Chris Umans

Christopher Umans
EducationWilliams College, University of California, Berkeley
Known forComputational complexity, algorithms, hardness of approximation, matrix multiplication
Scientific career
FieldsComputer Science
WorkplacesCalifornia Institute of Technology
Christos Papadimitriou

Christopher Umans is a professor of computer science in the Computing and Mathematical Sciences Department at the California Institute of Technology. He is known for work on algorithms, computational complexity, algebraic complexity, and hardness of approximation.

Academic biography

Umans studied at Williams College, where he completed a BA degree in Mathematics and Computer Science in 1996. He then received a PhD in Computer Science from University of California, Berkeley in 2000 under Christos Papadimitriou. Following his PhD, he was a postdoctoral researcher at Microsoft Research until joining Caltech in 2002.

Research

Umans' research centers broadly around algorithms and complexity. He has made notable contributions to varied areas within this space including random number generation, expanders, and algorithms for matrix multiplication. A notable example is his work on developing a group theoretic approach for matrix multiplication.

In 2008, Umans and his student Dave Buchfuhrer settled a 1979 conjecture on the complexity of unbounded Boolean formula minimization; the result won a best paper award at ICALP.

Awards and honors

Umans received an NSF CAREER award in 2004 and an Alfred P. Sloan Fellowship in 2005. Additionally, his work has received "Best Paper" awards at the International Conference on Automata, Languages, and Programming (ICALP) and the IEEE Conference on Computational Complexity (CCC).

References

  1. ↑ Cohn, H.; Umans, C. (2003), "A group-theoretic approach to fast matrix multiplication", 44th Annual IEEE Symposium on Foundations of Computer Science, 2003. Proceedings, pp. 438–449, arXiv:math/0307321, doi:10.1109/SFCS.2003.1238217, ISBN 978-0-7695-2040-7, S2CID 5890100
  2. ↑ Cohn, Henry; Kleinberg, Robert; Szegedy, Balász; Umans, Christopher (2005). "Group-theoretic Algorithms for Matrix Multiplication". Proc. 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS). IEEE. pp. 379–388. arXiv:math/0511460. doi:10.1109/SFCS.2005.39.
  3. ↑ Cohn, Henry; Umans, Christopher (2013). "Fast matrix multiplication using coherent configurations". Proc. 24th Annual ACM-SIAM Symposium on Discrete Algorithms (SODA). SIAM. pp. 1074–1087. arXiv:1207.6528. doi:10.1137/1.9781611973105.77.
  4. ↑ Alon, Noga; Shpilka, Amir; Umans, Christopher (2013). "On sunflowers and matrix multiplication". Computational Complexity. 22 (2): 219–243. doi:10.1007/s00037-013-0060-1.
  5. ↑ Blasiak, Jonah; Church, Thomas; Cohn, Henry; Grochow, Joshua A.; Naslund, Eric; Sawin, William F.; Umans, Christopher (2017). "On cap sets and the group-theoretic approach to matrix multiplication". Discrete Analysis. arXiv:1605.06702. doi:10.19086/da.1245.
  6. ↑ Blasiak, Jonah; Church, Thomas; Cohn, Henry; Grochow, Joshua A.; Umans, Christopher (2017). "Which groups are amenable to proving exponent two for matrix multiplication?". arXiv:1712.02302 [math.GR].
  7. ↑ Blasiak, Jonah; Cohn, Henry; Grochow, Joshua A.; Pratt, Kevin; Umans, Christopher (2023). "Matrix Multiplication via Matrix Groups". 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Schloss Dagstuhl - Leibniz-Zentrum für Informatik. pp. 19:1–19:16. doi:10.4230/LIPIcs.ITCS.2023.19.
  8. ↑ Buchfuhrer, David; Umans, Christopher (January 2011). "The complexity of Boolean formula minimization". Journal of Computer and System Sciences. 77 (1): 142–153. doi:10.1016/j.jcss.2010.06.011. This is an extended version of the conference paper: Buchfuhrer, David; Umans, Christopher (2008). "Automata, Languages and Programming" (PDF). In Luca Aceto; Ivan Damgård; et al. (eds.). Automata, Languages and Programming: 35th International Colloquium, ICALP 2008, Reykjavik, Iceland, July 7–11, 2008, Proceedings, Part I. Lecture Notes in Computer Science. Vol. 5125. Berlin / Heidelberg, Germany: Springer-Verlag. pp. 24–35. doi:10.1007/978-3-540-70575-8_3. ISBN 978-3-540-70574-1. Archived (PDF) from the original on 2018-01-14. Retrieved 2018-01-14. This won the Best Paper Award in Track A "Algorithms, Automata, Complexity and Games".
  9. ↑ Sloan Fellows