# Past Events — Lent 2017

*Unless otherwise stated, the talks are held at 7pm in MR2 at the Centre for Mathematical Sciences (the CMS), Wilberforce Road.*

### 24th January 2017 — Board Games and Pizza Night

*This event was held at 6:30pm.*

Traditionally well attended and popular with members, this event is a great way to relax for a couple of hours and get some tasty pizza!

### 28th January 2017 — Dr. Julian Holstein (Lancaster)

#### Bezout's theorem as a pathway to algebraic geometry

In how many points do two curves in the plane intersect? This question has a very nice answer that is unfortunately not entirely true. But sometimes in mathematics the answer to a question is so good that it is worth keeping, even if it is not correct. The new challenge is then to ask the question in a better way.

To find the right question in this case we will take a brief tour of algebraic geometry, meeting both classical and modern ideals. If time permits we will even catch a brief glimpse of the cutting edge of theory in algebraic geometry.

### 3rd February 2017 — Prof. Ciprian Manolescu (UCLA)

#### Manifolds

Manifolds (spaces that look locally like R^{n}), are the basic objects of study in topology. In this talk I will describe what is known about their classification. I will mention the different versions of Poincare conjecture, and also strange phenomena that appear in high dimensions: exotic smooth structures on the same manifold, and manifolds that cannot be triangulated.

### 7th February 2017 — Movie night

*This event was held at NCR, Pembroke College.*

The film will probably have some (possibly tenuous) link to maths...

### 24th February 2017 — Dr. Julia Godecke (DPMMS)

#### Universal Properties: a categorical look at undergraduate algebra and topology

Mostly without knowing, you have all already met lots of objects with universal properties throughout your undergraduate courses. Working with the universal property of an object rather than its concrete implementation can have huge benefits: it gives an implementation-independent definition, which can therefore be used in many different mathematical areas at once. It also gives much greater conceptual clarity about the object in question and what role it plays within its area. In general, the concept of universal property is a very important one and crops up in nearly all areas of pure mathematics. My own field of category theory is the natural setting to investigate this concept. After a short introduction to the ideas of category theory I will spend most of the talk highlighting the universal properties of objects you are very familiar with, such as cartesian products and quotients, as well as giving you insight into a few you may not yet have met.

Slides of the presentation can be found here.

### 3rd March 2017 — Prof. Colm-cille P. Caulfield (DAMTP)

#### To shake or to stir: The Mathematics of Mixing

Understanding the mixing of fluids of different properties is a fundamentally important challenge with applications from making of the perfect cocktail to describing the transport of heat and pollutants in the atmosphere and oceans. The underlying mathematics has a beauty all its own, due not least to a subtle and non-intuitive interplay and between a wide range of physical processes and the inherently nonlinear dynamics of fluid motion. In this talk, I both review some of the key successes in the mathematical description of mixing, and also introduce some facinating open questions.

### 5th March 2017 — Archimedeans Annual Dinner

*This event was held at Doubletree by Hilton Hotel.*

### 7th March 2017 — Elisenda Girgsby (Boston College)

#### Braids, surfaces, and homology-type invariants

It has long been known that closed braids arise naturally when studying the vanishing sets of complex 2-variable polynomials. On the other hand, it should come as no surprise that not every closed braid arises in this way. Indeed, Lee Rudolph has given us a clean topological characterization of those that do: they are precisely the braids whose associated mapping classes satisfy a condition he calls quasipositivity. I'll remind you what this all means, then--time permitting--how the algebraic structure of some braid and link invariants coming from ideas in physics can say things about quasipositivity and other related notions.

### 10th March 2017 — Prof. James Norris (Statslab)

#### Aggregation and coalescence

I will show how a simple model for random planar aggregation leads via some complex analysis to a continuum of coalescing random walks.