BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Mohammad Sadek DTSTART:20221024T130000Z DTEND:20221024T140000Z DTSTAMP:20260422T104759Z UID:FGC-IPM/23 DESCRIPTION:Title: How often do polynomials hit squares?\nby Mohammad Sadek as part of F GC-HRI-IPM Number Theory Webinars\n\n\nAbstract\nGiven a polynomial with r ational coefficients\, one may investigate the possible values that may be attained by these polynomials over the set of rational numbers. For centu ries\, number theorists have been giving due attention to square rational values assumed by rational polynomials. It turns out that seeking an answe r to this question connects number theory and geometry. Answering this que stion for a polynomial in one variable will lead us to study the arithmeti c of certain algebraic curves. We will spend some time explaining the geom etry beneath the question when the degree of the polynomial is at least 3. For polynomials in more than one variable\, the geometric structure is re mote. In the latter case\, we will present some of the old and recent deve lopments in the theory shedding some light on some classical Diophantine q uestions.\n\nZoom link: https://us06web.zoom.us/j/85613860958\nMeeting ID: 856 1386 0958\n LOCATION:https://researchseminars.org/talk/FGC-IPM/23/ END:VEVENT END:VCALENDAR