Guest Post: Topological Crystallography in Stockholm

Here I am at one of the beamlines at Petra synchrotron, at DESY, Hamburg. The tube behind me is where the beam comes from… scary!

Albert here! Some of you may recognise me from Haggis’ Twitter feed and from Haggis’ 2011 New Year’s post (along with the rest of our family!). Last week I was in Hamburg at PETRA III, a synchrotron at DESY. After some successful measurements there, I made the short hop across the Baltic Sea to the lovely city of Stockholm, for the 4^th International School on Crystal Topology.

First I should say a little about what I do. I’m interested in chemistry, especially materials called Metal-Organic Frameworks (MOFs).

An example of one of the first MOFs, MOF-5. Chemists use rigid organic struts (top left) to link clusters of metal atoms (in this case four zinc atoms, bottom left) to build open framework-like materials (right).

These are a new type of material made from clusters of metal and oxygen atoms which are linked together by long rigid linkers – think of it kind of like a climbing frame. These materials are interesting as they might help to combat climate change by sieving out CO₂ in a process called Carbon Capture and Storage (CCS made it into the Oxford English Dictionary recently!).

But what does this have to do with topology? Chemists simplify the structures of MOFs down to a series of rods (edges) and nodes where these rods meet (vertices) – the simplified structures are mathematical graphs. We can then see how the structure is connected together as a network, without unnecessary molecular clutter. As chemists we want a way to classify the networks of our materials for two reasons. Firstly, so we can see if similar networks have been made before by other researchers, and secondly to help us design new materials. We might, for example, find that a certain network is really good at storing CO₂; using a linker molecule which holds onto CO₂ really well and the right topology to form our target network, we could make a new material which is even better at capturing CO₂. To classify our networks we need to use graph theory.

Charlotte Bonneau (left), Michael O’Keeffe (middle left), the person I hitched a lift to Stockholm with (middle right), Xiaodong Zou (right)

However chemists are not normally trained in graph theory, so this was the aim of the Stockholm school. The school was taught by Prof. Michael O’Keeffe (emeritus Regents’ Professor at Arizona State University), who taught us about the mathematical ideas necessary to deconstruct a crystalline network, and Dr Charlotte Bonneau (currently a full time mother to the adorable Leonie), who focussed more on the use of software to analyse crystal structures, such as systre and Topos.

During Mike’s lectures we were told about the graph isomorphism problem of determining whether two finite graphs have the same connectivity. This is of importance to chemists, as we want to be able to compare our networks to see if they have been reported before! Graph isomorphism is also a specific example of one of the million dollar maths problems, P versus NP, which asks whether every problem for which a solution can be quickly checked, may also be quickly solved by a computer. One of Mike’s collaborators, Dr Olaf Delgado-Friedrichs, has attempted to address the graph isomorphism problem in the program systre. systre uses a barycentric method to raise the symmetry of a collection of atoms in a graph to the highest symmetry representation. The barycentric representation is effectively like replacing all the edges in the graph with springs and these pulling the vertices to their weighted average positions. Although systre is able to classify most graphs, it is unable to deal with graphs where applying the barycentric approach causes two nodes to collapse into one another (a so-called collision – see picture). So unfortunately, it’s not a complete solution to P versus NP.

A graph showing a collision. When you put this into a baricentric representation, the two red nodes collapse into one another. Back to the drawing board for a solution to the graph isomorphism problem then…

The rest of the course was full of lots of useful information which will help in making new materials and further classifying old ones. The course as a whole was a lot of fun and it was great to meet such a friendly bunch of people! That’s it from me for the minute, but look out for more photos of me on Twitter at exciting scientific/mathematical locations – Albert out.

Engaging with Engagement

I have been silent for an inexcusably long time but I hope that you will excuse me anyway, because I have faith that all you readers are lovely forgiving people like that. There have been 3 reasons for my protracted silence: writing/editing my thesis (don’t ask!), giving Open Studies lectures (which I hope to blog about in future) and a postgraduate engagement conference which just finished today.

