NUmber Theory Seminar 2026

Miscellaneous

In semester 1 we are meeting on an adhoc basis. Request to subscribe to the mailing list to receive announcements.

  • Wednesday 13 May, 11am in Peter Hall 107: Dividing to victory! by Tim Trudgian (UNSW Canberra).

    Abstract: Euclid’s algorithm for division allows us to divide two numbers, keep track of remainders, and recover GCDs. I will discuss other algebraic settings: some rings are known to be Euclidean (meaning they have this algorithm), some are known not to be; many are unknown. I will end with a summary of recent work done by Bagger, Booker, Kerr, McGown, Starichkova, and me, that resolves completely the case of cyclic cubic fields.

  • Friday 8 May, 10am in Peter Hall 162: Complex and p-adic multiple L-functions, by Hidekazu Furusho (Nagoya University).
  • Wednesday 6 May, 11am in Peter Hall 107: Emirps and the reverse Goldbach conjecture, by Daniel Johnston (UNSW Canberra).

    Abstract: In recent years, there has been an explosion of results related to the digital properties of prime numbers. In this realm, emirps have been a popular object of study. That is, prime numbers which are also prime when you reverse their digits in a fixed base. In this talk, I will present an overview of recent results on this topic, and also discuss soon to be released work on a "reverse" Goldbach conjecture.

  • Wednesday 22 April, 11am in Peter Hall 107: A Borel-Casselman theorem for non-tame double covers, by Edmund Karasiewicz (National University of Singapore).

    Abstract: The theory of automorphic forms sometimes requires working with covers of reductive groups, rather than with linear algebraic groups. For example, the Jacobi theta function naturally lives on the metaplectic group, a double cover of SL2, which is not linear. This motivates the study of representations of covers of p-adic reductive groups. For such covering groups one would like to prove a local Langlands correspondence (LLC). In the case of linear groups, the LLC was established for the principal Bernstein block by combining the Borel-Casselman Theorem, which reduces the problem to the representation theory of affine Hecke algebras, with the work of Kazhdan-Lusztig on the representation theory of these algebras. To extend this result to covering groups one must prove an analog of the Borel-Casselman Theorem. For tame covers this was accomplished by Savin, but the non-tame case has remained open. In this talk, I will describe recent joint work with Shuichiro Takeda in which we prove an analog of the Borel-Casselman Theorem for non-tame double covers.

  • Wednesday 1 April, 11am in Peter Hall 107: Volcanoes, explosives, and other arithmetic calamities, by Alex Ghitza. Report on joint work with Dhruv Gupta and Max Kortge.