# Akos Seress

### Quick Info

Budapest, Hungary

Columbus, Ohio, USA

**Akos Seress**was a Hungarian mathematician specialising in combinatorics and group theory.

### Biography

**Akos Seress**studied mathematics at Eötvös University, Budapest where he began publishing in combinatorics while an undergraduate. His first papers were

*k-sum-free decompositions*in Hungarian, and

*Gossiping old ladies*which was published in 1983. His own summary of the second of these papers reads:-

We consider the following problem: There are $n$ ladies each initially knowing a different piece of gossip. Anybody can speak to anybody and they exchange all of the pieces of gossip they know at that time. Is it possible to give a sequence of conversations such that everybody hears each piece of gossip exactly once? We determine all of the $n$'s for which this is possible.Seress went to the United States to obtain a doctorate. In 1985, he completed his Ph.D. at the Ohio State University, Columbus, Ohio, under Dijen Ray-Chaudhuri. He received the degree for his thesis

*The Gossip Problem*. The paper

*Quick gossiping without duplicate transmissions*, which he published in 1986, was based on work of his thesis. D J Kleitman writes in a review:-

$n$ people each start with one particular piece of information, and communicate through two-person telephone calls in which each participant tells all. The question addressed is: how many calls are necessary for everyone to learn everything with the restriction that nobody may hear already known information from anyone else? Such calls are only possible when $n > 1$ for even n and for $1 < n < 20$ only for $n$ divisible by 4. The exact bound $9n/4 - 6$ is obtained for $n$ divisible by 4, and a lower bound $(9n/4 - 4, 5)$ that is 1 away from the best upper bound is obtained for $n = 4k + 2$. The arguments are generally inductive, and quite complicated.He then returned to Hungary where he was appointed as a Research Associate at the Alfred Renyi Institute of Mathematics of the Hungarian Academy of Sciences. Continuing to work on combinatorics, he was one of six authors of the paper

*Coloring graphs with locally few colors*(1986). Paul Erdős was also one of the joint authors on this paper. At this stage he became an editor of the journal

*Combinatorica*, a task he undertook from 1986 until he left Hungary in 1989.

While working at the Alfred Renyi Institute of Mathematics in Budapest, Seress entered the field of algorithmic group theory with the paper

*On the degree of transitivity of permutation groups: a short proof*. It was the first in a series of joint papers with László Babai on the complexity of permutation group algorithms, some others being

*On the diameter of Cayley graphs of the symmetric group*(1988) and the three author papers

*Permutation groups*(1987) and

*Fast management of permutation groups*(1988) which had Seress, Babai and E M Luks as authors. He also continued to publish on the topic of his thesis with the papers

*Gossips by conference calls*(1987),

*Quick gossiping by conference calls*(1988), and

*Quick gossiping without duplicate transmissions*(1989).

In 1989 Seress returned to The Ohio State University where he was appointed as an Assistant Professor in the College of Mathematical and Physical Sciences. He continued his work in computational group theory with a series of important papers on the statistical theory of finite simple groups with Bill Kantor and others; this line of work contributed to a recent definitive result on the complexity of algorithms for matrix groups over finite fields by Seress and coauthors. He has also extensively contributed to the asymptotic theory of permutation groups, vertex-transitive graphs, extremal combinatorics, and the theory of designs. He published the important monograph

*Permutation Group Algorithms*in 2003. In an 'Acknowledgments' section, Seress writes:-

The writing of this book began in 1993, on the suggestion of Joachim Neubüser, who envisioned a series of books covering the major areas of computational group theory. The fact that the writing is finished in less than a decade is in no small part the consequence of my wife Sherry's continuous encouragement. I am thankful to both of them and to the editors of Cambridge University Press for their patience.The publisher, Cambridge University Press, gives the following description of the book:-

Permutation group algorithms are one of the workhorses of symbolic algebra systems computing with groups. They played an indispensable role in the proof of many deep results, including the construction and study of sporadic finite simple groups. This book describes the theory behind permutation group algorithms, up to the most recent developments based on the classification of finite simple groups. Rigorous complexity estimates, implementation hints, and advanced exercises are included throughout. The central theme is the description of nearly linear time algorithms, which are extremely fast both in terms of asymptotic analysis and of practical running time. A significant part of the permutation group library of the computational group algebra system GAP is based on nearly linear time algorithms. The book fills a significant gap in the symbolic computation literature. It is recommended for everyone interested in using computers in group theory, and is suitable for advanced graduate courses.Peter Neumann writes in a review that:-

... this monograph by Akos Seress, one of the leaders in the field, is a welcome contribution. ... the monograph is welcome not only for giving us an encyclopaedic account of the area, but also for its timeliness. A good author of a good book stamps his or her tastes and expertise firmly on the pages. That is what has happened here. In particular, because it should be of lasting value, it is a very appropriate addition to the Cambridge Tracts.Derek Holt writes in a review:-

This book provides a virtually complete state-of-the-art account of algorithms for computing with finite permutation groups. Almost all of the algorithms described are accompanied by complete and detailed correctness proofs and complexity analyses. It is very clearly written throughout, and is likely to become the standard and definitive reference work in the field.The next part of our biography is taken, with a few editorial changes, from [1].

