Thomas Tawfik
The University of Otago
Give me a quick overview of the type of mathematics you are studying, and/or the aims of your research and its potential applications/outcomes (how you would explain your work and studies to friends who don’t study maths?)
I am working in the area of Mathematical General Relativity, which is occupied with understanding mathematical aspects of general relativity, namely Einstein’s theory of gravity. Specifically, I am interested in analysing the asymptotic limits of Einstein’s equations in the field of cosmology, with the aim of better understanding the physical conditions near the Big Bang singularity. This would amount to understanding what could be considered, in some sense, the Beginning of the Universe.
How did you get into the mathematical sciences? Was there someone or something that inspired you to this field?
Back when I was in elementary and mid schools, maths did not seem as the subject I would end up studying later in my life given that I always wanted to take my time thinking about stuff that I had learnt, something that did not go quite well with school curriculums and exams. However, during high school, I slowly started to develop an interest in physics due to its impressive capability to describe phenomena around us using very elegant mathematical equations. This is the reason why I ended up studying physics in university, to realize only after that I was also curious about the interplay between physics and mathematics, and how that only certain types of mathematics feature in physical theories. At the end, this has got me into the field of mathematical physics.
Winter School is designed to give students a deeper understanding of their area of research and expose them to others working in different fields/industries. Tell me about your Winter School experience. What was the most valuable part of the program for you?
I found the Winter School experience really interesting as it helped to deepen my understanding of topics in geometric analysis, the thing that is relevant for the type of problems I work on in my research. The most valuable part of the program was the two lecture series on the Einstein metrics, as I previously had very little background on this subject and the lecturers did a great job in giving an overview of the topic.
What was your main take away/s from AMSI Winter School? Something you learnt? A connection you made? Do you have new ideas for your work/research or see it in a new light?
My biggest take away from the Winter School was the connection and similarities in techniques between Riemannian and Lorentzian geometry, and how that results on curvature flows in Riemannian setting can be adapted to derive interesting results in general relativity.
What surprised you most about Winter School?
The thing that surprised me most was the level of connections of the organizers of the event and their ability to put up a program including important figures from different fields, whether in academia or industry.
What is the importance of in-person communication at an event like Winter School?
In-person communication is always essential in big events such as the Winter School to help clear any possible confusion or misunderstanding in online communication through Slack or email. Also, in-person communication could be faster in resolving issues in many situations.
You received a grant to attend AMSI Winter School. How important was this in terms of your ability to attend, fully participate in the program and meet others studying in similar fields?
The travel grant was very important to be able to fully participate in the Winter School and get to meet other postgraduates from all over Australia. In particular, travelling from New Zealand, flights to Australia are usually not economic, let alone paying for accommodation for two weeks in Brisbane. Added to this issue is the limited amount of travel money available from my department for the whole duration of the PhD.
What advice would you give to someone who is considering applying for Winter School? How would you describe the conference to them?
I would highly encourage anyone who is considering applying for any of the winter schools of AMSI. It is a great opportunity to get to know about a certain field in mathematics from experts in the subject, present your research work to other postgraduates and finally spend some good time somewhere nice in Australia.
Tell us about a moment that changed a preconceived idea about your field?
A moment of this type could have happened during my studies for my undergraduate thesis. Back then, I wanted to look-into one of the well-established theorems in general relativity, namely the Singularity Theorems of Penrose and Hawking. At the time, I had the impression that this should be doable using the same physics-based, simple-maths techniques that I had learnt in my degree. However, while reading one of the classic texts on the subject, namely the Large-Scale Structure of Spacetime by Hawking and Ellis, I immediately realized the depths and rigour of techniques used in setting up and proving these theorems, the thing that introduced me after to the whole field of mathematical general relativity.
Where do you want the mathematical sciences to take you? Where do you see yourself in five, ten years time?
I would like to continue in academia in the long term, spending my time between better teaching the theory of general relativity to students and continuing to do research with the purpose of gaining a better understanding of various phenomena related to gravity. Maybe in the distance of five to ten year, I would manage to have my own research group, whether back home in Italy or somewhere else, which would be dedicated to trying to fill in gaps in our knowledge of the cosmos.
Any other feedback/comments you would like to provide on the travel grant or AMSI Winter School?
One feedback I would provide is that it would be better if all lecturers at the school provided lecture notes of the topics they were presenting, as this helps to eliminate many of the confusion that could arise from writing on the board during the lectures.