BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Gwen McKinley (San Diego) DTSTART:20210507T163000Z DTEND:20210507T173000Z DTSTAMP:20260423T020957Z UID:WCS/25 DESCRIPTION:Title: Cou nting integer partitions with the method of maximum entropy\nby Gwen M cKinley (San Diego) as part of Warwick Combinatorics Seminar\n\n\nAbstract \nWe give an asymptotic formula for the number of partitions of an integer $n$ where the sums of the $k$th powers of the parts are also fixed\, for some collection of values $k$. To obtain this result\, we reframe the coun ting problem as an optimization problem\, and find the probability distrib ution on the set of all integer partitions with maximum entropy among thos e that satisfy our restrictions in expectation (in essence\, this is an ap plication of Jaynes' principle of maximum entropy). This approach leads to an approximate version of our formula as the solution to a relatively str aightforward optimization problem over real-valued functions. To establish more precise asymptotics\, we prove a local central limit theorem using a n equidistribution result of Green and Tao.\n\nA large portion of the talk will be devoted to outlining how our method can be used to re-derive a cl assical result of Hardy and Ramanujan\, with an emphasis on the intuitions behind the method\, and limited technical detail. This is joint work with Marcus Michelen and Will Perkins.\n LOCATION:https://researchseminars.org/talk/WCS/25/ END:VEVENT END:VCALENDAR