BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Lasse Grimmelt (University of Oxford) DTSTART:20220228T120000Z DTEND:20220228T123000Z DTSTAMP:20260423T052755Z UID:POINT/42 DESCRIPTION:Title: G oldbach's Problem with Almost Twin Primes\nby Lasse Grimmelt (Universi ty of Oxford) as part of POINT: New Developments in Number Theory\n\n\nAbs tract\nThe Binary Goldbach and Twin Prime conjectures have shaped the deve lopment of Analytic Number Theory in the the last century in fundamental m anner. Among the strongest approximative results that we know are a power saving bound on the exceptional set of the first conjecture\, proved by Mo ntgomery and Vaughan\, and Chen’s result on almost Twin Primes. \n\nIn t his talk I present joint work with J. Teräväinen that aims to combine th e two just mentioned results. More precisely\, we show a power saving exce ptional set bound for sums of two primes $p_1\, p_2$ such that $p_1+2$ has at most 2\, $p_2+2$ at most 3 prime divisors. This improves previous resu lts of this type in both strength of saving and number of prime divisors o f the shifted primes. Our proof uses a wide range of techniques. I will gi ve a sketch of how they play together and what the limitations are.\n LOCATION:https://researchseminars.org/talk/POINT/42/ END:VEVENT END:VCALENDAR