A ces BSTRACTS ABSTRACTS mailing offi MATHEMATICS and additional of Papers Presented to the Periodicals postage 2010 paid at Providence, RI American Mathematical Society SUBJECT CLASSIFICATION Volume 33, Number 4, Issue 170 Fall 2012 Compiled in the Editorial Offices of MATHEMATICAL REVIEWS and ZENTRALBLATT MATH 00 General 44 Integral transforms, operational calculus 01 History and biography 45 Integral equations Editorial Committee 03 Mathematical logic and foundations 46 Functional analysis 05 Combinatorics 47 Operator theory Robert J. Daverman, Chair Volume 33 • Number 4 Fall 2012 Volume 06 Order, lattices, ordered 49 Calculus of variations and optimal Georgia Benkart algebraic structures control; optimization 08 General algebraic systems 51 Geometry Michel L. Lapidus 11 Number theory 52 Convex and discrete geometry Matthew Miller 12 Field theory and polynomials 53 Differential geometry 13 Commutative rings and algebras 54 General topology Steven H. Weintraub 14 Algebraic geometry 55 Algebraic topology 15 Linear and multilinear algebra; 57 Manifolds and cell complexes matrix theory 58 Global analysis, analysis on manifolds 16 Associative rings and algebras 60 Probability theory and stochastic 17 Nonassociative rings and algebras processes Abstracts for 18 Category theory; homological 62 Statistics algebra 65 Numerical analysis Akron, October 20–21, 2012 ....................... 929 19 K-theory 68 Computer science 20 Group theory and generalizations 70 Mechanics of particles and systems Tucson, October 27–28, 2012 ..................... 996 22 Topological groups, Lie groups 74 Mechanics of deformable solids 26 Real functions 76 Fluid mechanics 28 Measure and integration 78 Optics, electromagnetic theory 30 Functions of a complex variable 80 Classical thermodynamics, heat transfer 31 Potential theory 81 Quantum theory 32 Several complex variables and 82 Statistical mechanics, structure of matter analytic spaces 83 Relativity and gravitational theory 33 Special functions 85 Astronomy and astrophysics 34 Ordinary differential equations 86 Geophysics 35 Partial differential equations 90 Operations research, mathematical 37 Dynamical systems and ergodic programming theory 91 Game theory, economics, social and 39 Difference and functional equations behavioral sciences 40 Sequences, series, summability 92 Biology and other natural sciences 41 Approximations and expansions 93 Systems theory; control 42 Fourier analysis 94 Information and communication, circuits 43 Abstract harmonic analysis 97 Mathematics education ISSN 0192-5857 Pages 929–1050 AMS Abstracts of Papers Presented to the AMS Abstracts of Papers Presented ISSN 0192-5857 American Mathematical Society 201 Charles Street, Providence, RI 02904-2294 USA GST No. R121892046 AMS License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use 128 Pages on 40 lb paper • Spine: 3/16" • Print in Black Ink • Trim 7" x 10" SUBMISSION INFORMATION ABSTRACTS PUBLISHED IN THIS JOURNAL are those submitted by authors who intend to present them at AMS meetings (see the front cover). 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POSTMASTER: Send address change notices to Abstracts of Papers Presented to the American Mathematical Society, 201 Charles Street, Providence, RI 02904-2294 USA. c 2012 by the American Mathematical Society. All rights reserved. Printed in the United States of America. ∞ This journal is printed on acid-free paper and falls within the guidelines established to ensure permanence and durability. License or copyright restrictions may apply to redistribution; see https://www.ams.org/journal-terms-of-use 10 9 8 7 6 5 4 3 2 1 16 15 14 13 12 PAPERS PRESENTED AT MEETINGS THIS CALENDAR lists meetings of the Society which have been approved by the Council at which papers may be presented. Programs of Annual Meetings appear in the Notices andontheAMSwebsite;programs for sectional meetings appear on the AMS Web pages in the Meetings & Conferences section, and are electronically archived in the Notices section on the AMS website. ABSTRACT ABSTRACT MEETING # DATE PLACE DEADLINE ISSUE 1086 January 9–12, 2013 San Diego, CA September 25 Vol 34, No. 1 1087 March 1–3, 2013 Oxford, MS December 4 Vol 34, No. 2 1088 April 6–7, 2013 Chestnut Hill, MA February 12 Vol 34, No. 2 1089 April 13–14, 2013 Boulder, CO February 19 Vol 34, No. 2 1090 April 27–28, 2013 Ames, IA March 5 Vol 34, No. 2 1091 June 27–30, 2013 Alba Iulia, Romania TBA None 1092 October 5–6, 2013 Louisville, KY August 13 Vol 33, No. 3 1093 October 12–13, 2013 Philadelphia, PA August 20 Vol 33, No. 3 1094 October 18–20, 2013 St. Louis, MO August 27 Vol 33, No. 4 1095 November 2–3, 2013 Riverside, CA September 10 Vol 33, No. 4 1096 January 15–18, 2014 Baltimore, MD TBA Vol 35, No. 1 AKRON, OH, October 20–21, 2012 Abstracts of the 1084th Meeting. 00 General 1084-00-157 Mikhail Belkin*, Computer Science and Engineering, 2015 Neil Ave, DL 395, Columbus, OH 43210, and Qichao Que, Yusu Wang and Xueyuan Zhou. Toward understanding complex spaces: graph Laplacians on manifolds with singularities and boundaries. Algorithms based on graph Laplacian have received considerable attention both in practical applications and theoretical analysis. Much of the existing work has been done under the assumption that the data is sampled from a manifold without boundaries. However, singularities and boundaries are an important aspect of the geometry of realistic data. Boundaries occur whenever the data has a constraint; while singularities appear when two different manifolds intersect or if a process undergoes a “phase transition”, changing non-smoothly as a function of a parameter. We consider the behavior of graph Laplacians at points at or near boundaries and two main types of singularities: intersections, wheremanifolds come together and sharp “edges”. We show that the behavior of graph Laplacian near these singularities is different from that in the interior of the manifolds. Unlike in the interior of the domain, where graph Laplacian converges to the Laplace-Beltrami operator, near singularities graph Laplacian tends to a first-order differential operator, with different scaling behavior. One implication is that while points near the singularities occupy only a small part of the total volume, the difference in scaling results in a large contribution to the total behavior. (Received August 30, 2012) 01 History and biography 1084-01-102 Michael Todd Edwards* ([email protected]), Department of Teacher Education, 401 McGuffey Hall, Oxford, OH 45056.