Take 10 with... Melissa Tacy

Dr Melissa Tacy in the Department of Mathematics gives us 10 minutes of her time to discuss her research, which includes understanding functions that describe how waves move and interact.

1.  Describe your research to us in 10 words or less.

How do we construct complicated solutions from simple building blocks?

2.  Now explain it in everyday terms!

My primary interest is understanding how to analyse functions in terms of simple components. These functions arise as solutions to equations that model various real world phenomena. For instance, I spend a lot of time on functions that describe how waves move and interact. Generally the functions I’m looking at are pretty complicated so we try to break them down into combinations of simple functions that act as building blocks.

One of the real challenges is working out how those blocks go back together (synthesis). Usually the greatest challenges are when we are trying to synthesise fine scale detail, and that’s where my research is focussed. A typical result in my field would give a control on the amount of error introduced by a synthesis process. The level of error then determines how well we can resolve the problem.

3.  Describe some of your day-to-day research activities.

I spend a good amount of time inside my own head, thinking. Usually in this process I’m trying to map out a “plan of action” to attack a problem. Once I think I know how to do something I then need to back up my idea with a proof - this usually means a lot of calculations, and mostly by hand (computers aren’t particularly good at the kind of calculations I need).

I really enjoy the huge jumps forward you can make by just changing your perspective. Mathematics can often offer you many ways of looking at a problem (for instance algebraically or geometrically). Some of the best mathematics is done by simultaneously looking at a problem from multiple perspectives.

5.  Tell us something that has surprised or amused you in the course of your research.

How dangerous the phrase “well it's obvious that …” can be. There are an amazing number of paradoxes and pathological examples that disrupt all kinds of obvious things.

6.  How have you approached any challenges you’ve faced in your research?

One of the greatest challenges how to put aside a stalled project for a while. Sometimes when you are not progressing, it’s a good idea to take a break and come back with fresh eyes later. However, when you come back you don’t want to repeat all your old mistakes. Eventually I learnt to keep a record not just of progress but of all the things I tried but didn’t work (and why they didn’t work).

7.  What questions have emerged as a result?

Sometimes instead of coming back to previously stalled projects as I initially envisaged them, I find that when I do come back I go in another direction. Sometimes this is prompted by my seeing new things in the old work, but often it is because the research narrative of the field has moved on and some part of the old project becomes relevant to something new.

8.  What kind of impact do you hope your research will have?

It’s very hard to predict the impact of theoretical research in mathematics. Usually there is a big gap between the development of theory and its application. Instead, what I want to do is work on fundamental problems and deep patterns. History shows me that it is those things that have lasting impact, even if I don’t get to see it myself.

9. When you collaborate across the faculty or University, or outside the University, who do you work with and how does it benefit your research?

I mainly collaborate with people outside the university - actually mostly outside New Zealand. One of the major benefits I see in collaboration is opening myself up to new problems and modes of thought outside my own experience.

10.   What one piece of advice would you give your younger, less experienced research self?

Actively build your intuition both through heuristics and examples/non-examples. Once you develop a strong intuition in an area, have confidence in it. Strong intuition will point you in the right direction (even if there is a lot of work to turn intuition into mathematical proof).