# László Babai

László Babai | |
---|---|

László Babai at Oberwolfach in 2011 | |

Born |
Budapest | July 20, 1950

Nationality | Hungarian |

Alma mater | Hungarian Academy of Sciences |

Awards |
Gödel Prize (1993) Knuth Prize (2015) Dijkstra Prize (2016) |

Scientific career | |

Fields | Computer Science, Mathematics |

Institutions | University of Chicago |

Doctoral advisor |
Pál Turán Vera T. Sós |

Doctoral students |
Mario Szegedy Gábor Tardos |

**László "Laci" Babai** (born July 20, 1950 in Budapest)^{[1]} is a Hungarian professor of computer science and mathematics at the University of Chicago. His research focuses on computational complexity theory, algorithms, combinatorics, and finite groups, with an emphasis on the interactions between these fields.

## Contents

## Life[edit]

In 1968, Babai won a gold medal at the International Mathematical Olympiad. Babai studied mathematics at Eötvös Loránd University from 1968 to 1973, received a Ph.D. from the Hungarian Academy of Sciences in 1975, and received a D.Sc. from the Hungarian Academy of Sciences in 1984.^{[1]}^{[2]} He held a teaching position at Eötvös Loránd University since 1971; in 1987 he took joint positions as a professor in algebra at Eötvös Loránd and in computer science at the University of Chicago. In 1995, he began a joint appointment in the mathematics department at Chicago and gave up his position at Eötvös Loránd.^{[1]}

## Work[edit]

He is the author of over 180 academic papers.^{[1]}
His notable accomplishments include the introduction of interactive proof systems,^{[3]} the introduction of the term Las Vegas algorithm,^{[4]} and the introduction of group theoretic methods in graph isomorphism testing.^{[4]} In November 2015, he announced a quasipolynomial time algorithm for the graph isomorphism problem.^{[5]}^{[6]}^{[7]}

He is editor-in-chief of the refereed online journal *Theory of Computing*.^{[8]} Babai was also involved in the creation of the Budapest Semesters in Mathematics program and first coined the name.

### Graph Isomorphism in Quasipolynomial Time[edit]

From 10 November to 1 December 2015, Babai gave three lectures on «Graph Isomorphism in Quasipolynomial Time» in the «Combinatorics and Theoretical Computer Science» Seminar at the University of Chicago. He outlined a proof to show that the Graph isomorphism problem can be solved in quasi-polynomial time.^{[9]}^{[10]}^{[11]}^{[12]} A video of the first talk was published on 10 December 2015^{[13]} and a preprint was uploaded to arXiv.org on 11 December 2015^{[7]} and a note published on 14 January 2017.^{[14]}

We show that the Graph Isomorphism (GI) problem and the related problems of String Isomorphism

^{[15]}(under group action) (SI) and Coset Intersection (CI)^{[16]}^{[17]}can be solved in quasipolynomial time. The best previous bound for GI was where is the number of vertices (Luks, 1983); for the other two problems, the bound was similar, where is the size of the permutation domain (Babai, 1983).

The algorithm builds on Luks's SI framework and attacks the barrier configurations for Luks's algorithm by group theoretic «local certificates» and combinatorial canonical partitioning techniques. We show that in a well-defined sense, Johnson graphs are the only obstructions to effective canonical partitioning.

## Honors[edit]

In 1988, Babai won the Hungarian State Prize, in 1990 he was elected as a corresponding member of the Hungarian Academy of Sciences, and in 1994 he became a full member.^{[1]} In 1999 the Budapest University of Technology and Economics awarded him an honorary doctorate.^{[1]}

In 1993, Babai was awarded the Gödel Prize together with Shafi Goldwasser, Silvio Micali, Shlomo Moran, and Charles Rackoff, for their papers on interactive proof systems.^{[18]}

In 2015, he was elected^{[19]} a fellow of the American Academy of Arts and Sciences, and won the Knuth Prize.

