The Holgate Lectures and Workshops sessions scheme provides session leaders who are willing to give a talk or run a workshop on a mathematical subject to groups of students or teachers. The sessions are of mathematical content and are not, for example, careers talks. Rather they are intended to enrich and enhance mathematical education, looking both within and beyond the curriculum. Holgate session leaders do not charge a fee for giving talks, but local organisers are expected to pay travel expenses and subsistence costs, together with any local costs of organising the session. The LMS will pay an annual honorarium to the session leaders.

The scheme is named in memory of Philip Holgate, who helped ensure the success of the LMS Popular Lectures.

The Education Committee has chosen the below eight individuals to act as session leaders. The profiles below show their background and mathematical interests and provides contact details for anyone interested in organising a Holgate Session. The talks provided below are firmly intended as indicative and not comprehensive. Session Leaders will work with local hosts to develop and adapt sessions to the needs of the audience. The LMS strongly encourages schools hosting a Holgate session to consider collaborating with other local schools.

**In the interests of maximising the number of schools able to benefit from the Holgate Scheme, schools are asked not to arrange more than one session per academic year.**

Local hosts of a Holgate Session will be asked by the Society to complete a brief questionnaire about the session that will allow the Society to gather some feedback and develop the scheme.

Those interested in hosting a Holgate Session should contact the Session Leader directly by e-mail to discuss content and how the Session Leader can best work with hosts.

### HOLGATE SESSION LEADERS

KATIE CHICOT | STEPHEN CONNOR | ALAN DAVIES | TONY GARDINER |

PETER GIBLIN | SIMON GOODWIN | JOE WATKINS |

**KATIE CHICOT (BASED IN LEEDS)** - CV

**Contact:** k.m.chicot@open.ac.uk

**Mathematical Interests:** As a staff tutor at the Open University I am involved in the standard production of teaching materials and teaching. In addition I have worked on a large variety of non-standard projects. My Open University work is a unique educational role. It has allowed me to be involved with projects like the ‘Bridge2Success’ Gates project. This project was designed to overcome one of the major hurdles to returning to college education, the maths entrance test. It was nominated for the education-portal.com’s People’s Choice Award for ‘Most Interactive Resource (2012)’. It received an Honorable Mention and won the category in the Center for Digital Education 2012 Best of the Web/Digital Education Achievement Award. This project was awarded the Maryland Distance Learning Association’s *Program of the Year* award at their annual conference.

I have tried other means of communicating mathematics including co- creating the series ‘Patterns of life’ for OU iTunes. I have given a Facebook event as part of the OU Social Media Campaign and had two appearances on BBC radio 4’s 'More or Less.' I recently captained the OU’s team on BBC2’s Beat the Brain.

My research interests straddle Logic and Combinatorics. In particular I have worked with automorphism groups, the Small index property and transitivity properties all with respect to infinite designs.

I give talks in schools and also at teachers' conferences. My principal aim is to make mathematics accessible and engaging.

**Example Sessions:**

Title: *To Infinity and Beyond*

Age: 14 years to adult

Abstract: The infinitely large and the infinitely small are mind-blowing concepts that have helped mathematicians to solve some very real, and finite, problems. Katie Chicot explores the mysteries and misconceptions of infinity, from ancient puzzles to some of the very latest mathematical research, taking you to infinity…and beyond.

Title: *Big Ideas*

Age: 14 years to adult

Abstract: Be prepared to let your mind expand as we look at some of the terrifying consequences of Einstein's Theory of Relativity. Time, space and reality are not what you think. To see how the universe really works we will have to ride light beams and follow in the footsteps of the greatest thinker of our time.

Title: *Your country needs you*

Age: 8 years to adult

Abstract: A whistle stop tour of the history of code breaking. Students make and break codes and see how mathematics underpins all aspects of the coding arms race.

