What are necessary to study about Schramm Loewner evolution?

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I want to study about Schramm Loewner evolution.

I found many good sources to study about the concept including the lecture notes written by Greg Lawler.

Before studying with those lecture notes, I found that I must have concrete backgrounds in complex analysis and stochastic analysis.

Since I'm an undergraduate student in department of mathematics and statistics, I studied some fundamentals in real analysis and I'm studying basic probability theory and stochastic analysis. In stochastic analysis, what specific concepts are necessary to understand the concept?

I don't have background in complex analysis yet, so I'm planning to study complex analysis. I found that conformal mappings, Riemannian mapping theorem, etc. are crucial. Can I get some suggestions about what to study, and what textbooks are nice to study background knowledge?

Thank you very much for reading and sorry for my poor English skill...

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Professor Lawler has written excellent notes on many subjects.

For example, Introduction to Stochastic Calculus is well-written. It can be found on his website.

https://www.math.uchicago.edu/~lawler/inprogress