## Sources[edit]

- Professor László Babai’s algorithm is next big step in conquering isomorphism in graphs // Published on Nov 20, 2015 Division of the Physical Sciences / The University of Chicago
- Mathematician claims breakthrough in complexity theory, by Adrian Cho 10 November 2015 17:45 // Posted in Math, Science AAAS News
- A Quasipolynomial Time Algorithm for Graph Isomorphism: The Details + Background on Graph Isomorphism + The Main Result // Math ∩ Programming. Posted on November 12, 2015 by j2kun
- Landmark Algorithm Breaks 30-Year Impasse, Algorithm Solves Graph Isomorphism in Record Time // Quanta Magazine. By: Erica Klarreich, December 14, 2015
- A Little More on the Graph Isomorphism Algorithm // November 21, 2015, by RJLipton+KWRegan (Ken Regan and Dick Lipton)
- [Ласло] Бабай приблизился к решению «проблемы тысячелетия» // Наука Lenta.ru, 14:48, 20 ноября 2015

- copy from Lenta.ru // texnomaniya.ru, 20 ноября 2015

- Опубликован быстрый алгоритм для задачи изоморфизма графов // Анатолий Ализар, Хабрахабр, 16 декабря в 02:12

- Опубліковано швидкий алгоритм для задачі ізоморфізму графів // Джерело: Хабрахабр, перекладено 16 грудня 2015, 06:30

## References[edit]

- ^
^{a}^{b}^{c}^{d}^{e}^{f}Curriculum vitae from Babai's web site, retrieved 2016-01-28. **^**László Babai at the Mathematics Genealogy Project**^**Babai, László; Moran, Shlomo (1988), "Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class",*J. Comput. Syst. Sci.*,**36**(2): 254–276, doi:10.1016/0022-0000(88)90028-1.- ^
^{a}^{b}Babai, László (1979),*Monte-Carlo algorithms in graph isomorphism testing*(PDF), Tech. Report, Université de Montréal. **^**Cho, Adrian (November 10, 2015), "Mathematician claims breakthrough in complexity theory",*Science*, doi:10.1126/science.aad7416**^**Klarreich, Erica. "Landmark Algorithm Breaks 30-Year Impasse".*quantamagazine.org*. Quanta Magazine.- ^
^{a}^{b}László Babai. Graph Isomorphism in Quasipolynomial Time, 84 pages / abstract // arXiv.org > cs > arXiv:1512.03547 / version 1 [v1] Fri, 11 Dec 2015 08:04:26 GMT **^***Theory of Computing*editors, retrieved 2010-07-30.**^**Laszlo Babai (University of Chicago): Graph Isomorphism in Quasipolynomial Time I: The "Local Certificates Algorithm" // Combinatorics and Theoretical Computer Science seminar, 10 November 2015, 15:00 – 16:00**^**A Big Result On Graph Isomorphism // November 4, 2015, A Fast Graph Isomorphism Algorithm // November 11, 2015**^**Combinatorics and Theoretical Computer Science calendar // Theoretical Computer Science at the University of Chicago. November 24, 2015, Laszlo Babai (University of Chicago): Graph Isomorphism in Quasipolynomial Time II: The "Split-or-Johnson routine" (Combinatorics and TCS seminar)**^**Claimed Breakthrough Slays Classic Computing Problem // MIT Technology Review, by Tom Simonite on November 13, 2015**^**Graph Isomorphism in Quasipolynomial Time I, seminar lecture by László Babai on November 10, 2015. The University of Chicago // youtube, 1 год. 40 хв. Опубліковано 10 грудня 2015**^**László Babai: Fixing the UPCC case of Split-or-Johnson, posted on 14 January 2017**^****Definition 2.3.**String Isomorphism, in: Transactions on Computational Science V. Special Issue on Cognitive Knowledge Representation. Editors-in-Chief: Marina L. Gavrilova, C. J. Kenneth Tan. Editors: Yingxu Wang, Keith Chan / Lecture Notes in Computer Science / Volume 5540, Springer Verlag, 2009**^**Coset intersection problem // The Group Properties Wiki (beta)**^**Complexity of the coset intersection problem // Theoretical Computer Science Stack Exchange, asked Sep 25 2014 at 9:43**^**1993 Gödel Prize Archived 2015-12-08 at the Wayback Machine., ACM SIGACT, retrieved 2010-08-14.**^**American Academy of Arts and Sciences. 2015 Fellows and Their Affiliations

## External links[edit]

- Media related to László Babai at Wikimedia Commons
- Personal website.
- MathSciNet: "Items authored by Babai, László."
^{[permanent dead link]} - DBLP: László Babai.

- 1950 births
- 20th-century Hungarian mathematicians
- 21st-century mathematicians
- Hungarian mathematicians
- Hungarian computer scientists
- Members of the Hungarian Academy of Sciences
- Hungarian academics
- Combinatorialists
- Theoretical computer scientists
- University of Chicago faculty
- Gödel Prize laureates
- Knuth Prize laureates
- Hungarian emigrants to the United States
- Living people
- International Mathematical Olympiad participants
- Fellows of the American Academy of Arts and Sciences