BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vítězslav Kala (Charles University) DTSTART:20260407T120000Z DTEND:20260407T130000Z DTSTAMP:20260423T021438Z UID:OWNS/165 DESCRIPTION:Title: U sing geometric continued fractions for universal quadratic forms\nby V ítězslav Kala (Charles University) as part of One World Numeration semin ar\n\n\nAbstract\nAlready in the 18th century\, Lagrange proved that every positive integer can be expressed as the sum of four squares of integers. Nowadays we say that the sum of four squares is a universal quadratic for m. In the friendly and accessible talk\, I’ll discuss some results on un iversal quadratic forms over Z and over totally real number fields. In par ticular\, I'll focus on the role of continued fractions in many of the adv ances in the area over the last 10 years. First\, I'll talk about the conn ection between classical continued fractions and quadratic forms over real quadratic fields. Then I'll turn to the more complicated situation of hig her degree fields where we use geometric continued fractions as developed by Klein\, Arnold\, Karpenkov and many others. The talk is based on recent joint works with Valentin Blomer\, Siu Hang Man\, Magdalena Tinkova\, Rob in Visser\, and Pavlo Yatsyna.\n LOCATION:https://researchseminars.org/talk/OWNS/165/ END:VEVENT END:VCALENDAR