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My research interests are in algorithms, probability theory, combinatorics, and statistical physics. I have designed new algorithms and new probabilistic methods in combinatorics using ideas and intuition from statistical physics, while also proving theorems in statistical physics using algorithmic ideas.
I teach courses in the design and analysis of algorithms, in probability theory, and in combinatorics. The courses I teach in computer science are about the theory of computing and how to use mathematics to reason about the performance and limits of algorithms.
M. Jenssen, W. Perkins, and A. Potukuchi. On the evolution of structure in triangle-free graphs.
Advances in Mathematics 480 (2025), 110499
M. Michelen and W. Perkins. Potential-weighted connective constants and uniqueness of Gibbs
measures. Communications in Mathematical Physics 406.32 (2025)
W. Perkins. Searching for (sharp) thresholds in random structures: where are we now? Bulletin
of the American Mathematical Society 62.1 (2025), 113–143
M. Jenssen, W. Perkins, A. Potukuchi, and M. Simkin. Sampling, Counting, and Large Deviations
for Triangle-Free Graphs Near the Critical Density. 2024 IEEE 65th Annual Symposium on
Foundations of Computer Science (FOCS). IEEE Computer Society. 2024, pp. 151–165
W. Perkins and C. Xu. Frozen 1-RSB structure of the symmetric Ising perceptron. Random
Structures & Algorithms 64.4 (2024), 856–877. Extended abstract at STOC 2021