2025-2026
2026 Hilary Term
19/01/2026 (Week 1) - Fermat's Last Theorem for p-adics
Speaker: Pedro Lack
We have done Fermat's Last Theorem for polynomials in the past, so it shouldn't be too hard to do that for p-adics as well!
2025 Michaelmas Term
01/12/2025 (Week 8) - Olympiad Linguistics
Speaker: Elliot and Yutong Heng
Elliot and Yutong were both participants at the International Linguistics Olympiad 2025 that happened in Taipei, and wanted to share our enthusiasm for Linguistic Problems with others at PedroSoc.
This talk will be slightly more interactive as we try to guide you through the thought process of solving Linguistics Olympiad Problems, so more participants are encouraged to show up :)
24/11/2025 (Week 7) - Parking Functions, Trees and Polytopes
Speaker: Eshwar Kolli
This is a talk on a very cool relationship between a seemingly easy probability questions and some deep combinatorics / geometry - specifically the relationship between polytopes, parking functions and labelled trees.
17/11/2025 (Week 6) - The Aliens Trick
Speaker: Çağan Yanmaz
This talk explores a fascinating connection between a modern algorithmic technique and a classical concept from mathematics: the use of Lagrange multipliers. The technique, known as the Aliens Trick, was originally discovered in the context of the IOI 2016 problem Aliens and has since become a powerful optimisation method in Dynamic Programming.
I will begin with a gentle introduction to Competitive Programming and the role of Dynamic Programming in algorithm design. Then, I’ll explain how the Aliens Trick works, why it’s effective, and how it reveals links between different ways to solve optimisation problems. If time allows, I’ll demonstrate the full solution to the Aliens problem and show how similar ideas appear in other contexts.
The talk will be self-contained and accessible to all; a solid mathematical background will be helpful, but no prior knowledge of Computer Science is required.
17/02/2025 (Week 5) - Five mini talks
Do you desire to give a talk in PedroSoc, but you can't put together a full 1h30 talk? Do you want to test your skills, giving a shorter talk? The Week 5 talks series is for you! We will try to get 5 mini-talks (between 15 and 30 minutes) in one meeting! Hoping to see many of your submissions! Any ideas (not necessarily maths) invited!
| Speaker | Content |
|---|---|
| Inha Choi | The Structure of Paradox I shall present the various ways of paradox, their resolution, and their implications. |
| Edison Fu | Axiomatic Special Relativity What have you heard about special relativity? Spacetime is funny, sometimes time dilates and length contracts? This is boring stuff... In this talk, I will be proving all these classic results from Einstein's original two postulates. I will also be discussing the importance (and sheer beauty!) of symmetries in the geometry of spacetime, and how they clear up loose ends left by classical physics. |
| Jonathan Sakunkoo | Area of Lattice Polygon Have you ever doodled on graph paper? Connected the dots in some way, ended up with something interesting - perhaps something more complex, like your favorite cartoon character, or perhaps something simpler, like a smiley face? Perhaps you may even have wondered about such a geometric figure's area... (or maybe not, but come to my talk to find out anyways) Come to my talk to find out about an outrageously beautiful and simple formula that (arguably) trumps the others methods...! It'll be very accessible, that is, you'll understand :3 |
| Tom Davies | Trigonometric and Hyperbolic Functions Trigonometric functions are remarkable and versatile mathematical objects which show up everywhere. What has often interested me are the two, quite distinct approaches that one can take to discovering, (informally) defining and developing them: the geometric and analytic approaches. I will offer a (new?) way of linking these approaches which will (I hope) be intuitive and beautiful. I will also discuss generalisations, in particular hyperbolic functions. Please do come along if this sounds interesting! |
| Rico Chung | Mysteries of the Cantor set What does it mean for a set to take up space, or even more strangely, to take up no space at all? In this talk, I’ll give an introduction to measure theory and explore a fascinating set in analysis: the Cantor set. We will see that rearranging bits of “dust” can transform something that occupies no space into something that does and many other fascinating results. Join me as we uncover the surprising and beautiful properties of this mind-bending set, no prerequisites required! |
03/02/2025 (Week 4) - Motivating Neural Networks
Speaker: Samuel Lam
We shall motivate the concept of neural networks by piecewise linear functions, which is a class of neural networks and solves a non-parametric regression problem. If time allows, we will explain why depth matters for neural network.
03/02/2025 (Week 3) - All about Blackjack
Speaker: Anthony Hu
Feeling lucky? Tonight is all about Blackjack, a classic casino game for all ages (18 and over). We’ll be briefly outlining the rich history of the game, before exploring how to optimize play. However, unlike most Monte Carlo approaches, we’ll attempt to use analytical solutions to derive solutions from first principles. The maths should be very accessible to all attendees. So sit back, relax, sip on a virgin martini (that I’ll make), and enjoy the show!
And feel free to come in suit and tie, up to you!
27/01/2025 (Week 2) - The Mathemagician Show
Speaker: Yifu Zhang
Be prepared for a magic show, or a mathemagic show. Unlike magicians, mathemagicians always reveal their secrets, and tonight, we are spoiled with a great one. Yifu, our mathemagicians in residence, will be performing magic tricks in PedroSoc tonight. The talk is accessible for everyone (even those with no background in mathematics or mathemagics), and no matter who you are, I am sure you will leave with a cool magic trick to impress your friends. You will also learn a bit of modular arithmetic and knot theory (Reidemeister moves).
20/01/2025 (Week 1) - Irrational Numbers
Speaker: Pedro Lack
We shall start the year by proving the Fermat's last theorem (for polynomials)! It is very exciting, still should be quite easy to follow (no prerequisites)!