In 1983, Gerd Faltings proved the Mordell conjecture stating that curves of genus at least two have only finitely many rational points. This can be understood as the statement that most polynomial equations (in a precise sense)
f(x,y) = 0
of degree at least 4 have at most finitely many solutions. However, the effective version of this problem, that of constructing an algorithm for listing all rational solutions, is still unresolved. To get a sense of the difficulty, recall how long it took to prove that there are no solutions to
xⁿ + yⁿ = 1
other than the obvious ones. In this talk, I will survey some of the recent progress on an approach to this problem that proceeds by encoding rational solutions into arithmetic principal bundles and studying their moduli in a manner reminiscent of geometric gauge theory.
Mathematician Dr Anna Romanov (Visiting Researcher, Sydney Mathematical Research Institute) discusses her research and path in mathematics, as well as how an undergraduate project of hers caught the eye of xkcd’s Randall Munro.
Successful applicants for SMRI’s International Visitor Program – August 2020 include Sheehan Olver, Henri Guenancia, Christof Melcher, Rafał Kulik, Erwan Rousseau, Mark Andrea de Cataldo, Jana de Wiljes, Paul Griffiths, Ivan Angiono, Vladimir Kazakov and Martin Schmidt.
SMRI Algebra and Geometry Online Seminar Coherent categorification of quantum loop sl₂ Peng Shan (Tsinghua University) Monday, 26 October, 14:00–15:30 AEST (Sydney) Other time zones: Vancouver, Sun 20:00; Toronto, Sun 23:00; London, Mon 04:00; Cape Town, Mon 05:00; Mumbai, Mon 08:30; Beijing, Mon 14:00 We explain an equivalence of categories between a module category of …
Congratulations to Geordie who has been announced as a finalist in the 2020 Australian Museum Eureka Prizes, in the category of Leadership in Innovation and Science.
SMRI Algebra and Geometry Online Seminar Harmonic analysis on GLₙ over finite fields Shamgar Gurevich (University of Wisconsin, Madison) Thursday, 08 October, 11:00–12:30 AEST (Sydney) Other time zones: Vancouver, Wed 17:00; Toronto, Wed 20:00; London, Thu 01:00; Cape Town, Thu 02:00; Mumbai, Thu 05:30; Beijing, Thu 08:00 There are many formulas that express interesting properties …
Congratulations to the successful applicants of the Domestic Visitor Program – July 2020.
SMRI Algebra and Geometry Online Seminar Tate’s thesis in the de Rham setting Sam Raskin (University of Texas at Austin) Tuesday, 04 August, 11:00–12:30 AEST (Sydney) Other time zones: Vancouver, Mon 18:00; Toronto, Mon 21:00; London, Tue 02:00; Cape Town, Tue 03:00; Mumbai, Tue 06:30; Beijing, Tue 09:00 This is joint work with Justin Hilburn. …
SMRI Algebra and Geometry Online Seminar On the derived category of the Iwahori–Hecke algebra Eugen Hellmann (University of Münster) Monday, 06 July, 17:00–18:30 AEST (Sydney) Other time zones: Vancouver, Mon 00:00; Toronto, Mon 03:00; London, Mon 08:00; Cape Town, Mon 09:00; Mumbai, Mon 12:30; Beijing, Mon 15:00 In this talk I will state a conjecture …
International visitor Dr Nancy Scherich discusses her research on braids, life as an early career researcher, and her experience combining mathematics with her love of dance.