Charting Territories

It has been nearly a month since the inauguration of MICEMS. I was searching the media for any news item on this event but it only appeared in the STAR, to the best of my knowledge. Slightly earlier is the news item of UPM. Notwithstanding the small publicity, we will keep pushing on, making the centre work true to its name which I hope to address below. In a way, I'm perhaps more comfortable with working silently in the background. It has also been more than a month that INSPEM is without a director and I am taking up the duty for now. I hope the appointment of the new director will be resolved in the very near future so that the he/she will be in the centre of things, in particular with respect to MICEMS.

With MICEMS, once again the thoughts of charting out directions of research filled one's mind. What follows are simply my own personal reflections and in no way representing the view of the institute. When I first joined the institute, I have been 'asking' what directions are the institute taking and the publicly known secret question, what differentiates it from the mathematics department. The answer that one often gets is the one stated in one of INSPEM's listed objectives, namely high-end areas of mathematics. This could then be anything of course since any subject area can always be pushed to some high-end stuff and it is also subjective what will that be.

In a few exercises of the university to restructure the institute, the laboratories did go through some name changes perhaps reflecting some realignments. I remembered vaguely how difficult this can be, trying to find a focus of the institute while remaining inclusive of disparate expertise of our mathematicians. The difficulty stems from the different culture of mathematicians who often do not collaborate in large numbers (see here and also here for the different culture of mathematicians). My own personal hope was to make things more interdisciplinary whether within areas of mathematics themselves or with areas of other sciences. Consciously or unconsciously, some patterns did emerge from the last "restructuring" of the labs. Most of our labs now have something "computational" in nature; two of which are present in the name of the laboratories. The other two had for instance cryptography whose connection with computer science is obvious, while the educational lab has research on technological aspects and digitization of ethnomathematics manuscripts. Whether this is by design or merely coincidental, it remains that there is a common thread along the computational direction. At around the same time, I was toying around ideas of research in theoretical computer science in relation to quantum computing, quantum foundations and quantum logic. There was also an idea of forming an international laboratory with Auckland along these lines. Anticipating this, we had also designed a postgraduate field of study called Computable Structures and Scientific Computing. This field complements the field of study of Computational Mathematics which focuses more on numerics and algorithms (see here). Years went by and there seems no financially viable option to realise the intended laboratory. On the subject matter, we did not stop effortwise; some of my students are now pursuing the direction of complex networks (using graph theory to extract computable information) and categorical quantum mechanics (using category theory to elucidate logical structures of quantum theory).

For MICEMS, it has been suggested that the pursuance of research directions in mathematical sciences that are closely related to industries. This is very much the research direction of Disma of Polito - as it says on their website, fostering multi-faceted interactions in engineering and architectural sciences. In Malaysia, applications of mathematics have been pursued in a few places under the name of industrial mathematics and applied mathematics. Most notable is UTM Centre of Industrial and Applied Mathematics which has partnered with Oxford Centre of Industrial and Applied Mathematics. It will make good sense if we can complement what they have done. In overlapping areas, we should harness where our strengths are (either from the Italian side or the Malaysian side). From Polito, we can refer to their research group webpage and we will do well if we can match or align accordingly. More from a personal side, it would be nice if alignments can be made from the areas that I have pursued thus far. In connection to computable structures and scientific computing, it would be nice to think along the lines of big data analytics and even more exotic areas of theoretical and applied computer science. Personally, I would like to see unexpected areas of (pure) mathematics come into real world applications. I have already mentioned the use of graph theory in complex networks. Lie groups and Lie algebras have been used in robotics for instance. Algebraic topology has come into play in computer vision and data mining. These are but a few examples of how abstract mathematics are put into real applications. I would love to see some of these realised in MICEMS. We will see how things evolve. More importantly, INSPEM should boost up efforts and take an equal part in shaping up MICEMS for the benefit of both countries.