| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | June 6, 2015 |
| Latest Amendment Date: | June 6, 2015 |
| Award Number: | 1455798 |
| Award Instrument: | Standard Grant |
| Program Manager: |
James Matthew Douglass
mdouglas@nsf.gov (703)292-2467 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | July 1, 2015 |
| End Date: | June 30, 2017 (Estimated) |
| Total Intended Award Amount: | $39,932.00 |
| Total Awarded Amount to Date: | $39,932.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
845 N PARK AVE RM 538 TUCSON AZ US 85721 (520)626-6000 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
Tucson AZ US 85721-0001 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | ALGEBRA,NUMBER THEORY,AND COM |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
This award supports participation in the conference "Finite Simple Groups: Thirty Years of the Atlas and Beyond" taking place November 2-5, 2015, at Princeton University in Princeton, NJ. The concept of a group in mathematics grew out of the notion of symmetry. The symmetries of an object in nature or science are encoded by a group, and this group carries important information about the structure of the object itself. Group theory has had many important applications in physics and chemistry, particularly in quantum mechanics and in the theory of elementary particles. The main theme of the conference will be the interaction between theory and computation, and applications of group theory to other areas of mathematics. The list of invited participants features senior and junior researchers from across these fields and thus will foster further interaction and collaboration between them, during and after the conference. Conference activities will include informal working groups organized by experts in the field to discuss current and future research directions during the conference; a poster session; a webpage; and a wiki. The proceedings of the conference will be published.
The classification of finite simple groups, one of the most monumental accomplishments of the modern mathematics, was announced to be completed in 1983. Since then, it has opened up a new and powerful strategy to approach and resolve many, previously inaccessible problems in group theory, number theory, combinatorics, coding theory, algebraic geometry, and other areas of mathematics. This strategy utilizes information about finite simple groups, some of which is catalogued in the "Atlas of Finite Groups" and "An Atlas of Brauer Characters." It is impossible to overestimate the roles of the atlases and the related computer algebra systems in everyday life of researchers in many areas of contemporary mathematics. The conference will bring together a diverse group of researchers in group theory, representation theory, and computational group theory. The objective of the conference is to discuss numerous applications of the Atlases and to explore recent developments and future directions of research.
PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
The Classification of Finite Simple Groups, one of the most monumental accomplishments of the modern mathematics, was announced to be completed in 1983. Since then, it has opened up a new and powerful strategy to approach and resolve many, previously inaccessible problems in group theory, number theory, combinatorics, coding theory, and algebraic geometry -- to name a few. This strategy crucially utilizes various information about finite simple groups, part of which is catalogued in the ``Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups'', published in 1985, and ``An Atlas of Brauer Characters'', published in 1995. It is impossible to overestimate the roles of the Atlases and the related computer algebra systems in everyday's life ofresearchers in many areas of contemporary mathematics.
The main goal of the grant was to support the 4-day international conference``Finite Simple Groups: Thirty Years of the ATLAS and Beyond'' (Princeton, NJ, Nov. 2-5, 2015) and its follow-up ``Finite Simple Groups and their Representations'' (Tucson, AZ, March 25-26, 2017) , to discuss the numerous applications of the ATLAS and the Brauer Atlas (and their online parts) and to develop future directions of research. The Princeton conference featured 20 main speakers from the US, Australia, France, Germany, Israel, New Zealand, Spain, and the UK, and three poster sessions. It was attended by more than 90 participants, including experts in the field, seasoned mathematicians, young researchers and postdocs, and 15 Ph. D. students. The Tucson meeting featured 10 speakers from the US, Germany, and Spain.
The main objectives of the two conferences were to discuss numerous applications of the Atlases and to explore recent developments and future directions of research, with focus on the interaction between computation and theory and applications to number theory and algebraic geometry. Main topics of the lectures and discussion sessions at the conferences include
-- Classification of Finite Simple Groups (CFSG) and post-classification results using CFSG;
-- Computational projects, with focus on Brauer character tables and maximal subgroups of finite simple groups;
-- Recent parallel development in representation theory of finite groups of Lie type; and
-- Connections to combinatorics, number theory, algebraic geometry, and quantum field theory, including classifications of integral lattices and linear codes, vertex operator algebras, inverse Galois problem, etc.
The conferences also presented an excellent opportunity for the attending young researchers, postdocs, and Ph. D. students to interact with leaders in the field. Several collaborative projects have outgrown from the lectures and discussion sessions of the conferences and are being actively carried out.
The proceedings of the conference, edited by M. Bhargava (Princeton), R. M. Guralnick (USC), G. Hiss (RWTH Aachen), K. Lux and P. H. Tiep (U. Arizona), have just been published by the AMS, as volume 694 in the series ``Contemporary Mathematics'', and feature 18 peer-reviewed research articles and surveys. This book will be of interest to all mathematicians (and advanced graduate students) who work in algebra, group theory, representation theory, as well as in adjacent areas of combinatorics, number theory, algebraic geometry, coding theory, and mathematical physics.
Last Modified: 07/05/2017
Modified by: Pham Huu Tiep
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