BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yifeng Huang (UBC Vancouver) DTSTART:20221130T220000Z DTEND:20221130T233000Z DTSTAMP:20260423T023016Z UID:UBC_NTS/12 DESCRIPTION:Title: Unit equations on quaternions\nby Yifeng Huang (UBC Vancouver) as par t of UBC (online) Number Theory Seminar\n\n\nAbstract\nA classical theorem in number theory states that for any finitely generated subgroup $\\Gamma $ of $\\mathbb{C}*$\, the "unit equation” $x+y=1$ has only finitely many solutions with $x\,y\\in \\Gamma$. One can view it as a statement that re lates addition and multiplication of complex numbers in a fundamental way. Our main result (arXiv: 1910.13250) is an analog of this theorem on quate rnions\, where the multiplication is no longer commutative. We then explai n its connection to iterations of self-maps on abelian varieties\, and giv e a result about an orbit intersection problem as an application. The appr oach to our main result is based on the analysis of the Euclidean norm on quaternions\, and Baker’s estimate of linear combinations of logarithms. Time permitting\, I will sketch a proof focusing on how the difficulties caused by noncommutativity are miraculously addressed in our case.\n\nJoin Zoom Meeting\nhttps://ubc.zoom.us/j/67843190638?pwd=eUJsc1oyY2xhYnM4NmU3O W1sTEV2dz09\n\nMeeting ID: 678 4319 0638\nPasscode: 999070\n LOCATION:https://researchseminars.org/talk/UBC_NTS/12/ END:VEVENT END:VCALENDAR