## Braids in algebra, geometry and topology workshop

In May 2017,
ICMS hosted a workshop on** Braids
in algebra, geometry and topology**

Braids are a classical object of study in mathematics and physics. One often first thinks of a braid geometrically, in the sense of “plaits", with a natural group structure. Braids also describe the configuration space of points in a disk or plane; this in turn can be viewed as the space of roots of polynomials over the complex numbers. Hence braids play a prominent role in a wide variety of disciplines including knot theory and low-dimensional topology, number theory, algebraic geometry, geometric group theory, algebraic topology, and mathematical physics. Braid groups also play a huge role in many applied areas such as cryptography, robotics, fluid dynamics, and molecular biology.

The purpose of this workshop was to celebrate the breadth of the topic, with an eye on identifying common problems that admit multiple phrasings and multiple approaches

It was a busy week with over 20 talks, 16 lightening talks, an open problem session and a public lecture!

Delegates
from the *Braids in algebra,
geometry and topology* workshop, May 2017

Benson Farb gave a public lecture entitled *Polynomials, braids and you. *The talk featured parliamentary debate as
well as the music of the Ramones!

*Benson Farb, Polynomials, braids and you*

Whilst the workshop was on, we took the opportunity to speak the delegates in a bit more detail.

#### Rachael Boyd, University of Aberdeen

Rachael completed her undergraduate at Edinburgh and masters
at Cambridge, before returning north to Aberdeen. She is in the 3^{rd} year of her PhD
in the area of homological stability.

#### Tell me about today's event and your role in it

This is a broad workshop on braids, covering maths from lots of different areas. I am mainly here to listen and learn. I gave one of the 5-minute lightening talks, and I have been speaking to people about their research.

#### What brought you to this area of research?

I like it because it is a visual topic. You can get your head round the concepts by using small scale drawings. I was drawn to the area during my undergraduate and masters studies. My supervisor and I identified some common ground and that led me to choose a topic in this area for my PhD.

#### Other than exploring maths, what are the benefits of taking part?

You hear from people in different areas that you wouldn’t normally get the chance to meet. It is amazing to meet and speak to people in person and get face-to-face explanations of their work. You understand things in a way that is just not possible from reading papers alone.

#### What will you take back to your [day job/research/studies]?

I’ve learned a lot about where what I do fits in within the bigger world of maths, which is really nice. I have also found out about some specific approaches for my research, which is very helpful.

**Have you met interesting people,
and if so, what connections have you made?**

Lots, I have spoken to some professors who have really helped me with ideas for my research, and it has been really nice to meet young people in this area. They don’t have papers yet, so it’s great to hear what they are working on. You never know, there is a chance they will be my future collaborators in this area.

#### Do you have any advice for first-time ICMS attendees?

I’ve been to ICMS before, mainly to single day events, including a LMS Woman in Maths meeting. The main thing is do not be frightened to ask questions and speak to people.

#### Have you been to many other conferences? How does ICMS differ?

I’ve attended quite a lot of conferences. At ICMS the set up, dedicated conference staff/lecture rooms/dining areas etc, means that the workshop runs very smoothly and the participants can focus on the maths.

** **

#### If you could solve one maths problem, what would it be?

For the moment, my thesis problem. Once I’ve completed that I can think about moving on to other problems.

#### Do you have any thoughts regarding how we can raise the profile of maths?

Maths Blogs can help. I coauthor a maths blog (PictureThisMaths) with Anna
Seigal. Explaining maths to
non-mathematicians is important. Public
Lectures and Exhibitions help too. I
visited the Brilliant Geometry
Exhibition this week, which is great. Edinburgh seems to be well served with
exhibitions and public lectures, but there is always more that can be done here
and elsewhere**.**

#### Do you have any thought on how diversity in mathematics can be improved?

For gender diversity I think the Woman in Maths events are good, and in particular the panel discussions at these. Some things need to be done on a government/policy level, e.g. making academia more family friendly. For wider diversity, we could consider holding workshops such as this elsewhere, i.e. taking international workshops to countries less well served. It would provide the local mathematicians with a great opportunity to access world-leading mathematical research.

#### Who is your favourite mathematician and why?

I’m
not sure I have a favourite as such, however this week, Joan Birman gave an awesome talk. She is a leading figure in this area, still
active as she approaches her 90^{th} birthday. She is super inspirational!