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In-Person and Online Talk

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In the first talk, we will discuss the Hasse principle for rational points on intersection of two quadrics in P^N Ìýover function fields Ìý(of algebraic curves over a finite field). Among other things, the new tools here include an on-going work with Zhiwei Yun to establish a function field analog of (a strengthened) ÌýKolyvagin's theorem for elliptic curves and our previous work on Ìýa Higher Gross-Zagier formula Ìýrelating intersection numbers of certain cycles on moduli space of Drinfeld Shtukas to L-functions of elliptic curves.