My research is on the design and theoretical analysis of efficient algorithms and data structures. 
One research focus are dynamic algorithms (i.e., data structures) that maintain properties of dynamically changing graphs and matrices. These can be abstract problems like maintaining the solution of a linear system that changes over time, but it also covers applications like maintaining the fastest route in a road network under changing traffic conditions. 
Another research focus are optimization algorithms. Many of these algorithms are iterative and solve a sequence of smaller subproblems, whose solution can be maintained via the aforementioned dynamic algorithms. I develop new iterative methods and dynamic algorithms that complement each other, resulting in improved optimization algorithms.