SMRI Algebra and Geometry Online, 07 December: Minhyong Kim – Recent progress on the effective Mordell problem

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.

Anna Romanov

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 the International Visitor Program – August 2020

Visit information up to date as of 13 October 2020. For current information, see the visitor list. Sydney Mathematical Research Institute acknowledges the valuable contributions (financial and otherwise) to the International Visitor Program made by the School of Mathematics and Statistics at the University of Sydney and by the hosts and universities listed below. Sheehan …

SMRI Algebra and Geometry Online, 26 October: Peng Shan – Coherent categorification of quantum loop sl₂

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 …

Geordie Williamson is a finalist for the 2020 Eureka Prizes

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. The Eureka Prizes are Australia’s most comprehensive national science awards. This year’s winners will be announced on 24 November.

SMRI Algebra and Geometry Online, 08 October: Shamgar Gurevich – Harmonic analysis on GLₙ over finite fields

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 …

Successful applicants for the Domestic Visitor Program – July 2020

Visit information up to date as of 04 August 2020. For current information, see the visitor list. James Borger (Australian National University) Research interests: Algebra, number theory, algebraic geometry Dates: 7 September – 18 September 2020 Lance Gurney (Australian National University) Research interests: Prismatic cohomology, shtukas, Dieudonné theory, CM elliptic curves, Drinfeld modules, Lubin-Tate modules, …

SMRI Algebra and Geometry Online, 06 July: Eugen Hellmann – On the derived category of the Iwahori–Hecke algebra

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 …

Nancy Scherich

Dr Nancy Scherich (Visiting Assistant Professor, Wake Forest University, North Carolina) discusses her research on braids, life as an early career researcher, and her experience combining mathematics with her love of dance. Dr Scherich was the 2017 winner of the Dance your PhD competition.