**STEPHEN CONNOR (BASED IN YORK)** - CV

** Contact:** stephen.connor@york.ac.uk

**Mathematical Interests:** I'm a senior lecturer in the Department of Mathematics at the University of York, and my main research interests lie in the area of applied probability. Probability is a topic that humans seem to struggle with -- we often don't have a very good feel for how likely it is that something will happen, and are surprised by "coincidences" more often than we probably should be. I really enjoy studying a subject that involves so much fascinating theory, yet also relates to everyday life.

Particular interests include the study of how long it takes for a random process (such as a particle performing a random walk, or a pack of cards being repeatedly shuffled) to approach some sort of equilibrium. This is a problem that is also important in other subjects, such as chemistry and physics. In addition, I am interested in methods for using computers to simulate the long-term behaviour of random systems which are too complex for us to study analytically. Applications here include analysis of queueing systems with lots of servers, and restoration of "noisy" images.

As well as teaching and conducting research, I am a STEM Ambassador and the "Schools Liaison and Widening Participation Officer" for my department. I have led many interactive sessions at schools in and around York (for children aged 6 -- 18), given a number of public lectures, and have recently helped to organise Royal Institution Maths Masterclasses for North Yorkshire.

**Example Sessions:**

I generally prefer to run interactive sessions; if asked to give a lecture then I always endeavour to make this entertaining as well as informative! The suggestions given below are indicative only: I'm very happy to discuss other possibilities.

Title: *How many shuffles does it take to randomise a deck of cards?*

Age: 14 -- adult

Abstract: How many times should you shuffle a pack of cards? How do casinos (try to) ensure that their cards are well shuffled? Why should we care? And what has this to do with mathematics?

This session works best as a lecture: in it I give an idea of how these questions can be answered, and why the answers are interesting, using a heady concoction of (relatively simple) probability, group theory, combinatorics, analysis, and maybe even a little magic.

Title: *Surprising uses of randomness*

Age: 14 -- adult

Abstract: A look at how random numbers can be used to solve a variety of problems, from approximating the area of the UK, to image restoration, to decrypting simple codes.

Title: *Patterns and proofs*

Age: A-level students

Abstract: An introduction to the idea of mathematical proof through problem solving. This session encourages students to spot patterns in numbers and puzzles, and to then turn their observations into theorems; this should help students with the concepts of proof by induction and proof by contradiction, and give an insight into the world of university-level mathematics.

Title: *Skill vs luck*

Age: 8 -- 16

Abstract: Is your favourite sports star really skilful, or just lucky? How can we use probability and statistics to tell whether a run of great results is pure fluke? Students will spend some time investigating patterns in repeated tosses of a fair coin, before using the knowledge acquired to critically assess real-life data.

**ALAN DAVIES (BASED IN NORFOLK AND HERTFORDSHIRE)** - CV

**Contact**: a.j.davies@herts.ac.uk

**Mathematical Interests**: After a first degree in mathematics from Southampton University, Alan took a masters degree and a doctorate in structural engineering and numerical computation respectively from Imperial College. He has spent most of his working life as an academic at the University of Hertfordshire, formerly the Hatfield Polytechnic. He had short spells in industry working as a research engineer in the aircraft industry and as a process engineer in the food industry. During his time in Hatfield his major teaching activity has been with undergraduates and postgraduates in mathematics, science and engineering.

Since 1993 he has been the organiser of the Hertfordshire Royal Institution Mathematics Masterclasses for year 9 pupils. As a consequence of this work he has gradually increased his contacts with schools and now runs regular mathematics workshops for years 5 and 6 in primary schools and years 7-13 in secondary schools. The workshops and lectures usually reflect his interest in applied mathematics, in particular mechanics, however he has a general interest in all areas of mathematics and runs sessions on many other topics. He has also developed a series of public lectures on applications of mathematics and physics to a variety of problems aimed at a general audience, ages 8 to 108.

**Example Sessions:**

All sessions can be adapted to the audience background and age and can be straight lectures, usually with suitable demonstrations, or they can be hands-on workshops.

