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2023-2024

2024 Trinity Term

10/06/2024 - Decidability of Properties of Orbit-Finite Graphs

Speaker: Benjamin Solomon (aka Ben Solo)

We will study properties of orbit-finite graphs, in which both the set of vertices and the set of edges are definable by formulas over the theory of equality. We show that the Hamiltonicity of locally infinite orbit-finite graphs are decidable.

03/06/2024 - Simultaneously Small Fractional Parts of Polynomials

Speaker: Joshua Cheuk Fung Lau

We will study quantitatively on whether how we can make the fractional part of polynomial smaller. This is an improvement of the recent results by Baker, 2016 and Maynard, 2021.

20/05/2024 - Dirichlet's Theorem of Prime Numbers

Speaker: Sidharth P. Suresh

We will attempt to prove a quantitative version of the Dirichlet's Theorem, which states that any arithmetic progressions of integers contain infinite number of primes.

13/05/2024 - Applications of Galois Theory

Speaker: D. Pedro Lack

We have now learned what the Fundamental Theorem of Galois Theory is, let's look at its applications. We will touch on the following topics:

  • the constructibility of numbers by compass and straightedge and origami,
  • solvability of algebraic equations by radicals.