Me guarding all the tasty EwE prizes to be won by the best engagers. Sheep themed chocolate, of course.

Engaging with Engagement, or EwE as I like to call it*, had the aim of bringing together postgraduates from all over Scotland and teaching them techniques for communicating their research to the public. I was inspired to run a conference like this after attending one myself in Manchester last May, where I was introduced to engagement methods that I had never considered before. I still think that very few postgraduates would even think about making a short video of themselves talking about their research, let alone be brave enough to implement it and put it online.

Example of a solar flare

And yet communicating what we’re researching is more important than ever, what with all the science/maths in the news, in politics and in business. Many of the presentations at the conference were relevant to stuff that was in the papers this very week: for example, understanding solar flares that will disrupt satellite communications and controlling epidemics on the 10th anniversary of the foot-and-mouth outbreak. Other talks were about the latest cancer research, how to prevent disasters like the wobbling London Millennium Bridge, how Google finds the most relevant search results, how to predict option prices, and how to exploit symmetries to explain modern physics.

I’m really proud of all the participants for having been able to communicate their research so clearly to me after just an hour and a half of training.  Talking about maths is a really difficult task. It’s easy to pitch the explanation too simply (dumbing down) or too complicatedly (using loads of jargon). Some of the delegates, when asked about their research two days ago, would have started a sentence with “let D be a differential operator”, or would have simply given up and said “oh, I do some kind of geometry that I don’t want to tell you about”.

How many maths buskers does it take to serve lunch?

I have to attribute a lot of the conference’s success to the brilliant people we had come along to be our mentors.  The world’s only stand-up mathematician, Matt Parker, came along to teach people how to perform maths busking.  Bestselling author and broadcaster Rob Eastaway helped people improve their speaking skills and showed off his own with a wonderful public lecture in the evening. Writer-in-residence at the Genomics Forum Pippa Goldschmidt led a fun session about putting maths into fiction stories, while EUSci editors Frank Dondelinger and Kirsten Shuler taught people to write an engaging non-fiction article. Finally, video-making experts Vidiowiki let people loose with cameras and expertise to make 3-minute videos about their research. If anyone else out there is thinking of planning some similar workshops, I cannot recommend these guys (and gals!) highly enough.

Taking advantage of the beautiful ICMS building (a converted church) to make a video

What I hope most of all is that our postgraduates have come away with a new enthusiasm for doing public engagement. As they say: Where there’s a will, there’s a way! In this economic climate, funding for science and maths outreach is becoming harder and harder to find, despite its growing importance. But if the mathematical community care enough about doing it then we will succeed!

Given a few years of the kind of engagement I’ve seen this week, there is a danger of me meeting someone at a party or on the bus, being asked what I do for a living, and on saying that I’m a mathematician, having the other person look very excited and saying “Tell me more!”

[Picture credits go to Madeleine Shepherd - see her Flickr account for more photos.]

*I suspect there may be some participants who still haven’t realised the hidden sheep-based secret in the title.

Happy New Year!

Today is Twelfth Night, the end of Christmas, and the Christian feast day of Epiphany.  It seems like a good day to stop the partying and take stock of what has been happening over the festive season.

When I last left you, you were wondering whether Albert would ever make it to Buxton and whether we’d be able to get Michael and Julia to become friends.  But with my genius self in charge, how could anything go wrong?

(That was a rhetorical question, by the way.)

Here was the plan:

1) Engineer a ‘surprise’ meeting between Michael and Julia in some cafe.  (With all the things they have in common, this meeting alone would be sufficient to cause them to become best friends and want to meet again.)

2) Michael would then invite Julia to Buxton for New Year. (Inevitable given that Buxton is so pretty and Julia is complaining of not having seen hilly countryside for some time.)

3) Julia tells Michael how much she would love to meet all his sheep, forcing him to take them to Buxton with him.

