In week 5 we are joined via video link from Australia by Stephanie Hanson, a York Alumn, who will be talking on the patterns in the prime numbers. Abstract: "Humans have studied prime numbers for thousands of years but some of the biggest mysteries in mathematics revolve around these simple objects. What can we write as the sum of two…
We will give a short introduction to fractal geometry: What kind of sets are called fractals? How to find fractals? How to classify and compare them to each other? What kind of techniques are needed to study them? Along the way we’ll learn to understand iterated function systems, dimensions and measures. A Mathsoc public lecture.
Roger Colbeck gave an interesting public lecture entitled Generating Random Numbers by Winning 'Unwinnable' Games. The video of the lecture is now available online.
Abstract: "I will present some simple games that look, at first (and perhaps even second) sight, to be unwinnable. However, it turns out that whether these games can be won or not depends on physics: while players who exploit classical physics could not win such games, a player well-versed in quantum physics can. I will explain that, as well as saying something truly remarkable about the world, closely related to Einstein's 'spooky action at a distance', winning such games can be put to practical use. In particular, it allows us to certify the generation of random numbers, something that is also impossible in classical physics."
Renormalisation: the "Hocus Pocus" which fixed Quantum Physics by Alejandro de la Rosa Gomez (Video)
York Ph.D. student Alejandro de la Rosa Gomez gave a presentation on some of the tricks which have led to many breakthroughs in theoretical physics. You can now watch the video below.
Here's the abstract:
Nature is sneaky. Once we figure out how something works and can finally go to bed, she makes sure we wake up to a harder problem. To be fair, we're very ambitious: we would like a single, beautiful idea to explain everything we see. A priori, there's no reason why this should be true. But we might as well explore the possibility. After all, as humans, we enjoy pretty, simple things.
The truth is, the rules of the game which we've discovered so far are simple, but they're not easy. Something as simple as the behaviour of a hydrogen atom in a magnetic field took several decades to figure out precisely. And we had to sacrifice mathematical consistency to do so.
In fact, the trickstery used in that single discovery allowed us to explain a lot of phenomena. In this talk I will present to you the set of unconventional tricks we theoretical physicists use to make calculations, not before I review the ideas which lead to one of the most incredible scientific achievements of the last century.
In 2014 Richard Elwes gave a public lecture entitled "Gödel, Incompleteness & Unprovable Theorems", which YSTV kindly recorded for us. You can watch it here, or on the YSTV website at https://ystv.co.uk/watch/mathslectures/godel-incompleness/.
Shaun Isherwood has written an introduction to category theory and agreed to make it available via the MathSoc website. Category theory is one of the most fundamental and most enlightening areas of modern algebra, providing a general theory explaining many properties of mathematical systems, and pointing our the similarities in structure between many branches of mathematics, and I would highly…
We had a webinar talk on Goldbach's conjecture on January 23 2015, given by Stijn Hanson. You can now watch it here.
Back in 1742, Christian Goldbach wrote a letter to Euler suggesting that every even number could be written as the sum of two prime numbers. This is a notoriously unsolved problem but we endeavour to explain the machinery behind three of the best results we have towards understanding this famous conjecture and talk about some of the speaker's own work.
As part of her final year project, Juliet Cooke has written a brief introduction to homotopy, one of the key concepts in algebraic topology. She has agreed to allow us to make this available on the MathSoc website under the Creative Commons Attribution License. You can also download the article in full pdf form here. In this article I shall be…
In week 9, we are presenting an interesting geometry talk from Alan Haynes. Abstract: Given an infinite sheet of paper, an unmarked ruler, and a compass (for drawing circles), is it possible to divide an angle of 60 degrees into three equal angles? Well, the ancient Greeks couldn’t do it, and neither could anyone else for about the next 2000…
In week 5 of the Autumn 2014 term, we had a wonderful public lecture delivered by world renowned oxford number theorist Roger Heath-Brown, detailing the history of prime numbers, and some exciting recent progress in the field. We also had a great time talking with Roger after the event, and invite you to join us for future public lectures.