces for curves of genus 1 and 2

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If you have a question about this talk, please contact Macarena Arenas .

This talk will focus on the geometry of the surfaces which parametrise “congruences” of elliptic curves, following Kani and Schanz. I will discuss how this is related to the study of curves of genus 2 which admit a morphism to an elliptic curve, and mention the connection to number theory and Galois representations. If time permits I will sketch how we can compute explicit models for these surfaces (over Q).

This talk is part of the Junior Geometry Seminar series.

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CCIMI FW11 Seminar Room (William Gates Building) FW11, William Gates Building. Zoom link: https://cl-cam-ac-uk.zoom.us/j/4361570789?pwd=Nkl2T3ZLaTZwRm05bzRTOUUxY3Q4QT09&from=addon

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