Type: Seminar

Modified: Thu 26 Nov 2020 1400

Distribution: World

Expiry: 7 Dec 2020

CalTitle1: SMRI Algebra and Geometry Online: Kim - Recent progress on the effective Mordell problem

Auth: hannahb@10.165.80.8 (hbry8683) in SMS-LDAP

SMRI Algebra and Geometry Online ’Recent progress on the effective Mordell problem’ Minhyong Kim (University of Warwick) Monday 7th December 8:00pm-9:30pm (AEDT) Online via Zoom Abstract: In 1983, Gerd Faltings proved the Mordell conjecture stating that curves of genus at least two have only finitely many rational points. This can be understood as the statement that most polynomial equations (in a precise sense) f(x,y)=0 of degree at least 4 have at most finitely many solutions. However, the effective version of this problem, that of constructing an algorithm for listing all rational solutions, is still unresolved. To get a sense of the difficulty, recall how long it took to prove that there are no solutions to x^n+y^n=1 other than the obvious ones. In this talk, I will survey some of the recent progress on an approach to this problem that proceeds by encoding rational solutions into arithmetic principal bundles and studying their moduli in a manner reminiscent of geometric gauge theory. Register: https://uni-sydney.zoom.us/meeting/register/tZwucOCtrj8oE9fa-wb15lPFkt8ENLNFwFgk The speakers blog is here: https://minhyongkimpublic.wordpress.com Note: These seminars will be recorded (participants only when asking questions), and uploaded to the SMRI YouTube Channel https://www.youtube.com/channel/UCNrre_3ROSz7FqOka3lSMVA

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