John Harer | Scholars@Duke

John Harer
Professor of Mathematics

Professor Harer's primary research is in the use of geometric, combinatorial and computational techniques to study a variety of problems in data analysis, shape recognition, image segmentation, tracking, cyber security, ioT, biological networks and gene expression.

Current Appointments & Affiliations

Professor of Mathematics, Mathematics, Trinity College of Arts & Sciences 1993

Contact Information

109 Physic Bldg, Durham, NC 27708
Box 90320, Durham, NC 27708-0034
(919) 660-2845
http://cms.math.duke.edu/harer/?q=home

Background
Education, Training, & Certifications
- Ph.D., University of California at Berkeley 1979
- B.A., Haverford College 1974
Duke Appointment History
- Professor in the Department of Electrical and Computer Engineering, Electrical and Computer Engineering, Pratt School of Engineering 2011 - 2016
- Professor in the Department of Computer Science, Computer Science, Trinity College of Arts & Sciences 2001 - 2014
- Director of the PhD Program in Computational Biology and Bioinformatics, University Institutes and Centers, Institutes and Provost's Academic Units 2010 - 2012
- Vice Provost for Academic Affairs, Duke University 1999 - 2005
- Chair, Department of Mathematics, Mathematics, Trinity College of Arts & Sciences 1994 - 1999
- Visiting Professor, Mathematics, Trinity College of Arts & Sciences 1992 - 1993
Research
Selected Grants
- Geometric and Topological Methods for Multi-Modal Data Analysis and Fusion awarded by Air Force Office of Scientific Research 2018 - 2021
- BIGDATA: F: DKA: CSD: Topological Data Analysis and Machine-Learning with Community-Accepted Features awarded by National Science Foundation 2014 - 2019
- Quantifying Complex Spatiotemporal Systems 2016 - 2018
- EMSW21-RTG: Geometric, Topological awarded by National Science Foundation 2011 - 2018
- ATD: Online Multiscale Algorithms for Geometric Density Estimation in High-Dimensions and Persistent Homology of Data fo awarded by National Science Foundation 2012 - 2017
- Foundation of Information Systems awarded by Johns Hopkins University 2012 - 2017
- Analysis of High Dimensional Complex Spatio-Temporal Data awarded by Defense Advanced Research Projects Agency 2015 - 2016
- Inferring Network Controls awarded by Air Force Office of Scientific Research 2010 - 2015
- A Multidimensional Imaging Platform to Analyze Crop Root System Dynamics in Response to Changing Environments 2011 - 2013
- GEPR: Genome-wide analysis of root traits awarded by National Science Foundation 2008 - 2012
- Duke on Network Security awarded by Air Force Office of Scientific Research 2010 - 2011
- Doctoral Program in Management and Analysis of Large Data Acquired from Sensors awarded by Department of Education 2007 - 2011
- TRPGR Genomic Approaches to Identify Genes for Root System Architecture Traits awarded by National Science Foundation 2006 - 2008
- Distributed multiscale geometric processing on real-time sensor networks on radiation fields awarded by National Science Foundation 2002 - 2004
- Persistence, Combinatorial Morse Functions awarded by National Science Foundation 2001 - 2003
- (98-0205) Computational Geometry, Robotics, and Geographic Information Systems awarded by National Science Foundation 1998 - 2000
- (96-1030) The Moduli Space of Curves; Its Level-n Covers and Torelli Space awarded by National Science Foundation 1994 - 1997
- (94-0252) The Moduli Space of Curves, its Level n Covers and Torelli Space awarded by National Science Foundation 1994 - 1996
- (95-0888) The Moduli Space of Curves, its Level-n Covers and Torelli Space awarded by National Science Foundation 1994 - 1996
- (93-0786) Mathematical Sciences Mapping Class Group & Invariants of 3-Manifolds awarded by National Science Foundation 1992 - 1994
- (92-0802) Mapping Class Group and Invariants of 3-Manifolds awarded by National Science Foundation 1992 - 1994
Industry Relationships
- Geometric Data Analytics
- Mimetics LLC
Publications & Artistic Works
Selected Publications
- Books
  - Edelsbrunner, Herbert, and John Harer. Computational Topology - an Introduction.. American Mathematical Society, 2010.
- Academic Articles
  - Bendich, P., E. Gasparovic, J. Harer, and C. J. Tralie. “Scaffoldings and Spines: Organizing High-Dimensional Data Using Cover Trees, Local Principal Component Analysis, and Persistent Homology” 13 (January 1, 2018): 93–114. https://doi.org/10.1007/978-3-319-89593-2_6.