Motivated by the theoretical results on algorithms for permutation groups, Seress pioneered the implementation of these algorithms in the GAP computational algebra system. Developed in the 1990s, with the cooperation and support of the RWTH Aachen group based at Lehrstuhl D für Mathematik, Seress's packages delivered, for the first time, practical performance backed up by theoretical analysis. His modular design and black-box techniques allow an easy adaptation to other representations; his work is widely used today as infrastructure both for permutation groups and for matrix groups. More recently Seress and Max Neunhoeffer have developed efficient implementations of a suite of algorithms for matrix groups.

Seress has been a tireless builder of communities, his own work and example demonstrating the bridge between the "red-hats," those who create "paper-algorithms" with proven asymptotic performance guarantees, and the "green-hats," the computational group theorists who demand working code to study the structure of concrete groups. Seress, along with Bill Kantor, has been a chief organizer of a series of meetings that brought these two communities together.

Seress spent most of his professional career at the Ohio State University where he was promoted to Associate Professor in 1995 and to full Professor in 2000. He made extended visits to the University of Western Australia and spent a year at Lehrstuhl D für Mathematik, RWTH Aachen, as an Alexander von Humboldt scholar. This is the highest ranking scholarship in Germany for foreign scientists.

He died at the age of 54 of renal cell carcinoma, a particularly aggressive form of cancer, diagnosed only six months before his death. The disease struck him at the height of his creative powers. His paper "

*Construction of 2-Closed M-Representations*" received the Distinguished paper award at ISSAC 2012 (Intl. Symp. on Symbolic and Algebraic Manipulation) and was hailed as "a groundbreaking work" that "marks a turning point in Majorana Theory." His most recent work, with Harald Helfgott, under publication in the

*Annals of Mathematics*, gives a long-sought bound on the diameter of the alternating and symmetric groups and represents a tour de force in the study of the geometry of finite simple groups.

Although we have been quoting almost verbatim from [1], let us emphasise that the following tribute to Akos Seress is by the authors of [1], Laszlo Babai and Eamonn O'Brien:-

Akos has been a most generous friend, colleague, and mentor. His passing will be felt deeply by all around the globe whose lives he touched and whose careers he enriched. Our hearts go out to his wife Sherry and his son Laszlo.Charles Leedham-Green writes in [2] about Akos Seress as a lecturer:-

The content of his lectures was of central importance; but Akos added another ingredient. To hear him lecture was to think: What fun; I should like to work in this area. His pleasure in being invited to give a lecture at the 2006 International Congress of Mathematicians in Madrid was a splendid example of this infectious enthusiasm.He also gives this tribute to Seress [2]:-

Akos was a great man. He carried all before him in a wave of enthusiasm, hard work, and insight, an insight that comprehended a great range of mathematical issues, an understanding of what needed to be done and how to do it, and a cheerful empathy with all around him. To meet Akos was to make a friend and collaborator for life.I [EFR] would like to end this biography with some personal comments. In December 2003 I talked to Akos at a conference at Aachen, Germany. He explained that he was working on a conjecture in finite geometries and asked if I thought it was possible to construct a finitely presented group with certain properties which he specified. After some discussion, I suggested that Graham Higman's finitely presented simple group should give him the example he was seeking and pointed him towards a reference. I thought no more about it until I received an email in April 2004. This was from Peter Brooksbank, who was working with Akos at this time:-

... a short paper has been written that constructs a counter-example to a conjecture in finite geometries that we had previously imagined to be true. The example is based on a group introduced by Graham Higman in 1951, but it is likely that we would not have discovered this construction were it not for the connection with finitely presented groups established by ... you.I was invited to be a coauthor on the paper

*On Dowling geometries of infinite groups*, an extremely generous offer. Since Akos Seress had published a paper with Erdős, it is through this very generous act that I have an Erdős number of 2.

### References (show)

- L Babai and E O'Brien, Akos Seress,
*GAP Forum*(15 February 2013). - C Leedham-Green, Akos Seress,
*London Math. Soc. Newsletter***424**(April 2013), 33.

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Written by J J O'Connor and E F Robertson

Last Update May 2013

Last Update May 2013