Further details, of these and other sessions, can be found on the Mathsdiscovery website, http://www.mathsdiscovery.co.uk

**Rainbows**

We shall see a wide variety of rainbow phenomena some of which will be familiar to all of us, others will be not so well-known. We shall explain the double bow and why the colours are always in the same order. We’ll see rainbows in places other than in the sky and we shall answer the question “Can you see that rainbow?” This talk can be expanded to include other atmospheric phenomena such as haloes, glories, the green flash etc.**Anamorphic art**

Anamorphosis is a transformation technique by which pictures are presented in a manner in which they are difficult to interpret. In order to recognise the picture it must be viewed from a specific point. Typical of the idea is the advertising logo seen on sports fields. The picture is painted in such a manner that the three-dimensional nature of the field is transformed to a two-dimensional picture on the television screen. Conical anamorphosis leads to some interesting pictures on the surface of a cone and can be understood by all ages.

This session is best delivered as a hands-on workshop and is appropriate for all ages. There will be a wide variety of examples and all participants will have plenty of opportunities to produce an anamorphic image.**Mechanics**

In this session we shall introduce the basic laws of mechanics via a lecture demo. Many people find mechanical concepts non-intuitive and a helpful way to overcome this is to perform simple mechanical experiments, usually using very simple equipment.

The session can be adapted to suit a specific theme, e.g. we have a session called ‘The mechanics of superheroes’.**The fascinating number π**

The number π has been a fascination for mathematicians for some four thousand years. The amount work involved has been enormous and the associated literature is vast. We shall look at the historical development of some of the ideas focussing on specific aspects such as Archimedes’ mathematical description and how a dartboard can be used to make an estimate of the value of π. The decimal expansion of a transcendental number such as π should be random and we shall look at some of the repurcussions.

**TONY GARDINER (BASED IN DORSET, BUT HAPPY TO TRAVEL)** - CV

**Contact:** anthony.d.gardiner@gmail.com

**Mathematical Interests**: Tony is a mathematician who has been closely involved with schools for many years. He has worked in group theory, algebraic graph theory, number theory, analysis, history and philosophy of mathematics, and mathematics education. His publications include numerous resources for schools, mainly for more able students - including Mathematical puzzling (Dover), Understanding infinity (Dover), Discovering mathematics (Dover), The mathematical olympiad handbook (Oxford), and the series Extension mathematics (Oxford 2007). He started the national pyramid of Challenges and olympiads and ran them for 10 years. A new book (with Alexandre Borovik) The essence of mathematics - through elementary problems should appear shortly

**Example Sessions**: I hesitate to give a list of possible titles - since I would prefer to design each talk (in consultation with the teacher issuing the invitation) to suit the intended age group and their background. This attempt to design the session appropriately may be achieved via an initial e-mail exchange followed by telephone contact.

Mathematics requires exposition - so any session needs to be structured. However, school students have limited experience of accessing mathematics solely through exposition; so each session is likely to require a degree of student activity (though the underlying style could range from an extended structured exposition to a workshop).

Whatever the chosen format, any session would be intended to offer an unfamiliar, but important, glimpse of serious mathematics.

If I were to indicate the possible range of topics it would certainly include various gems from recreational mathematics, from number theory, from geometry, from algebra, from combinatorics, and from analysis - all with added historical flavour. All are likely to emphasise the connection between apparently separate topics that is characteristic of mathematics.

**PETER GIBLIN (BASED IN LIVERPOOL)** - CV

**Contact:** pjgiblin@liverpool.ac.uk

**Mathematical Interests**: My research area is singularity theory and its applications to differential geometry and computer vision. I have worked on many geometrical problems such as the study of light caustics by reflexion in mirrors, symmetry of various kinds, recovery of three-dimensional shape from two-dimensional images (that is the objective of ‘computer vision’) and geometrical properties of surfaces in 3- and in 4-dimensional space. In all these cases particular interest attaches to the question of what happens when something changes or moves—this might be a curve, surface, mirror, scene in the world or camera position or orientation. Naturally such questions involve a significant use of calculus, and in fact singularity theory can be seen as one of the significant directions in which differential calculus has moved in the last 50 years or so.

