Time has passed swiftly since my arrival in Champaign, and now that spring is here, I have already experienced an autumn and winter in this city.
Looking ahead, my future research focus will center on the theory and applications of Distributionally Robust Optimization (DRO), which poses a new challenge. Specifically, I will explore the potential of combining Learning Theory and AI for optimization purposes.
To prepare for this task, I have planned to spend the next few months consolidating my mathematical fundamentals, starting from basic concepts and moving on to advanced ones. This will enable me to meet the challenges that lie ahead with confidence.
My plan includes studying texts such as
Analysis I & II by Tao,
Discrete Mathematics and its Application by Rosen,
Linear Algebra and its application by Strang,
Probability: Theory and Examples by Durrett,
Real Analysis and Probability by Dudley.
Additionally, it is essential to make good use of my holidays by reviewing the three books covered in my PhD qualifying exam, namely
Introduction to Linear Optimization by Bertsimas,
Integer and Combinatorial Optimization by Nemhauser,
Introduction to Probability Models by Sheldon M. Ross.
With these efforts, I am determined to make the best of the remainder of the year.
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