Göttingen Junior Number Theory Seminar
04.11.2014 - Julia Brandes: Learning how to count
Abstract: Once upon a time (i.e. roughly 15 years ago) in a land far, far away (Michigan) there was a PhD student we'll call STP for the time being, to whom his supervisor had set the problem of finding a lower bound on the number of linear spaces on certain hypersurfaces. He solved the problem to his supervisor's satisfaction and eventually got a PhD awarded for his work, but when he submitted it to a journal, the referee complained that he wasn't really counting what he claimed to count. STP wanted nothing so much as to get his work published, so he devised a crude argument that gave some lower bound, albeit not the expected one, but then he didn't really care about the issue, knowing that morally it should not make any difference, and the matter was settled.
That was, however, only for the time being. Many years later, and on a different landmass, the same supervisor set a related problem to one of his later PhD students. This time round, it was about not about lower bounds for the number of linear spaces, however, but about asymptotics. The problem was the same, though: The student didn't actually count the things she pretended to count (although so far no referee has complained about that). She would have included a crude argument similar to that of STP, but that would destroy the asymptotics, so in the first go she simply ignored the issue and got her PhD without tackling the problem.
The question kept haunting her, though. Will she be able to once and for all answer the question STP's referee posed back in the days? Will she be able to count actual linear spaces? This is your opportunity to find out!
18.11.2014 - Fabian Dehnert: On Waring's Problem for cubes
02.12.2014 - Oscar Marmon: The determinant method
09.12.2014 - Oscar Marmon: The determinant method, part II
16.12.2014 - Tomos Parry: The third moment for primes via Hooley
13.01.2015 - Peter Maga: The four squares theorem via automorphic forms
20.01.2015 - Peter Maga: The four squares theorem via automorphic forms, part II
16.03.2014 - Lutz Helfrich: N/A
Abstract: Im Vortrag werde ich eine Kurzeinführung in das zehnte hilbertsche Problem (Entscheidbarkeit der Lösbarkeit diophantischer Gleichungen) geben. Insbesondere werde ich in diesem Zusammenhang auf Suchschranken für die kleinste Lösung einer quadratischen diophantischen Gleichung eingehen und das Ergebnis meiner Dissertation vorstellen, das diese Suchschranken auf Zahlkörper verallgemeinert.
Home Junior Number Theory