BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Jan Philipp Wächter DTSTART:20251111T140000Z DTEND:20251111T150000Z DTSTAMP:20260421T154144Z UID:UEAPS/62 DESCRIPTION:Title: E quations in Wreath Products of Abelian Groups\nby Jan Philipp Wächter as part of ANTLR seminar\n\nLecture held in NEWSCI 0.08.\n\nAbstract\nSol ving equations is among the most classical and fundamental questions in\nM athematics. Typically\, equations are solved over fields of numbers such a s\nthe rational\, real or complex numbers. Solving equations over the ring of\nintegers (Hilbert’s 10th problem) is famously known to be undecidab le. If\,\ninstead of considering the two operations of addition and multip lication of a\nring\, we restrict ourselves to a single one\, we very natu rally arrive at the\nDiophantine problem over a group: given a system of/a single equation(s)\ncontaining variables and constants (from the group)\, can we decide whether we\nmay substitute the variables with some group el ements such that the equation\nholds? In many groups this problem is gener ally undecidable. However\, we can\nrestrict the question further and cons ider only quadratic equations (where\nevery variable appears at most twice \, counting positive and negative\ninstances).\nIn the talk\, we will disc uss (ongoing) joint work with Ruiwen Dong and Leon\nPernak to solve quadra tic equations in (restricted) wreath products of abelian\ngroups. The talk will contain a short introduction on equations over groups\,\nthe lamplig hter group and its generalization to wreath products of abelian\ngroups. T hen we will look at the case of nonorientable equations over these\ngroups .\n LOCATION:https://researchseminars.org/talk/UEAPS/62/ END:VEVENT END:VCALENDAR