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### From UCL Undergrad Maths Colloquium

# **UCL Undergrad Maths Colloquium**

**Winter 2014 Organizers:** Dea Bankova, Atheeta Ching - About The Colloquium

The UCL Undergrad Maths Colloquium meets weekly (*Tuesdays, 5pm at UCLU Building Level 7, Mathematics Department Room 707*) during term to discuss and share interesting mathematical topics outside of (or complimentary to) our normal lecture courses. Each week an undergraduate gives a talk on a mathematical subject or problem, e.g. p-adic numbers, noncommutative geometry, applied mathematics, et cetera. Additionally, the Colloquium arranges weekly study group sessions in a variety of topics.

## Upcoming events

The Colloquium is open to all and the talks should be accessible to anyone with a first years' undergraduate background in mathematics and/or a willingness to learn. We hope to encourage all current undergrads (regardless of their mathematical background) to attend and/or give talks.

## Study Groups

- TBA
- Is there a subject you'd like to study contact Matthew Eric Bassett, Nadine Amersi, Atheeta Ching, or Dea Bankova

## Updates and Info

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## Winter 2014 Colloquium

Organisers: Dea Bankova, Atheeta Ching

#### 14 Jan 2014

**Free groups and the topology of 1-dimensional complexes** Sam Williams (UCL Year 4)

Group theory and topology are two areas of mathematics which on first appearance seem to be distinctly unrelated. This in fact couldn’t be further from the truth. In this talk we will be bridging the connection between the topology of 1-dimensional cell complexes, or in layman’s terms graphs, and the theory of algebraic structures known as free groups.

#### 21 Jan 2014

**Introduction to high frequency wave scattering** Kin Quan (UCL Year 4)

The physical properties of waves have many practical applications and yet they are extremely difficult to solve. In this talk I will the examine the governing equations and show techniques that mathematicians use to show the behaviour of the equations without having to compute the exact solutions. This talk requires no knowledge of applied mathematics but is aimed at an audience who wishes to specialise in applied mathematics for their degrees!!!

#### 28 Jan 2014

**On The Ternary Goldbach Conjecture** Christoph Haeusser (UCL Year 4)

The binary Goldbach conjecture, which says that all even integers greater than 2 can be expressed as a sum of two prime numbers, is a famous open problem in number theory that was first conjectured by Christian Goldbach and Leonhard Euler in the 18th century.

In 2013, Harald Helfgott proved a closely related problem also posed by Euler and Goldbach. He showed that every odd integer greater than 5 can be written as a sum of three primes. This is the statement of the ternary Goldbach conjecture.

In my talk I will present a first result towards the ternary Goldbach conjecture due to Vinogradov and explain the underlying idea in a proof for it. Having done this, I will move on to talk about Helfgott’s contribution to solving the problem.

#### 4 Feb 2014

**Distributional Derivatives** Kun-Hung (Rick) Hsueh (UCL Year 4)

It is quite possible to have a step function involved in setting up a system of differential equations, which models a real world problem, and in some cases, one can run into the difficulty of needing to differentiate a discontinuous function so as to obtain the solution to the differential equations. To deal with this awkwardness, one can introduce the concept of distributional derivative. In this talk, we define Schwartz functions, linear functionals, and tempered distributions and we state and prove enough results for us to compute an example of how to find derivatives in the distributional sense.

#### 11 Feb 2014

**No Colloquium this week**

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#### 18 Feb 2014

**Reading Week: No Colloquium**

#### 25 Feb 2014

**An Introduction to Vortex Shedding** Graham Benham (UCL Year 4)

Have you ever turned your coffee spoon and wondered about those dancing whirlpools which spin around the cup? In fact the phenomenon of vortex shedding from sharp edged objects is one of great attention in the world of fluid dynamics. It has major significance in the design of aeroplane wings and the modelling of the atmosphere and oceans. In this talk I will outline one of the analytical techniques used to model this curious effect. No prior knowledge needed but a basis in complex analysis and applied maths will help.

#### 4 Mar 2014

**Euler's proof of Fermat's "two-square" theorem** Mladen Georgiev (UCL, Year 1)

A great mathematician, such as Pierre de Fermat, will always find mathematical proofs a source of inspiration. The more aesthetically pleasing the proof is, the greater the desire to share it is. Usually. Well, Fermat perceived this differently.Once a mathematician stumbles upon an intriguing conjecture, the pursuit of a proof begins immediately and it, really, goes on forever. One proof is never enough, never perfect. Fermat discovered a precise statement which enabled him to characterise all prime numbers that are sums of two squares. Surely, he attempted to prove it. Did he succeed or was he simply looking for another proof? Leonhard Euler published a proof of Fermat's intriguing conjecture. In fact, a proof that many mathematicians found pleasing. Perhaps, Fermat did too.

#### 11 Mar 2014

**Fractal theory and its applications** Naomi Kraushar (UCL, Year 2)

What happens when you have a relatively simple process that generates a set with intricate detail on every scale? In this talk I will introduce the idea of a fractal set and discuss the concepts of dimension and measure in fractal theory. We will also look at examples of fractal sets in a wide range of applications.

#### 18 Mar 2014

**Chocolate fountains, teapots and mayonnaise** Adam Townsend (UCL, PhD)

Chocolate fountains are popular features at special events. But why do they almost never use white chocolate? Would they work with water? And why, when the chocolate falls, does it fall slightly inwards? We start by entering the world of mathematical modelling: how do we pick the important features of chocolate and turn it into maths? Then we look at other common foodstuffs: does chocolate behave anything like them, and can we use our model to learn about them? With some messy experiments you can replicate at home, enjoy this introduction to non-Newtonian fluids. Marshmallows are provided for happy volunteers.

#### 25 Mar 2014

**No Colloquium this week**

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# Past Colloquia

- Winter 2014 Colloquium
- Autumn 2013 Colloquium
- Winter 2013 Colloquium
- Autumn 2012 Colloquium
- Winter 2012 Colloquium
- Autumn 2011 Colloquium
- Winter 2011 Colloquium
- Autumn 2010 Colloquium
- Winter 2010 Colloquium

# Past Study Groups

Founded Jan 2010 by Matthew Eric Bassett and Nadine Amersi.