Welcome! I am a computer science PhD student in the Theory of Computation group at Harvard. I'm fortunate to be advised by Professor Salil Vadhan.
Before this, I graduated with a BS in mathematics from the University of Central Florida. While at UCF, I completed an honors undergraduate thesis under the supervision of Professor Zi-Xia Song.
If you have questions about my research or are interested in collaboration, feel free to contact me at jakeruotolo at g.harvard.edu.
Research Interests: My interests are in combinatorics and theoretical computer science, especially the intersection of these two areas. Much of current research focuses on spectral methods in algorithms and combinatorics.
Papers:
Singular Values Versus Expansion in Directed and Undirected Graphs [arXiv]
with Salil Vadhan.
Sparsest Cut and Eigenvalue Multiplicities on Low Degree Abelian Cayley Graphs [arXiv]
with Tommaso d'Orsi, Chris Jones, Salil Vadhan, and Jiyu Zhang,
Theory of Computing, to appear.
A preliminary version appeared in APPROX 2025.
Multicolor Ramsey Numbers for Double Stars [arXiv]
with Zi-Xia Song,
Discrete Mathematics, 2024
An Asymptotically Sharp Bound on the Maximum Number of Independent Transversals [arXiv]
with Kevin Wang and Fan Wei,
The Electronic Journal of Combinatorics, 2024.
Teaching:
Discrete Mathematics for Computer Science (CS 20, Spring 2026)
Pseudorandomness and High-Dimensiona Expanders (CS 2253, Spring 2026)
Spectral Graph Theory in CS (CS 229 cr, Spring 2023)
Undergraduate Advising:
Easton Singer (co-advised with Salil Vadhan): Eigenvalue Multiplicities In Abelian Cayley Graphs
Ashley Zhuang (co-advised with Salil Vadhan): Sparsity Bounds for Spectral Approximations of Graphs