Mathematics Research Communities

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The American Mathematical Society announces Mathematics Research Communities The AMS invites mathematicians just beginning their research careers to become part of Mathematics Research Communities, a program to develop and sustain long-lasting cohorts for collabora- tive research projects in many areas of mathematics. Women and underrepresented minorities are especially encouraged to partici- pate. The AMS will provide a structured program to engage and guide all participants as they start their careers. The program wHi include: • One-week summer conference for each topic • Special Sessions at the national meeting • Discussion networks by research topic • Longitudinal study of early career mathematicians The summer conferences of the Mathematics Research Communities will be held in the breathtaking mountain setting of the Snowbird Resort, Utah, where participants can enjoy the natural beauty and a collegial atmosphere. The application deadline for summer 2011 is March I, 2011. This program is supported by a grant from the National Science Foundation. June 12-18,2011 The Geometry of Real Projective Structures Organiurs: Virgirde Charette (Universite de Sherbrooke), Daryl Cooper (University of California, Santa Barbam). William Goldman (Uni\'ersity of Maryland), Anna Wienhard (Princeton University) June 19-25, 2011 Computational and Applied Topology Organizers: Gunnar Carlsson (SlanfOrd University). Robert Ghrist (University of Pennsylvania), Benjamin f;lann (Ayasdi. Inc.) June 26-July 2, 2011 The Pretentious View of Analytic Number Theory Orgnnizers: Andrew Granville (Universite do Montreal), Oimitris Koukoulopoulos (Universite de Montreal), Younes8 Lamzouri (University of Illinois at Urbana· Champaign), KRnmm Soulldnrarajan (Stanford University), Frank Thorne (Stanford University) http://www.ams.org/programs/ ~AMS ••••••••••• ...,.,""""""' ••'<11'" research·communities/mrc I ••••••.••••-""1' I.

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Topological Pattern Recognition for Point Cloud Data∗
Acta Numerica (2014), pp. 289–368 c Cambridge University Press, 2014 doi:10.1017/S0962492914000051 Printed in the United Kingdom Topological pattern recognition for point cloud data∗ Gunnar Carlsson† Department of Mathematics, Stanford University, CA 94305, USA E-mail: gunnar@math.stanford.edu In this paper we discuss the adaptation of the methods of homology from algebraic topology to the problem of pattern recognition in point cloud data sets. The method is referred to as persistent homology, and has numerous applications to scientific problems. We discuss the definition and computation of homology in the standard setting of simplicial complexes and topological spaces, then show how one can obtain useful signatures, called barcodes, from finite metric spaces, thought of as sampled from a continuous object. We present several different cases where persistent homology is used, to illustrate the different ways in which the method can be applied. CONTENTS 1 Introduction 289 2 Topology 293 3 Shape of data 311 4 Structures on spaces of barcodes 331 5 Organizing data sets 343 References 365 1. Introduction Deriving knowledge from large and complex data sets is a fundamental prob- lem in modern science. All aspects of this problem need to be addressed by the mathematical and computational sciences. There are various dif- ferent aspects to the problem, including devising methods for (a) storing massive amounts of data, (b) efficiently managing it, and (c) developing un- derstanding of the data set. The past decade has seen a great deal of devel- opment of powerful computing infrastructure, as well as methodologies for ∗ Colour online for monochrome figures available at journals.cambridge.org/anu.
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Topology and Data
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Lecture Notes in Mathematics
Lecture Notes in Mathematics For information about Vols. 1-1145 please contact your bookseller Vol. 1173: H. DeHs, M. Knebusch, Locally Semialgebraic Spaces. XVI, or Springer-Verlag. 329 pages. 1g95, Vol. 1146: 5eminaire d'Aigebre Paul Dubreil et Marie-Paula Malliavin. Vol. 1174: Categories in Continuum Physics, Buffalo 1982. Seminar. Proceedings, 1g63-1984. Edite par M.-P. Malliavin. IV, 420 pages. Edited by F.W. Lawvere and S.H. Schanuel. V, t26 pages. t986. 1985. Vol. 1175: K. Mathiak, Valuations of Skew Fields and Projective Vol. 1147: M. Wschebor, Surfaces Aleatoires. VII, 11t pages. 1985. Hjelmslev Spaces. VII, 116 pages. 1986. Vol. 1t48: Mark A. Kon, Probability Distributions in Quantum Statistical Vol. 1176: R.R. Bruner, J.P. May, J.E. McClure, M. Steinberger, Mechanics. V, 12t pages. 1985. Hoo Ring Spectra and their Applications. VII, 388 pages. 1988. Vol. 1149: Universal Algebra and Lattice Theory. Proceedings, 1984. Vol. 1t77: Representation Theory I. Finite Dimensional Algebras. Edited by S. D. Comer. VI, 282 pages. 1985. Proceedings, t984. Edited by V. Dlab, P. Gabriel and G. Michler. XV, 340 pages. 1g86. Vol. 1150: B. Kawohl, Rearrangements and Convexity of Level Sets in Vol. 1178: Representation Theory II. Groups and Orders. Proceed PDE. V, 136 pages. 1985. ings, 1984. Edited by V. Dlab, P. Gabriel and G. Michler. XV, 370 Vol 1151: Ordinary and Partial Differential Equations. Proceedings, pages. 1986. 1984. Edited by B.D. Sleeman and R.J. Jarvis. XIV, 357 pages. 1985. Vol. 1179: Shi J .-Y. The Kazhdan-Lusztig Cells in Certain Affine Weyl Vol. 1152: H. Widom, Asymptotic Expansions for Pseudodifferential Groups.