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  - Hughes, Michael E., Katherine C. Abruzzi, Ravi Allada, Ron Anafi, Alaaddin Bulak Arpat, Gad Asher, Pierre Baldi, et al. “Guidelines for Genome-Scale Analysis of Biological Rhythms..” Journal of Biological Rhythms 32, no. 5 (October 2017): 380–93. https://doi.org/10.1177/0748730417728663.
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  - Bendich, P., S. P. Chin, J. Clark, J. DeSena, J. Harer, E. Munch, A. Newman, et al. “Topological and statistical behavior classifiers for tracking applications.” Ieee Transactions on Aerospace and Electronic Systems 52, no. 6 (December 1, 2016): 2644–61. https://doi.org/10.1109/TAES.2016.160405.
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  - McGoff, Kevin A., Xin Guo, Anastasia Deckard, Christina M. Kelliher, Adam R. Leman, Lauren J. Francey, John B. Hogenesch, Steven B. Haase, and John L. Harer. “The Local Edge Machine: inference of dynamic models of gene regulation..” Genome Biology 17, no. 1 (October 19, 2016). https://doi.org/10.1186/s13059-016-1076-z.
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  - Perea, Jose A., Anastasia Deckard, Steve B. Haase, and John Harer. “SW1PerS: Sliding windows and 1-persistence scoring; discovering periodicity in gene expression time series data..” Bmc Bioinformatics 16 (August 16, 2015). https://doi.org/10.1186/s12859-015-0645-6.
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  - Perea, J. A., and J. Harer. “Sliding Windows and Persistence: An Application of Topological Methods to Signal Analysis.” Foundations of Computational Mathematics 15, no. 3 (June 27, 2015): 799–838. https://doi.org/10.1007/s10208-014-9206-z.
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  - Munch, E., K. Turner, P. Bendich, S. Mukherjee, J. Mattingly, and J. Harer. “Probabilistic Fréchet means for time varying persistence diagrams.” Electronic Journal of Statistics 9 (January 1, 2015): 1173–1204. https://doi.org/10.1214/15-EJS1030.
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  - Farr, Robert S., John L. Harer, and Thomas M. A. Fink. “Easily repairable networks: reconnecting nodes after damage..” Physical Review Letters 113, no. 13 (September 26, 2014). https://doi.org/10.1103/physrevlett.113.138701.
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  - Bristow, Sara L., Adam R. Leman, Laura A. Simmons Kovacs, Anastasia Deckard, John Harer, and Steven B. Haase. “Checkpoints couple transcription network oscillator dynamics to cell-cycle progression..” Genome Biology 15, no. 9 (September 5, 2014). https://doi.org/10.1186/s13059-014-0446-7.
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  - Turner, K., Y. Mileyko, S. Mukherjee, and J. Harer. “Fréchet Means for Distributions of Persistence Diagrams.” Discrete and Computational Geometry 52, no. 1 (January 1, 2014): 44–70. https://doi.org/10.1007/s00454-014-9604-7.
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  - Turner, K., Y. Mileyko, S. Mukherjee, and J. Harer. “Fréchet Means for Distributions of Persistence Diagrams.” Discrete & Computational Geometry, 2014.
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  - Deckard, Anastasia, Ron C. Anafi, John B. Hogenesch, Steven B. Haase, and John Harer. “Design and analysis of large-scale biological rhythm studies: a comparison of algorithms for detecting periodic signals in biological data..” Bioinformatics (Oxford, England) 29, no. 24 (December 2013): 3174–80. https://doi.org/10.1093/bioinformatics/btt541.
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  - Topp, Christopher N., Anjali S. Iyer-Pascuzzi, Jill T. Anderson, Cheng-Ruei Lee, Paul R. Zurek, Olga Symonova, Ying Zheng, et al. “3D phenotyping and quantitative trait locus mapping identify core regions of the rice genome controlling root architecture..” Proceedings of the National Academy of Sciences of the United States of America 110, no. 18 (April 11, 2013): E1695–1704. https://doi.org/10.1073/pnas.1304354110.
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  - Topp, H. F., H. F. CN, A. S. Iyer-Pascuzzi, J. T. Anderson, C. -. R. Lee, P. R. Zurek, O. Symonova, et al. “3-dimensional phenotyping of growing root systems and QTL mapping identifies core regions of the rice genome controlling root architecture.” Pnas 110 (2013): E1695-1704.
  - Munch, E., M. Shapiro, and J. Harer. “Failure filtrations for fenced sensor networks.” International Journal of Robotics Research 31, no. 9 (August 1, 2012): 1044–56. https://doi.org/10.1177/0278364912451671.
