BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Arul Shankar (University of Toronto) DTSTART:20200603T150000Z DTEND:20200603T160000Z DTSTAMP:20260513T222450Z UID:CMI/11 DESCRIPTION:Title: Squ arefree sieves in arithmetic statistics\nby Arul Shankar (University o f Toronto) as part of CMI seminar series\n\n\nAbstract\nA classical questi on in analytic number theory is: given a polynomial with integer coefficie nts\, how often does it take squarefree values? In arithmetic statistics\, we are particularly interested in the case of discriminant polynomials. I n this talk\, I will present several different cases of this question. Fir st\, we will consider a classical result of Davenport--Heilbronn which con siders the case of discriminants of binary cubic forms. Then\, I will disc uss joint work with Bhargava in which we consider the case of discriminant s of ternary cubic forms.\n\nThird\, I will describe joint and ongoing wor k with Bhargava and Wang\, in which we consider different families of degr ee-n polynomials in one variable\, and determine the proportion of those h aving squarefree discriminant. Finally\, I will describe various applicati ons of these results\n LOCATION:https://researchseminars.org/talk/CMI/11/ END:VEVENT END:VCALENDAR