In sporting news this week, our Badminton A team beat Red Panda Society 6 - 0, and our Football team won 7 - 0 against Gardner FC.
On Wednesday (30th), we will be running Maths Café in the UG Workroom as always, from 1300 to 1500. As usual, we will be bringing some food for you to enjoy.
If you have any academic questions, our academic support officers (and many other attendees) will be happy to help. Also feel free to ask any questions about LaTeX.
Celebrate Halloween with WMS! Join us for a spooky drinking circle, good vibes, and great company. Wednesday (30th), starting at 1900 in Fusion.
On Thursday (31st), we have our regularly scheduled WMS Talk in MS.04, starting at 1800. This time, we have two student speakers, Kyle Thompson and Kit Liu.
Title: Sheaves and the Serre–Swan Theorem
Abstract:
What is geometry? The study of shapes. What’s a shape? A space with some structure. What structure? A sheaf. Sheaves arise in mathematics all over the place, from geometry to logic, and – while complicated – they arise from the simple goal of studying the functions on a space. This talk focusses on studying the most basic applications of sheaves to construct the natural category in which to do geometry: the category of locally ringed spaces.
Additionally, once we have a space, we care about what are called “vector bundles” over this space – objects constructed by taking a space and attaching a vector space to each point. By viewing these objects in terms of sheaves we can gain insight into their algebraic structure by introducing the powerful so-called Serre–Swan theorem. A theorem that has applications to topology, differential geometry, and algebraic geometry, giving us a comprehensive characterisation of the possible vector bundles we can define over any (reasonably nice) space.
Title: Structural Foundations
Abstract:
Suppose you were asked, “is 3 ∈ N?” Being a natural number, 3 is indeed a member of N, so the answer is “yes”. On the other hand, the question, “is π ∈ Q?”, would quickly receive an answer of “no”. Now, suppose you were then asked, “is π ∈ log?”
You’d might pause for a moment, before again answering in the negative, but for a different reason than before. After all, π is a number, and log is a function, so π being a member of log – whatever that means – would be ridiculous! A better answer might be to declare the question as meaningless.
However, in the standard foundational framework of ZFC – Zermelo–Fraenkel set theory with Choice – everything is a set, so the question “is π ∈ log?” should have a yes-or-no answer.
In this talk, we present the structuralist’s answer to this problem; a way of formulating the foundations of mathematics that more closely resembles how mathematicians actually manipulate sets in practice (or, at least in algebraic settings).
On Friday (1st), we are running Coffee and Cake, our weekly welfare event, from 1600 to 1700, in MS.01. Drop in to get a hot drink and some food, and relax with others in an informal and friendly environment.
Next Monday (4th), we are hosting Round 1 of the UK University Integration Bee, starting at 1800 in MS.01! You will be competing against your peers, as well as teams from the UK and Singapore, at universities including Oxford, Cambridge and Imperial. Just bring yourself, paper, and pen!