BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Yasuaki Gyoda (Nagoya University\, Japan) DTSTART:20260717T153000Z DTEND:20260717T155500Z DTSTAMP:20260710T111455Z UID:CANT2026/64 DESCRIPTION:Title: Generalized discrete Lagrange–Markov spectra\nby Yasuaki Gyoda (Na goya University\, Japan) as part of Combinatorial and additive number theo ry seminar (CANT 2026)\n\nLecture held in Science Center in the CUNY Gradu ate Center (4th floor).\n\nAbstract\nThis talk concerns a discrete extensi on of the classical Lagrange and Markov\nspectra\, motivated by generalize d Markov equations. In the classical case\,\nthe discrete spectral values below $3$ are organized by Markov numbers and are\ndescribed through conti nued fractions\, Christoffel words\, and Cohn matrices.\nI will explain ho w an analogous picture can be developed for generalized\nMarkov numbers ar ising from \n $$ x^2+y^2+z^2+k_1yz+k_2zx+k_3xy\n =(3+k_1+k_2+k_3)xyz.\n$$\ nFor each generalized Markov number\, one obtains an explicit spectral val ue\nwhich is realized both as the Lagrange constant of a quadratic irratio nal and\nas the Markov constant of an indefinite binary quadratic form wit h rational\ncoefficients. The emphasis of the talk will be on the main ide a of the\nconstruction: generalized Cohn matrices and symbolic sequences c oming from\nstraight-line codings play the role classically played by Chri stoffel words and \nCohn matrices. The aim is to present a combinatorial a nd matrix-theoretic\nframework for viewing classical and generalized discr ete Diophantine spectra in\na unified way.\n LOCATION:https://researchseminars.org/talk/CANT2026/64/ END:VEVENT END:VCALENDAR