See Home, for my areas of interest. Below are more specific topics I've found interesting.
Combinatorial Optimization - combinatorial algorithms and approximation algorithms (maybe more LP based methods in the future)
Graph Algorithms and Graph Theory - cuts, flows, graph decompositions, partitioning, metric embeddings, Steiner problems, routing, spectral techniques, and s-t series parallel graphs
Algorithms under Uncertainty - stochastic probing problems, adaptivity gaps, online MTS, and ML predictions in online algorithms
Algorithmic Game Theory - information design, congestion games, persuasion, and price of anarchy
Many fun problems lie in most of the main categories such as stochastic probing problems in metric spaces and metrical task system problems. Some of my favorites of these kinds are the Adaptive Traveling Salesman Problem, the Bayesian Canadian Traveler's Problem, and the Multilevel Aggregation Problem. I've also been getting into using ML predictions in online algorithms to achieve improved performance.
I also like problems that have applications to or motivations from other fields such as bioinformatics, AGT, and ML. It's really fun finding connections between completely different areas. I'm particularly intrigued by connections between psychology and computer science especially in the context of machine learning and AGT. One particular work of this type I find fascinating is the study of consciousness using TMs.
A D-competitive algorithm for the Multilevel Aggregation Problem with Deadlines [arXiv]
Approximating Pandora's Box with Correlations
with Shuchi Chawla, Evangelia Gergatsouli, and Christos Tzamos, in submission.
Algorithmic Mechanism Design
Noble Deceit: Optimizing Social Welfare for Myopic Multi-Armed Bandits [Games, EC Poster]
with Ashwin Maran and Nathaniel Sauerberg, Games 2020.