Dipartimento di Matematica, Aula Magna.
The Chow ring of moduli of curves is an important invariant which is the subject of extensive investigations and conjectures, since Mumford first introduced the topic in his pioneering work. Chow-Witt groups are a recent refinement of the usual Chow group, and it is then a natural question to ask whether one can say something on the Chow-Witt groups of moduli of curves. In this talk, I would like to present a recent computation of the Chow-Witt ring of the moduli stack of smooth/stable elliptic curves and explain the meaning of the generators of these rings in terms of quadratic invariants of families of elliptic curves. Joint work with Lorenzo Mantovani.
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