Mathematical Physics Talk for USM

Some time ago, I received an invitation from the organizers of USM Physics Coffee Talk. It was a pleasant surprise for me to be invited there. So all this week and parts of last week, I was gearing up and preparing for this talk. I shelve most other tasks to actually prepare for the talk including a proposal paper for the collaboration with UniMaP and UTM. I had to apologise for my minimal involvement in putting up the details of the proposal paper, delegating the tasks to my younger colleague Dr. Nurisya. Below is the poster prepared by the organizers:

They also had this put up introducing me as the speaker (not sure where they get this from).

For the last item under the experience box, I didn't quite remember what my involvement really is, but I guess it was minimal (to the point of forgetting). There were many other more significant events that I have taken up but of course, they are not recent. In any case, this is really a minor point.

One of my bad habits when preparing talks is that I tend to brood more than I should, looking up all possible perspectives and references, and usually ending up less time for me to prepare the slides. For this talk, for instance, I was doing my last two slides just about forty minutes before the talk. What happened was, I searched my collection of books and papers for the preparation of the talk, two of which are my own notes from Prof. Herbert Green's lectures and the conference proceedings of an international conference of quantum physics that was organized in Kuala Lumpur in 1997. For Prof. Green's notes, I know I had them in the attic hidden under piles of papers; so finding it seems impossible and I gave up just the day before. I wanted to show to the audience the kind of topics that was covered in the lectures (some of which I have forgotten). For the proceedings, I knew it was not in the attic and I probably misplaced it in one of the rooms. Just three hours before the talk, I made one last search in the room of my eldest son and there it was. I quickly scanned the cover and the first page of Cecile deWitt-Morette's contribution to the proceedings (see below). I also wanted to find the group photo but I just could not find it. We had so many luminaries in the conference: von Klitzing (Nobel laureate), 't Hooft (at the time, yet to receive his Nobel prize), Paul Townsend (my own invitation), Charles Bennett, Bryce deWitt, R.J. Baxter, John Klauder, Pavel Exner and many more.

The page above was not quite the page I intended to show (I completely forgotten what I have read). There was the sentence "Somewhat awed by what I had unthinkingly offered I began gathering material on quantum physics as seen by mathematicians, and recollecting the role of mathematics in my life as a physicist" in the above but this does not give the impact I wanted. The real sentence that I wanted was on the next page: 

"As I was pondering the rich and multifaceted interactions between Mathematics and Quantum Physics, a student of mine, Alexander Wurm, brought me a mathematics dictionary which includes a synoptic table of physics disciplines and mathematics theories. Very interesting, but again too rich a fare: the whole of mathematics is relevant to Quantum Physics."

The last sentence was the thing I wanted to highlight to the audience - the broad spectrum of mathematics that one needs to cover for quantum theory. If Cecile deWitt-Morette was overwhelmed with the scope she needs to cover for the talk at the conference, then I would be very much more overwhelmed with the task of explaining mathematical physics. The only difference here is my audience is a student audience (mostly) and not expert researcher audience. This is also the reason why I had only two slides that contain equations in them.

I was actually hoping to do more. The plan is to have another short section just after the (Un)Resonable Effectiveness slide to talk about the history of relativity and history of quantum theory; this would be the section on the growth of physics with the help of maths (as suggested by the organizers in the title of the talk). There, I would mention Grossmann helped Einstein with tensor calculus and differential geometry; and Born and Jordan helped Heisenberg with matrix mechanics. Having said matrix mechanics, I was also supposed to mention that Prof. H.S. Green (being a disciple of Born) had a book on Matrix Methods in Quantum Mechanics, which was given praises by some  experts. It is also interesting that Cecile deWitt-Morette mentioned in her article that "All throughout my life, I have a needed a mathematician friend willing to tutor me 'as needed' " - a thing that I have always wished that I could have.

Now, I have this section called "Standards" where I would just review (selected) mathematical ideas behind the basic theoretical subjects of physics. (Note: if I had more time, I would put up section dividers before starting a new section, but then I need to finish the real content first.) Thereafter, I really wanted to do a "Beyond" section, where I would delve into some of my research interests: contextuality in quantum foundations and complex networks using graph theory, entanglement geometry via group actions on complex projective spaces and symplectic topology, quantum chaos and even Langlands program via modular forms plus categorical quantum mechanics and topos quantum theory. However these would have taken me more (infinite) time to prepare.

Overall, I was not satisfied with my own talk - I wished I could have said more. As it is, it may appear to be of a mumbo-jumbo to some. I really wanted to get some feedback about my talk but then again, why do I have to put more stress on my own self. I have my own recording of the talk, which is available here: https://www.youtube.com/watch?v=99qHg5Pxr0w. The audio during Q&A is not good - perhaps the organizer will have a better video later.