4) Julia then takes me along to Buxton too, and….PARTY.

Easy, right?  Humans are totally predictable.

Except that I was nearly thwarted at the very first hurdle.  I told Albert to bring Michael to Black Medicine, which is a very friendly laid back coffee shop not far from the station.  I had betted on this being one of Julia’s favourite places, and on her wanting to go to it after her morning masterclass was finished.  What I hadn’t betted on was that she’d also be wanting food and company, so I was quite horrified when she texted a friend to meet her and headed instead for the St Giles Cafe on the Royal Mile.  Luckily for me, the bad snowy weather meant that the cafe was completely full up, as was the next one she tried, so she had to settle for Black Medicine after all. Phew.  In the meantime, Michael was ignoring Albert and heading to Anteaques to stock up on more tea for Christmas.  Thankfully, the bad weather once again made Black Medicine (in its proximity to the station) seem like a much better idea, and so they ended up in the same place at the same table after all.

Australian pirate John Skelton with Baggis

The rest of the plan went pretty much according to, er, plan!  Michael was enthralled by knot theory and Julia wanted to hear more about using crystallography for carbon capture, so new year in Buxton was inevitable.  Baggis decided to come along too, which was not such a good idea because the poor thing is prone to getting involved with the wrong kind of people.  For example, he was nearly captured by this Australian pirate (see pic) down on the south coast of England!

Let me tell you a bit about Buxton, in case you’ve never been there.  It is a little spa town not too far from Manchester, just on the edge of the Peak District.  You might have heard of it from its most famous export: Buxton water.  I would advise not paying loads of money for the bottled stuff, and instead rocking up to the town with some empty containers, for you can get the tasty liquid at St Ann’s Well in the middle of Buxton.  The well and the hot geothermal waters were both thought to have healing properties, and have been visitor attractions for a few hundred years.  Buxton became even more popular in the 1780s, when the Duke of Devonshire built a beautiful crescent (modelled on the Royal Crescent in Bath) and a giant dome – at the time the largest in the world.  And you’ll never believe what it was built for… Stables!  Gee, people love their horses even more than their sheep.  Inexplicable, that.

It remains for me to tell you about our amazing New Year’s Eve party and all the new sheepy friends I’ve made.  Here’s a group pic of all of us in the middle of our celebrations:

New Year's sheepy party!

Starting from the front, we have our three childish troublemakers: Giovanni, Maxwell and Albert. (Sadly no McHaggis.)  They had spent the evening playing with GeoMag and were very proud of their Platonic solid sculptures.

Troublemakers with their GeoMag sculptures

Then there were the draught excluder sheep, one of whom (Maximillian) has an easy life on the back of a sofa (much like our own friend Draggis) whilst the other one (unnamed!!) has a hard life guarding the front door and being trampled on all the time.  It was no wonder he wanted to get dressed up and console himself with a stiff drink.

Enjoying the night off with a whisky

Another of our working sheep is called Goggle, and he is a doorstop.  Or so he says – I think that perhaps he might be so heavy just because he has been stealing mince pies every night when all the humans have gone to bed.  After a few glasses of port he decided to wear the Christmas decorations as earrings, which attracted the admiration of the rest of the gang:

Admiring the bauble on Goggle

I particularly like the picture below of Baggis, Fernilee and I admiring our beautiful reflections.  Fernilee is the one in the green scarf.  He is named after a local reservoir, and only narrowly escaped being called Errwood instead (which is a much less pretty name).

Beautiful reflection: Baggis, Haggis and Fernilee

It was really wonderful to make so many new friends, and I hope that they will be able to visit me in Edinburgh sometime soon.

Until then, it is time again to concentrate on the thesis and on communicating my love of maths to the general public.  Next week signals the beginning of mine and Julia’s Open Studies course on “How Mathematical Ideas Shaped the World”, so I shall keep you updated on how that is going. (Don’t forget to sign up for it if you live in Edinburgh and haven’t done so!)  The thesis is in the final stages of its long and drawn-out life and will hopefully be finished before I get Alzheimers and forget what on earth it’s about.

