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Mathematics Research Communities (MRC), American Mathematical Society (AMS)
Workshop: Combinatorial Representation Theory in Data Analysis
Organizer: Michael Orrison, Harvey Mudd College
Co-organizer: Risi Kondor, University of Chicago
Date: June 2014

This research community will introduce young mathematicians to research bridging pure'' mathematics and various applications amenable to the analysis of discrete models. Mathematicians trained in areas such as algebra, topology, geometry, and combinatorics are often unaware of the extent to which they are prepared to tackle open problems in fields such as biology, the social sciences, data analysis, and optimization. There is also significant benefit in attacking applied problems from a discrete perspective with algebraic, topological, geometric and/or combinatorial tools.

The participants of this MRC will be grouped into five teams, each focusing on a particular application. During an intense week at Snowbird, the teams will work on specific open problems selected by the organizers. Participants will be expected to do background reading in advance of the workshop and come ready to collaborate and build strong research ties. Although each team will focus on a different application, there are common themes and methods, and the weekly activities will facilitate interactions between groups. The five focus areas are:

(1) Combinatorial Topology in the Social Sciences,
(2) Representation Theory in Data Analysis,
(3) Combinatorics in Molecular Biology,
(4) Algebraic and Geometric approaches in Neuroscience,
(5) Algebraic and Geometric methods in Optimization.

This MRC will bring together participants with diverse backgrounds and strengths. We welcome the entire spectrum of applicants, from those who are familiar with the applications but wish to broaden their mathematical tools to young mathematicians trained in algebra, topology, geometry, or combinatorics who are interested in exploring applications.

References:

Group Representations in Probability and Statistics, by Persi Diaconis.

• Chapter 5: Examples of Data on Permutations and Homogeneous Spaces
• Chapter 8: Spectral Analysis

More references:

BOOKS

[1] Diaconis, Persi: Group representations in probability and statistics. Institute of Mathematical Statistics Lecture Notes - Monograph Series, 11. Institute of Mathematical Statistics, Hayward, CA, 1988. vi+198 pp. ISBN: 0-940600-14-5. [ https://projecteuclid.org/euclid.lnms/1215467407 ]

[2] Marden, John I.: Analyzing and modeling rank data. Monographs on Statistics and Applied Probability, 64. Chapman & Hall, London, 1995. xiv+329 pp. ISBN: 0-412-99521-2.

[3] Fassler, A.; Stiefel, E.: Group theoretical methods and their applications. Translated from the German by Baoswan Dzung Wong. Birkhauser Boston, Inc., Boston, MA, 1992. xii+296 pp. ISBN: 0-8176-3527-0.

[4] Terras, Audrey: Fourier analysis on finite groups and applications. London Mathematical Society Student Texts, 43. Cambridge University Press, Cambridge, 1999. x+442 pp. ISBN: 0-521-45718-1.

[5] Clausen, Michael; Baum, Ulrich: Fast Fourier transforms. (English summary) Bibliographisches Institut, Mannheim, 1993. ii+181 pp. ISBN: 3-411-16361-5.

[6] Ceccherini-Silberstein, Tullio; Scarabotti, Fabio; Tolli, Filippo: Harmonic analysis on finite groups. Representation theory, Gelfand pairs and Markov chains. Cambridge Studies in Advanced Mathematics, 108. Cambridge University Press, Cambridge, 2008. xiv+440 pp. ISBN: 978-0-521-88336-8.