Unfortunately, there won’t be a TMS talk tonight. Instead, we will be guiding you around Cambridge for the TMS Pub Crawl. To join us, go to Trinity College Bar at 8:30 tonight (30 October), and we will take you to various pubs, including the Maypole, the Mitre and the Pickerel. We hope to see lots of you there!

# Dr Michael Tehranchi – The Prices of Call Options

Tomorrow’s talk will be given by Dr Michael Tehranchi

**Talk**

Speaker: Dr Michael Tehranchi

Title: The Prices of Call Options

A call option is a basic example of a financial derivative. Black, Scholes and Merton published in 1973 a theory for ‘rational pricing’ of call options, for which the Nobel Prize was awarded in 1997. This talk will briefly explain this theory, and discuss how the pricing of call options has some interesting mathematical properties – touching on probability, convex analysis and even algebra.

The talk will take place at 8:30PM on Monday 23 October in the Winstanley Lecture Theatre. As usual there will be free port and juice served before the talk at 8:15PM. This talk is for members only, but there will be a chance to sign up for TMS life membership for £2.50.

# Dr Andras Zsak – Embedding Structures with Distortion

Tonight’s talk will be given by Dr Andras Zsak

**Talk**

Speaker: Dr Andras Zsak

Title: Embedding Structures with Distortion

There is a wide variety of structures that are equipped with a distance. A familiar example is three-dimensional Euclidean space: here the distance is the length of the straight line segment joining two points. In this example there is an additional feature: the presence of vector addition and scalar multiplication. There are examples, however, that do not possess such additional features, and it is an important question to determine whether such arbitrary structures can be embedded into ones with a vector structure like Euclidean space. This has consequences for large data, algorithms, compressed sensing, etc., some of which have emerged in unexpected and surprising ways.

The talk will take place at 8:30PM on Monday 16 October in the Winstanley Lecture Theatre. As usual there will be free port and juice served before the talk at 8:15PM. This talk is for members only, but there will be a chance to sign up for TMS life membership for £2.50.

# Prof Imre Leader – Infinite Games

The TMS is up and running again for the new academic year!!

The first talk of the year will be tomorrow and will be given by Prof Imre Leader.

**Talk**

Speaker: Prof Imre Leader

Title: Infinite Games

Abstract: Suppose that we are playing a game, but the game might go on forever and so not end. How could we assign a winner or loser in that situation? This sounds like a silly question, but in fact it isn’t, and it leads to some very interesting phenomena.

The talk will take place at 8:30PM on Monday 9 October in the Winstanley Lecture Theatre. As usual there will be free port and juice served before the talk at 8:15PM. This talk is for members only, but there will be a chance to sign up for TMS life membership for £2.50.

# Garden Party 2017

To mark the end of exams and some (hopefully) excellent weather, the TMS is holding its annual Garden Party on Saturday 10th June. It will go from 1:30 to 3:30 on the Trinity College Fellows’ Bowling Green (off Great Court, entrance by the clock tower). In the event that the weather does take a turn for the worse, it will be held under the cloisters by the Wren Library.

Besides an assortment of snacks, cheeses and fruits, there will be Pimm’s and 12 gallons of ice cream available. Flavours include Vanilla, Strawberry, Creme Brulee and (of course) Brown Bread.

Entry is free for all members of the TMS but if you are not one, then it is very easy to join at the door for £2.50.

We hope to see many of you there!

# TMS AGM 2017

The TMS annual general meeting happened on Wednesday 15th March, and a new committee was elected as follows:

President | Jason Kwong |

Vice President | Damon Zhong |

Secretary | Warren Li |

Junior Treasurer | Alan Sun |

Membership Secretary | Peter Andreev |

Constable | George Fortune |

We would like to thank the previous committee for their good work this year.

The Trinity Mathematical Society is proudly sponsored by Jump Trading and ATASS Sports.

# Prof Timothy Gowers – A problem about triples of integers

Tomorrow’s talk will be given by Prof Timothy Gowers

**Talk**

Speaker: Prof Timothy Gowers

Title: A problem about triples of integers

Abstract: I shall talk about a problem that sounds like a reasonably easy IMO-style question, but which, rather surprisingly, is still unsolved. I shall talk about some non-trivial partial results, which are joint work with Jason Long, that fall well short of what is believed to be true.

