# Past Events — Lent 2015

*Unless otherwise stated, the talks are held at 7pm on Zoom. For every talk, a sign-up form will be circulated via the mailing list and posted on the Facebook page.*

### 15th January 2015 — Professor Barry Simon (Caltech)

#### Singular Eigenvalue Perturbation Theory

Eigenvalue Perturbation Theory is central to the theory of nonrelativistic quantum mechanics going back to Schrodinger's first papers. This lecture will review what is known about the eigenvalues in physical situations where one doesn't have simple convergence to a new isolated eigenvalue. Included are the anharmonic oscillator and Zeeman effect (divergent series and summability), autoionizing states in atoms (complex scaling and resonances), Stark effect (exponentially small resonances) and double wells (instantons).

### 16th January 2015 — Pizza and Board Games Night

### 23rd January 2015 — Professor Béla Bollobás (DPMMS)

#### Distances, Sums and Products

Paul Erdös had an amazing ability to pose problems that are easy to understand, look innocent, perhaps even trivial, and are not only hard, but eventually also open up entirely new areas of mathematics. In this talk I shall present some of Erdös's favourite problems, and discuss recent developments.

### 29th January 2015 — Professor Ben Green (Oxford)

#### No-three-in-a-line problems

Let S be a set in some vector space. What's the largest subset of S with no three collinear points? This simple question (for various choices of S) has led to some interesting mathematics touching on a diverse range of subjects from combinatorial number theory to algebraic geometry. I will discuss some of these topics from an elementary viewpoint.

### 5th February 2015 — Professor Raymond Goldstein (DAMPT)

#### Evolution of Biological Complexity

It is a general rule of nature that larger organisms are more complex, as measured by the number of distinct types of cells present. Yet, increasing size has both costs and benefts, and the search for understanding the driving forces behind the evolution of multicellularity is becoming a very active area of research. In this talk, I will discuss the mathematics and physics underlying this biological problem.

### 15th February 2015 — Problems Drive

Compete in pairs in this light-hearted contest in witty mathematics and mathematical wit. There will be various prizes for different achievements and light refreshments for all those who attend.

### 26th February 2015 — Professor Geoffrey Grimmett (Statslab)

#### The self-avoiding walk problem

How many n-step self-avoiding walks exist on a given infinite graph? This question is easy to state but notoriously hard to answer. I will describe the history of the problem, and will summarise progress and open questions, one of which may seem quite elementary.

### 28th February 2015 — Annual Dinner

*This event was held at Doubletree Hilton Hotel.*

The Archimedeans cordially invite you to join us for our annual dinner on Saturday 28^{th} February. This will be a three course meal with wine included, preceded by a drinks reception.

We are delighted to announce that we will be joined this year by Professor Béla Bollobás, who will be our guest speaker at the event.

Details

- Date: Saturday 28
^{th}February - Timings: 7pm, Reception; 7:30pm, Dinner
- Location: Doubletree Hilton Hotel
- Map: here
- Price: £20 for members, £25 for non-members
- Payment Deadline: Friday 13
^{th}February - Dress Code: Black tie preferred

If you have any enquiries, please address them to the external secretary , with 'Archimedeans Annual Dinner' in the subject line.

### 5th March 2015 — Professor Imre Leader (DPMMS)

#### Eating and Racing

We'll consider some interesting finite games and some interesting infinite games.