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 five 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 Society would very strongly encourage schools hosting a Holgate session to consider collaborating with other local schools.**

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 (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.

**TONY GARDINER (BASED IN DORSET)** - 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 GIBLI**N** (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.

**VICKY NEALE (BASED IN OXFORD)** - Personal Website Details

**Contact:** vicky.neale@maths.ox.ac.uk

**Mathematical Interests:** I'm the Whitehead Lecturer at the Mathematical Institute and Balliol College, University of Oxford. My job combines undergraduate teaching with work on public engagement with mathematics and working with mathematically inclined teenagers. Before moving to Oxford in August 2014 I spent several years as Fellow and Director of Studies in Mathematics at Murray Edwards College, University of Cambridge, where amongst other things I worked with NRICH and the Millennium Mathematics Project. I have been a volunteer with the UK Maths Trust for many years, and have contributed to several programmes on BBC Radio 4. My mathematical interests are particularly in pure mathematics; my research background is in number theory and combinatorics. I have given numerous talks and led numerous workshops for all sorts of audiences, from groups of secondary school students of varying ages through to adults. I am keen for as many people as possible to have a taste of working mathematically, and this informs my approach to working with students. I love sharing my enthusiasm for mathematics with anyone I can!

**Example Sessions: **I have a few standard talks that I am happy to adapt for individual audiences. These include 'Addictive Number Theory' and '7 things you need to know about prime numbers', both of which discuss some key (solved and unsolved) problems in number theory and recent progress on them. I can adapt them for slots from 30 to 60 minutes, and for audiences with different levels of prior mathematical knowledge. I gave one version of the Addictive Number Theory talk for the LMS popular lectures in 2013; a recording is available online [link to https://www.youtube.com/watch?v=gII2g4TD_7g ]. A video of my talk "7 things you need to know about prime numbers" that I gave to some year 12 students is at http://mmp.maths.org/neale-7Things-Jun15-video.

I am also happy to lead interactive workshops. I have a repertoire of problems suitable for various age groups and looking at various mathematical ideas, all based on my desire for the students to do as much as possible for themselves, so that they can experience the excitement and challenges of working on mathematical problems. I particularly like using open-ended activities that give lots of scope for exploration, conjecturing, proof, asking questions, and so on. Examples include sessions on modular arithmetic, continued fractions, Euclid's algorithm via an interactivity [link to http://nrich.maths.org/psum/picture-this/ ], and several based on my favourite NRICH [link to http://nrich.maths.org/ ] problems such as Take Three From Five [link to http://nrich.maths.org/1866 ], Sticky Numbers [link to http://nrich.maths.org/6571 ] and Got It [link to http://nrich.maths.org/1272 ]. I am used to discussing with an event organiser what they are looking for and what the expected audience will be like, in order to select appropriate activities. I feel most comfortable working with teenagers and adults but am happy to work with secondary school students of any age, and to discuss possibilities for younger students.

**JANE WHITE (BASED IN BATH)** - CV

**Contact:** k.a.j.white@bath.ac.uk

**Mathematical Interests:** am interested in mathematical modelling of problems arising from the healthcare sciences with a focus on control and monitoring. There are two strands to this work: control of infectious diseases and drug absorption and monitoring.

With the infectious disease modelling, I am interested in exploring the impact of different control strategies on population level infection profiles. For example, should the HPV vaccination programme be extended to include teenage boys? With a limited budget, should intervention focus only on high risk cohorts or does population surveillance also contribute to infection control? What can control engineering techniques tell us about whether we can control infection outbreaks in a population?

My work on drug absorption and monitoring uses mathematical models to understand the problems associated with using the skin as a route for drug delivery and subsequent drug monitoring. The skin is potentially a very important organ for delivery and monitoring drugs non-invasively. But it is also a highly heterogeneous barrier which functions to prevent flow in and out of the body. Mathematical models help to determine the conditions, such as the type of drug molecule, that will facilitate the use of the skin for delivery and monitoring.

Alongside my research and teaching activities, I have been involved in working with schools and colleges to provide mathematical opportunities for students in the school sector.

I am a member of the Wessex Masterclass committee and have delivered sessions to year 8 students on a range of applied themes including population growth and introductory mechanics.

As the departmental link for widening participation, I have delivered a number of lectures and workshops for students in KS4 including sessions on curve sketching and graphical interpretation; number bases; and rate equations. I have motivated the sessions by linking the mathematics to my research in the context of the biological and healthcare sciences and, on occasions, to the art of card tricks.

At KS5, I have developed the departmental outreach programme for A level mathematics students which includes a series of real world mathematics sessions for year 12 students and a year-long problem solving and STEP programme for year 13 students. I have also been the academic lead for a mathematics programme to supplement the curriculum for BTEC enhanced diploma students in local FE colleges studying computer science, engineering and sports science.

**Example Sessions: **Interactive talks for groups of pretty much any size and content tailored to the audience (I have put suggestions in brackets below); typically lasting 50 minutes

· Number bases and card tricks (Year 6 – 8)

· The logistic map and its applications to biology (Year 7 – 10)

· Name that curve! (Year 9 – 10)

· Population growth/infectious diseases (Year 12)

Workshops for groups up to around 25-30 students, KS3 & KS4; typically 90 minutes

· Practical introduction to matrices. Motivated by examples from population biology, and moving onto investigating properties of matrices (multiplication, inverse etc.)

· Maths at the drugstore. To encourage students to think seriously about studying A level mathematics if they might want to study nursing, pharmacy etc. Dilution problems, safety measures etc. Ideas of half-life and exponential decay.

PGCE students/CPD for teachers

· The optimal way: a ubiquitous phenomenon. A general interest talk for teachers to motivate A level teaching, particularly of calculus and integration.

If you have another idea, please do get in touch and I will see if I am able to help.

Submitted by Duncan Turton on