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  - Bendich, Paul, Jacob Harer, and John Harer. “Persistent Homology Enhanced Dimension Reduction.” Foundations of Computational Mathematics, 2012.
  - Galkovskyi, Taras, Yuriy Mileyko, Alexander Bucksch, Brad Moore, Olga Symonova, Charles A. Price, Christopher N. Topp, et al. “GiA Roots: software for the high throughput analysis of plant root system architecture..” Bmc Plant Biology 12 (January 2012). https://doi.org/10.1186/1471-2229-12-116.
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  - Michael Jenista, W. A. “Realizing Boolean Dynamics in Switching Networks.” Siam Journal of Applied Dynamical Systems, 2012.
  - Bendich, P., T. Galkovskyi, and J. Harer. “Improving homology estimates with random walks.” Inverse Problems 27, no. 12 (December 1, 2011). https://doi.org/10.1088/0266-5611/27/12/124002.
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  - Mileyko, Y., S. Mukherjee, and J. Harer. “Probability measures on the space of persistence diagrams.” Inverse Problems 27, no. 12 (December 1, 2011). https://doi.org/10.1088/0266-5611/27/12/124007.
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  - Bendich, P., and J. Harer. “Persistent Intersection Homology.” Foundations of Computational Mathematics 11, no. 3 (June 1, 2011): 305–36. https://doi.org/10.1007/s10208-010-9081-1.
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  - Bini, Gilberto, and John Harer. “Euler characteristics of moduli spaces of curves.” Journal of the European Mathematical Society, 2011, 487–512. https://doi.org/10.4171/jems/259.
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  - Cohen-Steiner, D., H. Edelsbrunner, J. Harer, and Y. Mileyko. “Lipschitz functions have Lp-stable persistence.” Foundations of Computational Mathematics 10, no. 2 (April 1, 2010): 127–39. https://doi.org/10.1007/s10208-010-9060-6.
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  - Iyer-Pascuzzi, Anjali S., Olga Symonova, Yuriy Mileyko, Yueling Hao, Heather Belcher, John Harer, Joshua S. Weitz, and Philip N. Benfey. “Imaging and analysis platform for automatic phenotyping and trait ranking of plant root systems..” Plant Physiology 152, no. 3 (March 2010): 1148–57. https://doi.org/10.1104/pp.109.150748.
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  - Edelsbrunner, H., and J. Harer. “The persistent Morse complex segmentation of a 3-manifold.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 5903 LNCS (December 1, 2009): 36–50. https://doi.org/10.1007/978-3-642-10470-1_4.
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  - Cohen-Steiner, D., H. Edelsbrunner, J. Harer, and D. Morozov. “Persistent homology for kernels, images, and cokernels.” Proceedings of the Annual Acm Siam Symposium on Discrete Algorithms, September 21, 2009, 1011–20.
  - Cohen-Steiner, D., H. Edelsbrunner, and J. Harer. “Extending persistence using poincaré and lefschetz duality (Foundations of Computational Mathematics DOI 10.1007/s10208-008-9027-z).” Foundations of Computational Mathematics 9, no. 1 (February 1, 2009): 133–34. https://doi.org/10.1007/s10208-008-9038-9.
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  - Cohen-Steiner, D., H. Edelsbrunner, and J. Harer. “Extending persistence using poincaré and lefschetz duality.” Foundations of Computational Mathematics 9, no. 1 (January 1, 2009): 79–103. https://doi.org/10.1007/s10208-008-9027-z.
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  - Fink, T., S. Ahnert, R. Bar On, and J. Harer. “Exact dynamics of Boolean networks with connectivity one.” Prl, 2009.
  - Edelsbrunner, H., J. Harer, and A. K. Patel. “Reeb spaces of piecewise linear mappings.” Proceedings of the Annual Symposium on Computational Geometry, December 12, 2008, 242–50. https://doi.org/10.1145/1377676.1377720.
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  - Edelsbrunner, H., J. Harer, A. Mascarenhas, V. Pascucci, and J. Snoeyink. “Time-varying Reeb graphs for continuous space-time data.” Computational Geometry: Theory and Applications 41, no. 3 (November 1, 2008): 149–66. https://doi.org/10.1016/j.comgeo.2007.11.001.
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  - Attali, D., H. Edelsbrunner, J. Harer, and Y. Mileyko. “Alpha-beta witness complexes.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) 4619 LNCS (December 1, 2007): 386–97.
