I hope that resuming and continuing is as smooth as abandoning.

I am, as always, passionate about learning mathematics, but I didn’t feel that passionate about life during the time I didn’t post any. In short, let’s simply say that a lot of bad things happened. Though I am still adjusting my mindset, things are going in the right direction now. Hope that these bad things made me more experienced and gave me more strength and confidence to move forward.

Sooner or later, I will begin to update the Project page section so that I can also review my previous study. Maybe I will also update the Magic page section later, but the schedule for the Music page section may be indefinite because there are many other things I have to deal with.

## Quantum Trajectory

This is a completely unfamiliar field for me to jump into, but I challenged myself to do this research project with Professor Martin Fraas. Fortunately, I don’t have to learn the whole quantum mechanics behind the quantum trajectory theory. The thing we are concerned about is the purification condition described as Theorem 1 in this paper by Hans Maassen and Burkhard Kummerer. We want to try to improve the theorem to the infinite-dimensional case based on an alternating proof from this paper by T. Benoist, M. Fraas, et al. I am currently in a state that I barely understand the basic and saw some examples and counterexamples in infinite dimension. My plan this week is still to read the proof and the setup again and again. Meanwhile, I will try to apply those examples to the setup to get a better understanding.

## Riemann-Hilbert Problem

This is a continuing study of the last summer reading course with Professor Craig Tracy (Update later). I will learn the Riemann-Hilbert problem and the whole thing all the way through starting from the basics with a graduate student at UCDavis. This will be a reading experience learning from each other.

## Review and Beyond

Since I studied many different fields of mathematics before, there are lots of important materials that I forgot. I think that I will start from Stochastic Differential Equations and Machine Learning related, following by Combinational Optimization and maybe Algebra later. And yes, these are primarily for the application of internship experiences. Meanwhile, I plan to learn some Statistics and knowledge about Mathematical Finance. I haven’t decided where to start but I think that it will be really soon.

Stay Strong