BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jeff Lagarias (Michigan) DTSTART:20211014T210000Z DTEND:20211014T220000Z DTSTAMP:20260423T022810Z UID:UCSD_NTS/43 DESCRIPTION:Title: Complex Equiangular Lines and the Stark Conjectures\nby Jeff Lagaria s (Michigan) as part of UCSD number theory seminar\n\nLecture held in APM 7321 and online.\n\nAbstract\nThis talk is expository. It describes the hi story of an exciting connection made by physicists between an unsolved \n problem in combinatorial design theory- the existence of maximal sets of $ d^2$ complex equiangular lines in ${\\mathbb C}^d$-\nrephrased as a probl em in quantum information theory\, and topics\n in algebraic number theory involving class fields of real quadratic fields. Work of my former studen t\nGene Kopp recently uncovered a surprising\, deep (unproved!) connectio n with\nthe Stark conjectures. For infinitely many dimensions $d$ he pred icts the existence of maximal equiangular sets\, \nconstructible by a spec ific recipe starting from suitable Stark units\, in the rank one case. Num erically computing\nspecial values at $s=0$ of suitable L-functions then p ermits recovering the units numerically to high precision\, \nthen reconst ructing them exactly\, then testing they satisfy suitable extra algebraic identities to yield a construction\nof the set of equiangular lines. It h as been carried out for $d=5\, 11\, 17$ and $23$.\n\npre-talk at 1:20pm\n LOCATION:https://researchseminars.org/talk/UCSD_NTS/43/ END:VEVENT END:VCALENDAR