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Three Keynote Lectures Delivered By: ▫ Prof. Gunnar Carlsson, Stanford
Three keynote lectures delivered by: . Prof. Gunnar Carlsson, Stanford University, USA . Prof. Samad Hedayat, University of Illinois at Chicago, USA . Prof. Edriss Titi, Texas A&M University, USA Gunnar Carlsson: Gunnar Carlsson is a Professor of Mathematics at Stanford University. A highly influential mathematician, he is most well-known for his proof of the Segal Burnside Ring conjecture and for his work on applied algebraic topology, especially topological data analysis. He was a Professor at Princeton University before joining the Stanford Mathematics Department in 1991 where he also served as a Chairman. He was invited at the International Congress of Mathematicians to speak about his work in homotopy theory. More recently his work on persistent homology and topological data analysis has opened up new fields of research with a large number of followers. Whether through his numerous publications or keynote addresses, Gunnar Carlsson has been having an enormous influence on present day mathematical research and its applications to as far afield as cancer treatment. He has co-authored two books on mathematical education. He served as a consultant to the education boards of the State of Texas and State of California concerning the Content Standards in Mathematics and currently is a member of Texas Instruments California Advisory Board on K-12 education. He is the recipient of many awards and grants including the Alfred P. Sloan Fellowship, NSF grants, DARPA and Air Force Office of Scientific Research grants. He is the editor of several internationally respected mathematics journals in topology and algebra. More information about Professor Gunnar Carlsson can be found at http://math.stanford.edu/~gunnar/ Samad Hedayat Professor Samad Hedayat is a UIC Distinguished Professor at Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago (UIC).
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Gunnar Carlsson Professor, Department of Mathematics Stanford University
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David Donoho COMMENTARY 52 Cliﬀ Ord J
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John Gunnar Carlsson Epstein Department of Industrial And
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CV of Yuan YAO
CV of Yuan YAO Contact Hong Kong University of Science and Technology Phone: (852) 2358-7461 Information Department of Mathematics Fax: (852) 2358-1643 3430 Academic Building, Clear Water Bay, Kowloon E-mail: yuany@ust.hk Hong Kong SAR, P.R. China WWW: yao-lab.github.io Academic University of California at Berkeley, USA Qualifications Ph.D. Mathematics, December 2006 • Dissertation: A dynamic theory of learning: online learning and stochastic algorithms in Reproducing Kernel Hilbert Spaces • Committee: Stephen Smale (chair), Peter Bartlett, and Steve Evans. City University of Hong Kong, Hong Kong SAR, China M.Phil. Mathematics, June 2002 Harbin Institute of Technology, Harbin, China M.S. Control Engineering, July 1998 B.S. Control Engineering, July 1996 Academic Hong Kong University of Science and Technology, China Positions Department of Mathematics Department of Chemical and Biological Engineering (by courtesy) Department of Computer Science and Engineering Associate Professor Aug 2016 - present Peking (Beijing) University, China School of Mathematical Sciences Department of Probability and Statistics Associate Professor with Tenure July 2015 - present Professor of Statistics in the Hundred Talents Program1 July 2009 - present Stanford University, USA Department of Mathematics and Computer Science Postdoctoral Fellow August 2006 { August 2009 Awards and Hong Kong RGC General Research Fund, award 16303817 Grants Principal investigator Aug 2017 - Jul 2020 Social Choice, Crowdsourced Ranking, and Hodge Theory Tencent AI Lab, collaborative research award Principal investigator 2017 - Regularizations in Deep Learning Microsoft Research Asia, collaborative research award 1The Program was introduced 10 years ago by Peking University to attract overseas talents, in which I was appointed as Professor in the traditional Chinese academic ranking system.
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A Singer Construction in Motivic Homotopy Theory
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Equivariant Homotopy and Cohomology
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