The talk will take place at 8:30PM on Monday 13 March in the Winstanley Lecture Theatre. As usual there will be free port and juice served before the talk at 8:15PM. This talk is for members only, but there will be a chance to sign up for TMS life membership for £2.50.

# Symposium 2017

This year’s Trinity Mathematical Society Symposium is running from 10:00 to 18:00 on Sunday 26nd February. We have talks by fellows and PhD students, ranging across all areas of mathematical research. The event is free and open to all; no particular specialist knowledge is assumed. There is no need to stay for the whole day – just drop in on talks you find interesting.

**The program is:**

12:15 – 14:00 Curve Fever: Curve Fever

**12:15 – 13:15 BRUNCH**

**15:30 – 16:00 BREAK**

**19:45 – Annual Dinner**

(Made possible by the kind support of the Heilbronn Fund)

# Prof Tim Pedley – Spherical squirmers

Tonight’s talk will be given by Prof Tim Pedley.

**Talk**

Speaker: Prof Tim Pedley

Title: Spherical squirmers – models for swimming micro-organisms: how a Tripos question led to a new field of research.

Abstract: In 1952, Sir James Lighthill (FT) introduced the simplest possible model of a swimming microorganism of finite size, intended as a model of a single-celled protozoan covered in beating cilia. The model consisted of a sphere, on the surface of which material points undergo small-amplitude oscillations. In 1971, Lighthill’s student, John Blake (FT), completed the calculations and in particular showed how to model the ‘metachronal’ wave patterns exhibited by beating cilia. In 1986 the speaker set a Part II Tripos question, to analyse an even simpler model consisting of a sphere whose surface moves tangentially with timeindependent velocity: a steady spherical squirmer. This has led to a substantial body of research on the optimisation pf the swimming and nutrient uptake of individual squirmers (Eric Lauga, FT), and on the hydrodynamic interactions between pairs of steady squirmers and their influence on self-diffusion in suspensions. The final topic describes measurements and modelling of metachronal waves in Volvox, the only truly spherical multicelled ‘organism’, culminating in the prediction of the mean swimming speed and angular velocity of free-swimming Volvox. The predictions are compared with experimental observations. [FT ≡ Fellow of Trinity]

The talk will take place at 8:30PM on Monday 20 February in the Winstanley Lecture Theatre. As usual there will be free port and juice served before the talk at 8:15PM. This talk is for members only, but there will be a chance to sign up for TMS life membership for £2.50.

# Annual Dinner & Double Talk Week

**Annual Dinner**

**7:45pm, Sunday, 26th of February**in the Old Kitchens. There will be a half hour reception with sparkling wine and apple juice. This year, to better accommodate people’s timetables, we’ll be staggering the ticket releases across the following times and dates:

**Double Talk Week**

Speaker: Dr Thomas Sauerwald (Computer Lab)

Title: Multiple Random Walks

Abstract: Consider a simple random walk on a finite network. The expected time it takes for a single walk to visit all nodes is a well-studied quantity and has been computed for many topologies including paths, grids, random graphs and hypercubes. But how long does it take for two or more independently running random walks? This talk will explain why this may be an interesting question and present a few surprising results.

Thursday 16 February, 6:15PM

Speaker: Dr Sander Dieleman (Google DeepMind)

Title: Deep learning for music recommendation and generation

Abstract: The advent of deep learning has made it possible to extract high-level information from perceptual signals without having to specify manually and explicitly how to obtain it; instead, this can be learned from examples. This creates opportunities for automated content analysis of musical audio signals. In this talk, I will discuss how deep learning techniques can be used for audio-based music recommendation. I will also briefly discuss my ongoing work on music generation with WaveNet.

Both talks will take place in the Winstanley Lecture Theatre. As usual there will be free refreshments 15 minutes before the talk. The talk on Monday is for members only, but there will be a chance to sign up for TMS life membership for £2.50. The talk on Thursday is free for all.