I really enjoyed Professor Vafa’s course. Here are a few questions that arose from it.

From my understanding the harmonics of a string can be described using the partition function, and if there is a string that wraps around the six minuscule dimensions necessary for string theory then the greater the number of harmonics of that string, the greater the weight of that string wrapped around those dimensions. This results in the creation of an extremely dense point, which becomes the singularity of a black hole. It is important that the harmonics are described by the partition function because as n increases the number of partitions of n increase exponentially, so with a fairly small number of harmonics a string wrapped around the six dimensions can still have an incredible density and form a black hole. I want to check that my understanding is correct, and I was also wondering what is thought to be the number of harmonics needed for a string to create a black hole.

I was fascinated by the concept of duality, and was wondering what, if any, examples of duality occur with respect to partitions. Would the commutative property of addition actually be considered a duality? 3+1 and 1+3 are considered to be the same partition of four – is this actually a very simple example of duality with respect to partitions?

Are there other connections between the partition function and entropy besides black holes and string theory?

What are some sources from which I could learn more about the Hardy-Ramanujan partition function and more about theories surrounding partitions in general? I was fascinated by this topic, and had heard very little about it prior to this course, and I would love to expand my knowledge on this subject.

We know that there are many connections between math and theoretical physics. Given that one of the main goals of grand unification between G.R. and Q.T. is mathematical aesthetics (ideally having the universe in one equation), could one, in some sense, establish an isomorphy between physics and unification of mathematical topics? In other words, could one find, for every mathematical fact, a corresponding fact in physics?

Gödel’s Incompleteness Theorem works off of the fact that mathematics is supposed to return a definitive true/false answer to everything. Could a similar trick be applied to physics, potentially disqualifying some theories that would allow for a statement about the theory to be of oscillating truth? Has this already been done, and if so, how successful was it?

I would like to know more about the Information Paradox, especially its “solution” in the sense of the theory of holography (in which gravity in 3 spatial dimensions is equivalent to special 2D electromagnetic forces on the edges of black holes and the universe). What might holography mean for the microstates of strings and black holes, if anything, and could that mean that our universe might just be a giant black hole in some multiverse (which could also theoretically be a yet bigger black hole in an infinite multi-multi-…-multiverse expanse), in which case (a) the Big Bang would rather have been the Big Collapse of some star in the multiverse, which over time absorbed everything in the universe we have today, and (b) the universe would ultimately succumb to Hawking Radiation and black hole decay. But then, what would happen to the information of the particles at the edge of the universe that would be Hawking Radiation-itized? Could it be possible that collision with one particle of the virtual pairs might erase the particle completely, leaving only very distorted traces of the particle’s information and giving off a minuscule amount of energy?