Reading list

Some things I have recently been trying to understand:

• the progress on cutoff for mixing times of Markov chains presented in Justin Salez's survey

• strong convergence via Ramon van Handel's survey (shorter version for ICM)

• concentration of measure and high-dimensional probability. I enjoyed:

  • Roman Vershynin's High-Dimensional Probability

  • Ramon van Handel's lecture notes on Probability in High Dimension

  • A. Bandeira, A. Singer, and T. Strohmer's Mathematics of Data Science

  • M. Ledoux's survey The Concentration of Measure Phenomenon

  • M. Talagrand's Upper and Lower Bounds for Stochastic Processes

Various ML stuff (with the knoledge that everything changes fast):

• Machine Learning: A Probabilistic Perspective (and newer versions)

• Pattern Recognition and Machine Learning

• Reinforcement Learning: An Introduction

• The Elements of Statistical Learning

Similar sites

Bulgarian researchers in probability (with similar sites) that I know of are E. Dimitrov, I. Hartarsky, and L. Lichev.

Additionally, you can explore S. Apostolov's blog, which covers a wide range of intriguing mathematical subjects.

Misc

My master's thesis was going through Cutoff on all Ramanujan Graphs by E. Lubetzky and Y. Peres for which I clarified the proofs and found a non-trivial mistake (in Proposition 6, p<2). I was extremely lucky to be supervised by J. Salez.

I have written notes for the entry exam for the PhD program in FMI and for the exam after the first year and second year in it.

Around 2020, I was often recommending the online course Financial Markets and the specialization Deep Learning. I think the first is still educational and fun. For some basic understanding of gpt-like models,  Karphaty's nanochat, Stanford's Language Modeling from Scratch, and some of the deeplearning.ai courses were useful to me.