# Miscellaneous

Sorry for the bad formatting on this page. It is more for me to keep track of things I am currently working on/interested in working on. If for whatever strange reason you care to know what I'm working on - well, hopefully this is satisfactory, though I doubt it will be. Also, for anyone who cares, here is my research summary. It was last updated sometime in October 2020. Here is some more light-hearted fun.

Here is a list of problems I am actively working on:

1. Is PP equivalent to AC over ZF? This question is explored here and here. There is also a discussion on MathOverflow regarding the first of these links.
2. Can an isomorphism of subgroups of a finite group always be extended to an automorphism?
3. What are the analytic properties of random sequences in $$\{0,1\}^{\omega}$$?
4. A topology is often stated to be the minimal structure we are required to impose on a sets $$x,y$$ in order to be able to talk about continuity of functions $$f:x\to y$$. But minimal with respect to what? Is it not conceivable that we can impose some other Godelian structure on sets and some other property between these and still discuss continuity such that in if the sets are subsets of the reals, the our notion of continuity reduces to our familiar notion of real continuity? Related is the question here. I will do a write-up of this problem soon and link it here.

You can contact me at: venkatb(AT)math(DOT)mcmaster(DOT)ca