Fingers crossed on this portentious day for an epiphany about modulo 3 matrices…

Happy New Year everyone!

[P.S. Credit goes to MW for photography and JC for the lovely sheep outfits.]

An anteaque encounter

An unexpected thing happened to me about a month ago.  My fleet of carrier pigeons in the loft brought news from the frozen north.  (Yes, Julia thinks the pigeons are just random vermin nesting in the roof, but little does she know that they are in my employ!)

They told me tales of a whole family of ‘goggle-eyed’ sheep such as myself, living just outside of St Andrews.  Trapped inside a cold cold house in a cul-de-sac in deepest darkest Fife, they had been sending smoke signals for a week before my minions spotted them.  But what could I do to help?  I decided to meet with the smallest and wisest of the sheep, Albert, to find out what the situation was.

He said he would meet me in a shop called Anteaques; a tiny place not far from my flat which I had never noticed before.  Thinking that it was just a standard antiques shop, I had walked past it for many years not realising what wonderful tea and cakes lay within.  In the front of the shop I found 100 different varieties of tea, served to customers in pretty china cups by the owners Cedric and Andrew, dressed handsomely in smart black waistcoasts.  In the back of the shop was a higgledy-piggledy assortment of old things: crockery, furs, swords, teapots, pictures, books, candlesticks…  I even found this old top hat, which I think made me look quite sophisticated!

I ordered some tea and cakes and sat down to wait for my mysterious guest.He arrived a little late due to the delays on the winter trains and was glad to find a big pot of tea waiting for him.  Albert was rather shy at being photographed on our first meeting, so I shall have to describe his appearance to you.  He has the colouring of McHaggis, with a black face, green eyes and a scruffy-looking creamy coat of wool.  But unlike McHaggis, he sits upright with thin dangly legs that just make me want to fatten him up with a ton of calorific food.  He also wears a badge on his left arm advertising a band from Manchester called Fear of Music (who apparently don’t exist any more).  Well, I think it’s advertising the band and not Albert’s actual fear of music.

“Lay it on me, brother”, I said.  “What can I do for you?”

“Well…” he paused, looking a little shy at first. “There are two things I would really like to happen.  The first is that I and my housemates – Fernilee and Maxwell – would love to go down to the Peak District for Christmas.  Our shepherd, Michael, always abandons us for the festive season in our cold flat, when what we’d really like is to travel with him to Buxton to celebrate with the rest of our sheepy family.”

“There are more of you??”, I asked in wonder. How could I not have known this?

“Yes! Nine of us altogether I think.  You should definitely come to visit – we could have a real party together!”  I could see the light shining in Albert’s eyes; it was clearly a long time since he had been to a party.

“I’ll see what I can do.  What was the other thing you wanted?”

“This one is a bit more tricky.  You see, I think Michael needs some sort of new distraction in his life.  It’s getting boring listening to him talk about his chemistry experiments all the time.”

” What can I do about it?  I’m busy with my own maths communication work you know!”

“No, but you live with someone, right? Someone female?” he asked hopefully.

“Yes, but Julia is busy finishing her thesis.  We’ll have no men around disturbing her, thank you very much.  It is my duty to protect her from such distractions until she’s officially a Doctor,” I explained.

Albert looked a bit crestfallen. “But he needs cheering up somehow. What else can I do?  He’s been a good master to me; I want to help.”

“Ok” I relented, “we can try getting them to become friends, and they can have tea together once a week.  But not more often than that!  How about it?”  Albert nodded enthusiastically.  “It’s a deal!”

“More tea, dear brother?” I asked, as I sat back to ponder how I could fix the Christmas trip to Buxton…Tune in next time to see if I did!

In the meantime, a very merry Christmas to all of you. May the festive season bring you much sheepy goodness.