It all began with my face-to-face discussions with Assoc. Prof. Dr. Zabidin Salleh. I knew him since his student days (under the supervision of Prof. Adem Kilicman). He has been a regular participant of my EQuaLS event. Thus, when he mooted the idea of me giving a talk at his School of Informatics and Applied Mathematics in Universiti Malaysia Terengganu, I naturally agreed. At the time, I jokingly mentioned that please invite me during the school holidays, so that I can bring my children along. And so I did. The talk was scheduled on 31 May 2016, when the school holidays had just started. To clear up any doubts about my trip, I would also have gone to give the talk there even if the invitation is not during the school holidays because I have been eyeing on building research relationship with either him or Roslan Hasni (the two whom I know at UMT that work in mathematical areas that are not common in Malaysia) and also to get to know the community there (see here). In any case, I have always tried to maximise the benefit of a trip in whatever way I could and in this case, making my family equally happy. One of my son who is studying at UPM could not however make it for this trip, but we already have planned another trip for him to Terengganu when my other half attends a conference there at the end of July (I will stay back then with my youngest). To further eliminate any criticism, most of my time during this trip was spent on preparing the slides (the day before), the talk and the extended discussion with members of the school (and not sight-seeing) and of course the travel. We had decided to drive there to save us the cost of buying flight tickets and also my family gets to use the car for their own sight-seeing . The long drive was bearable since we took turns driving between myself, my other half and my eldest son.
The talk that I gave was pretty much general but hinges in the areas of my research. I had given myself the title "Aspects of Interaction Between Theoretical Physics and Mathematics: Geometry, Algebraic Structures and Graphs", agreed upon by my host. My idea was to get the mathematicians to be interested in some topics of theoretical physics that we do. The contents of my talk is outlined as follows:
- Introducing Physics-Mathematics Interplay
- Geometry & Classical Mechanics
- Enter Quantum Reality (At Your Own Risk)
- Hyperbolic Excursions
- Network Detour
- Summary & References
It took me quite a while to think on how to start off the talk and finally I thought I should begin with the age-old question of whether mathematics is discovered or invented giving the position of a platonist or a formalist respectively. I have always thought that philosophy has a way of analysing things that delineates extreme positions (labeling each accordingly) and that one should not be trapped in this Boolean dichotomy but rather should entertain the whole spectrum between the two. Thus, I relate physics in its way of describing (modeling) external reality with all its abstractions and generalizations, leading to a platonist standpoint. The formalist standpoint comes from further abstraction and generalization that are far divorce from describing any external world, turning mathematics into a gameplay. Having mentioning this, then I started to describe surprises from the physics-mathematics interplay from physicists creating new ideas in mathematics and mathematicians inventing ideas that later led to a surprising usage in physics.
After the introduction, I began to speak on my own research interests. I had to begin with generalized description of classical mechanics in relation to phase spaces the (co-)tangent bundle of R^n as a start and generalised further to nonlinear phase spaces. At this juncture, I also digressed into symbolic dynamics via cutting sequences in the hope to connect with an interest I have in hyperbolic geometry.
With classical mechanics explained, then the discussion proceeded to quantum mechanics via the similarities of the algebras from classical mechanics. This allows me to dwell a bit on the topic of quantization and in fact I did it too long. This leaves me little time to speak on the next topic of quantum theory, namely Kochen-Specker theorem and quantum contextuality. Here I begin introducing graphs with their two-coloring problem and operator algebras. Had I have more time, I would have also introduced geometric contextuality as explained by Planat and collaborators. Another topic I would have loved to introduce is the use of category theory in formalising quantum mechanics via Coecke's diagrammatic calculus; had to limit myself though to certain mathematical ideas in the talk (as mentioned in the title).
The hyperbolic excursion essentially came from my interest in quantizing a particle system on hyperbolic surfaces. I explained that we had to delve into numerically computing eigenfunctions on the surfaces to see the role of the discrete groups appearing in forming the hyperbolic surfaces. Showed the nice pictures that Chan had produced. I also describe some open problems regarding this work. Classical billiards on hyperbolic surfaces exhibit chaotic motion and hence considering quantum theory on these surfaces may lead to research on quantum chaos. I did not get to mention this and neither did I mention the symbolic dynamics which have nice connections to number theory.
The last topic was finally the use of graphs in complex networks, that seems to be a bit far from what I usually do. I explained then that my interest in this was spurred by the few available works in relating hyperbolic geometry with complex networks. Of course, the other point of attraction is its use in describing diverse systems with large datasets. All theorists have this secret dream of having his work being used even in the normal day-to-day experiences and hence my interest in complex networks.
Finally I summarised with some observations and remarks. I did not get to mention my other interest in mathematical cosmology. I would have loved to say the group-gemetry interplay in describing space-times and even connect with hyperbolic geometry through ideas of cosmic crystallography but that would have been too much. In any case, I'm phasing out my cosmology research for now.
Besides this talk, I also gave an introduction to INSPEM as a publicity drive for the institute (in fact it was requested). Discussions that follow thereafter is the idea of INSPEM as a national institute. The Deputy Dean of the School, Assoc. Prof. Dr. Abdul Fatah Wahab was formerly a staff in the Maths Dept of UPM and he mentioned that he had helped draft the concept paper of the institute. My reply is that I was not there during the initial formulation of the institute and would have not known what are the goals and strategies toward the setting up of a national institute. So far, I did say that INSPEM has been allowing academics from other universities to be external research associates and are welcomed to use available facilities of the institute. Having said this, I can see now two options (which I did not say in the discussion) to go in the direction of a national institute: (1) apply for the MOHE Centre of Excellence; (2) leverage on MICEMS set-up within INSPEM. Both requires high commitment from its members and a lot of hard work.
After the two talks, the discussion went on beyond lunch time, much to ideas being churned out on possible research and on how we can collaborate. My own view is that we have to take what is natural; we first get to know each other's research first and then if something clicks, then we will be able to collaborate better. Finally, we (Zabidin, Roslan, Abdul Fatah, Gobi and myself) went for a late lunch at a seafood restaurant. They discovered later that I do not take seafood. During my parting with them, the idea of a joint seminar with them in INSPEM was mooted. Hopefully we get to realise this.
Here are some pics:
While I was busy preparing my slides and the day I gave the talk, my family went out to do sight-seeing and souvenir-hunting. I only joined them in the trip to the Crystal Mosque, the Monument Park of Taman Tamaddun Islam nearby and in the evening after the talk, the Batu Buruk beach. Here are more pics.
The Crystal Mosque
... and the boat ride
The Monument Park is a couple of minutes walk from the Crystal Mosque and is part of Islamic Heritage Park. They display down-sized models of mosques, monuments and tombs (with interior decorations replicated) all around the world.
Late evening, after the talk we went to Batu Buruk beach:
In the late evening (before the morning when we left), I got to meet and a student of mine, Cikgu Ramli Abdullah. He was a school teacher who went on to get his Bachelor degree and he had to take my quantum mechanics class (sorry for him and his colleagues). We talked about old times and some fellow students during then.
All in all, it was a fun working holiday trip.