There is a Rough Guide to my research on my webpage, http://www.liv.ac.uk/~pjgiblin/newsletter.pdf

Most of the dozen students I have supervised for PhD worked in the area of singularity theory, and several of their theses, as well as other works by my students, are on my webpage http://www.liv.ac.uk/~pjgiblin This includes a number of essays written by high-school students under my supervision during work experience or Nuffield Bursary summer projects. A full list of my publications is also available via a link from the same webpage.

Outreach Work

At the University of Liverpool we had a succession of EPSRC grants under the ‘Partnerships for Public Engagement’ heading (or similar ones) which allowed us to employ outreach officers to develop the Funmaths Roadshow http://www.maths.liv.ac.uk/lms/funmaths/ and take it into schools nationwide (and sometimes internationally). I was the Principal Investigator on a number of these grants, before I retired. The grants also helped us to run a Maths Club http://www.maths.liv.ac.uk/~mathsclub/ which has flourished for many years now. (The University now employs outreach officers as permanent members of staff, taking over from the EPSRC grants.) My personal outreach work has revolved around going into schools to give mathematics talks, the Maths Club, and the two organizations Mathematical Education on Merseyside (MEM) http://www.maths.liv.ac.uk/~mem/ and the Liverpool Mathematical Society (LivMS) http://www.livmathssoc.org.uk I have given many masterclasses and other presentations in the University and in schools under the auspices of these organizations. I have also run interactive ‘problem-solving’ workshops where the problems/puzzles are more formal.

**Example Sessions**: As a rule I make my presentations interactive, that is involving the ‘audience’ in actually doing some mathematics. Thus a more descriptive name is often a ‘workshop’. Only rarely have I given ‘talks’ or ‘lectures’. My presentations are generally aimed at Year 11/VI form but can be for Years 8-9 which is the age of MEM Masterclass pupils. Many sample presentations (roughly Year 11/VI form) are on the Maths Club archive http://www.maths.liv.ac.uk/~mathsclub/talks.php though I rarely repeat an old talk without redesigning it to some extent. Here are a few ideas I have used in the past. I hope also to develop a presentation or two on mechanics.

1. *Card tricks that are ‘doomed to succeed’* There are many mathematically based card tricks which, though puzzling, can be explained with some elementary mathematics. This presentation can involve a smallish ‘audience’ trying the tricks for themselves or, for a larger one, volunteers can try them out. The presentation can be combined with ideas about shuffling cards and with other things that ‘must work’ such as number puzzles.

2. Counting This can involve various aspects of combinatorics: counting things in different ways to obtain striking results. Fibonacci numbers figure in this quite often, as do magic squares, partitions and probability.

3. *From maxima and minima to surface shape* This is a somewhat more formal ‘talk’ which starts with problems of maxima and minima solved without calculus and moves through properties of curves to fairly modern ideas of using mathematics to measure the symmetry of shapes and to compare one shape with another.

4. *Universal cycles* This also has connexions with card tricks, though it is mainly a mathematical topic, involving use of graphs (networks) in the plane to find sequences of 0s and 1s with special properties (de Bruijn sequences). This enables a set of five cards chosen from a pack to be identified knowing only which are the black cards. There are many ways in which this topic has been developed over the last decade, and I talk about some of them. There is opportunity for audience participation.

5. *Graphs, trees and Brussels sprouts* Graphs (networks) in the plane are studied, Euler’s theorem (vertices minus edges plus finite regions = 1 for a connected graph) is introduced and the theorem used to de-bunk a pencil and paper game, showing that the winner can be predicted from the start.

