SMS scnews item created by Catherine Meister at Thu 20 Nov 2025 1001
Type: Seminar
Distribution: World
Expiry: 11 Dec 2025
Calendar1: 21 Nov 2025 0900-1100
CalLoc1: SMRI Seminar Room (Macleay A12 Room 301)
CalTitle1: IFS: Diophantine approximation in one dimension
Auth: cmeister@ac02gr132pn7c.shared.sydney.edu.au (cmei0631) in SMS-SAML

Informal Friday Seminar: Shulga

Diophantine approximation in one dimension


Nikita Shulga, University of Sydney


Informal Friday Seminar, 21st November 2025


9 am – 11 am, SMRI Seminar Room (A12 Macleay Room 301)


Abstract: In the talk I will provide an introduction to (a part of) Diophantine approximation in one dimension, a field concerned with the approximation of real numbers by rational numbers or algebraic numbers of higher degree. I will formulate some classical results like theorems by Dirichlet, Hurwitz, Lagrange, and Legendre; talk about Lagrange spectrum and continued fractions, state recent advancements in problems like Wirsing Conjecture and Zaremba’s conjecture; and provide a surprising reformulation of the Markoff Uniqueness Conjecture. Some elementary results will be proven. No prerequisites needed, and the talk is planned to be rather understandable.

The Informal Friday Seminar is a space where members of our research group can explain interesting things to each other in a casual setting. The rules of the seminar are the following:

  1. Any question/additional explanation from the audience is allowed.
  2. Ego out the window.
  3. Examples, examples, examples.

    4. The seminar is intended to be conversational, so come ready to engage. If you choose to give an IFS talk, it's important to know that part of the IFS philosophy is that learning is not linear. In other words, it if perfectly acceptable to give a talk that is a prerequisite for a talk that already happened. For IFS updates, please see the IFS website