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I am an ex-academic researcher who has pivoted to working in industry. I love art, science, movies, music, gaming and all sorts of other things. If I’m not reading a research paper, or working on one of my own, I am usually watching a movie or stream.
Posts cover a vast variety of topics and projects, so don’t be alarmed.
Posts
12 May 2021
What is a Zero Knowledge Proof? #
Informally a zero-knowledge proof is a way to “prove” that you have access to some information without anyone else gaining access to the information itself. As you can see this is intrinsically tied to the spirit of cryptography. Most of the procedures commonly associated with cryptography are about transmitting information between two parties in such a way that the information is not able to be accessed by a non-intended (third) party. We usually handle this by employing some scheme (usually encryption) that hides the information from people who do not have access to the “keyword” which will reverse the scheme (decrypt the information). This however assumes that we can trust another party, what if we can’t? What if we have access to some sensitive information, and want to prove to someone else that we do, but do not want to give access to the information to the verifier. The most reasonable way to do this would be to have both parties communicate in a specific way (that we can formalize) such that the verifier can ask questions and the person with the information can answer them, but in a way such that it provides no new information about the object with which was discussed. This method of proving things requires interaction, and is commonly called an interactive proof system, however keep in mind that there are versions of zero-knowledge proofs that do not require interaction. The papers that introduce non-interactive zero-knowledge proofs and elaborate on them are more complicated, and require an extra assumption so we will only be talking about interactive zero-knowledge proofs, unless stated otherwise on this page.
10 Dec 2018
Getting started in Infinite Dimensional Smooth Manifolds
What is a manifold? #
Intuitively it is best to think of a manifold as a topological space with certain properties. The most important of which is that given any section of the space, the section overall looks similar to euclidean space. Which is what we refer to as being “locally euclidean”. This is similar to the notion that “locally” the Earth looks flat, but once we back up we realize that it is actually round. In fact almost every geometrical constructions can be thought of as a manifold.
10 May 2018
An Overview of the Properties of Surfaces #
Surfaces are a key aspect in the study in all of mathematics. Abstractions and investigations of these inherently tied to Differential geometry, Algebraic topology, and Lie Algebras. In fact all of Algebraic topology can be thought of as the study of classification of surfaces, and generalizations of this notion. However in this paper we are only going to focus on two-dimensional submanifolds of $\mathbb{R}^3$. That definition requires a certain level of mathematical maturity, but intuitively we can think of a surface as plane that has been stretched, punctured, and twisted into various shapes.