Computational complexity and logic

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I plan on continuing my research in both computational complexity and proof complexity. My current work in complexity theory is motivated by the problem of separating logarithmic space (deterministic and nondeterministic) from polynomial time. My collaborators and I have formulated a computational problem (the Tree Evaluation Problem), for which we have a conjectured space-optimal algorithm requiring superlogarithmic space. We use the branching program model of computational space, for which a superpolynomial lower bound on the number of states implies the desired separation. We have proved such a lower bound for restricted branching programs, and will work toward gradually removing the restrictions. In proof complexity I will continue working with my students on projects motivated by understanding the complexity of concepts needed to prove combinatorial theorems.