**SIMON GOODWIN (BASED IN BIRMINGHAM)** - CV

**Contact details:** s.m.goodwin@bham.ac.uk

**Mathematical interests:** My research is in the areas of pure mathematics called representation theory and group theory, which are concerned with understanding symmetry. Given the abundance of symmetry in nature and in mathematics, representation theory has far reaching connections and applications in mathematics and sciences. In my teaching at the University of Birmingham I enjoy sharing my enthusiasm when teaching the first and second year courses on algebra. In these courses we develop the theory of fundamental algebraic structures, like groups and rings, whilst seeing applications and motivation for this abstraction. I have developed and run interactive workshops in variety of areas of mathematics and aimed at different age ranges. In these workshops I like to share my enthusiasm and get the audience to experience the joy of mathematical problem solving and discovery. When I'm not doing mathematics, I like to spend my time outdoors and enjoy cycling, running and walking - though sometimes I'll be thinking about maths at the same time.

**Example sessions:** Titles of interactive workshops that I have previously run are given below; here interactive means that the participants do some of the maths. A target age group is given though these sessions can also be adapted to be suitable for other age groups. Further details are available on request and many other topics can be covered.

Mathematical mindreading (year 10-11)

Puzzles, probability, permutations and paradoxes (year 12-13)

Symmetry, shuffling and solutions (years 10-11 and years 12-13)

The Fibonacci sequence, the golden ratio and the worst game of snakes and ladders (years 10-11)

Using maths to win at gameshows (years 10-11)

What are the chances? (years 10-11)

**JOE WATKINS (BASED IN CANTERBURY)** – CV

**Contact details:** J.Watkins@kent.ac.uk

**Mathematical Interests**

My research interests have tended to focus around spectral theory, specifically on the relationship between spectral determinants and zeta functions. This has included the study of such functions within Quantum Mechanics, which was the main focus of my PhD research. I have also completed some work in the mathematics of juggling and the link between this and musical tiling (inspired by the work of a University of Kent student, Rachael Whyman).

Since then I have become more interested in how mathematics can be used within Social Sciences, both as a precise tool for measurement but also as a means of providing accessibility to people who are non-expert in such disciplines. Consequently I have begun a research programme to investigate how colour can be rigorously and consistently used in order to provide intuitive interpretations of large datasets, thereby mitigating the need for technical analysis. This has included the development of a simple heat-mapping technique and several projects to demonstrate the usefulness of this method.

I also have an interest in investigating how research can be effectively communicated and understood through Public Engagement and Outreach events, and to what extent such work can be influential in encouraging students to study STEM subjects at A-Level and beyond.

**Examples of Sessions Offered**

The following are examples of sessions that can be offered. All talks or workshops tend to feature an interactive element and are as hands-on as possible. The sessions below are examples and I can work with local organisers to develop sessions according to need.

The Mathematics of Juggling

This session provides an introduction to the ‘Siteswap’ notation, which describes the mathematics of juggling in a very neat, simple way. As well as learning how to speak this language, participants will understand the hidden and beautiful rules that determine exactly which juggling patterns are possible and which are little more than nonsense. This talk suits most audiences from Secondary School upwards and can be run for a very large group.**The Art of Codebreaking**

After understanding some basic concepts of modular arithmetic, this session uses computer graphics to demonstrate why encryption is so powerful. We investigate additive, multiplicative and exponential methods of encryption, demonstrating why the final choice is ultimately the most secure system to use for sending secret messages. This talk would be suitable for a mature audience or for Secondary School students with an interest in mathematics.**Build a Theorem**

How do we define a triangle? Of course, everybody knows what a triangle is, but putting this into words is a lot more subtle than you might think. After exploring the basis of writing a good mathematical definition, we show how simple algebraic concepts can be used to give powerful results about geometry and tessellations. This talk would work best for a smaller audience of enthusiasts, preferably with experience of A-level or higher.