  - Bendice, P., D. Cohen-Steiner, H. Edelsbrunner, J. Harer, and D. Morozov. “Inferring local homology from sampled stratified spaces.” Proceedings Annual Ieee Symposium on Foundations of Computer Science, Focs, December 1, 2007, 536–46. https://doi.org/10.1109/FOCS.2007.4389523.
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  - Cohen-Steiner, D., H. Edelsbrunner, and J. Harer. “Stability of persistence diagrams.” Discrete and Computational Geometry 37, no. 1 (January 1, 2007): 103–20. https://doi.org/10.1007/s00454-006-1276-5.
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  - Agarwal, P. K., H. Edelsbrunner, J. Harer, and Y. Wang. “Extreme elevation on a 2-manifold.” Discrete and Computational Geometry 36, no. 4 (January 1, 2006): 553–72. https://doi.org/10.1007/s00454-006-1265-8.
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  - Cohen-Steiner, D., H. Edelsbrunner, and J. Harer. “Stability of persistence diagrams.” Proceedings of the Annual Symposium on Computational Geometry, December 1, 2005, 263–71. https://doi.org/10.1145/1064092.1064133.
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  - Edelsbrunner, H., J. Harer, V. Natarajan, and V. Pascucci. “Local and global comparison of continuous functions.” Ieee Visualization 2004 Proceedings, Vis 2004, December 1, 2004, 275–80.
  - Agarwal, P. K., H. Edelsbrunner, J. Harer, and Y. Wang. “Extreme elevation on a 2-manifold.” Proceedings of the Annual Symposium on Computational Geometry, September 29, 2004, 357–65.
  - Edelsbrunner, H., J. Harer, A. Mascarenhas, and V. Pascucci. “Time-varying Reeb graphs for continuous space-time data.” Proceedings of the Annual Symposium on Computational Geometry, September 29, 2004, 366–72.
  - Cole-McLaughlin, K., H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. “Loops in Reeb graphs of 2-manifolds.” Discrete and Computational Geometry 32, no. 2 (January 1, 2004): 231–44. https://doi.org/10.1007/s00454-004-1122-6.
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  - Collins, A. D., P. K. Agarwal, and J. L. Harer. “HPRM: A hierarchical PRM.” Proceedings Ieee International Conference on Robotics and Automation 3 (December 9, 2003): 4433–38.
  - Cole-McLaughlin, K., H. Edelsbrunner, J. Harer, V. Natarajan, and V. Pascucci. “Loops in Reeb graphs of 2-manifolds.” Proceedings of the Annual Symposium on Computational Geometry, July 28, 2003, 344–50.
  - Edelsbrunner, H., J. Harer, V. Natarajan, and V. Pascucci. “Morse-Smale complexes for piecewise linear 3-manifolds.” Proceedings of the Annual Symposium on Computational Geometry, July 28, 2003, 361–70.
  - Edelsbrunner, H., J. Harer, and A. Zomorodian. “Hierarchical Morse-Smale complexes for piecewise linear 2-manifolds.” Discrete and Computational Geometry 30, no. 1 (January 1, 2003): 87–107. https://doi.org/10.1007/s00454-003-2926-5.
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  - Goulden, I. P., J. L. Harer, and D. M. Jackson. “A geometric parametrization for the virtual euler characteristics of the moduli spaces of real and complex algebraic curves.” Transactions of the American Mathematical Society 353, no. 11 (December 1, 2001): 4405–27.
  - Agarwal, P. K., A. D. Collins, and J. L. Harer. “Minimal trap design.” Proceedings Ieee International Conference on Robotics and Automation 3 (January 1, 2001): 2243–48. https://doi.org/10.1109/ROBOT.2001.932956.
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  - Edelsbrunner, H., J. Harer, and A. Zomorodian. “Hierarchical Morse complexes for piecewise linear 2-manifolds.” Proceedings of the Annual Symposium on Computational Geometry, January 1, 2001, 70–79.
  - Bern, Marshall W., David Eppstein, Pankaj K. Agarwal, Nina Amenta, L Paul Chew, Tamal K. Dey, David P. Dobkin, et al. “Emerging Challenges in Computational Topology.” Corr cs.CG/9909001 (1999).
  - Harer, J. “The third homology group of the moduli space of curves.” Duke Mathematical Journal 63, no. 1 (January 1, 1991): 25–55. https://doi.org/10.1215/S0012-7094-91-06302-7.
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  - Harer, J. L. “Stability of the homology of the moduli spaces of Riemann surfaces with spin structure.” Mathematische Annalen 287, no. 1 (March 1, 1990): 323–34. https://doi.org/10.1007/BF01446896.
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  - Harer, J., and D. Zagier. “The Euler characteristic of the moduli space of curves.” Inventiones Mathematicae 85, no. 3 (October 1, 1986): 457–85. https://doi.org/10.1007/BF01390325.
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  - HARER, J., A. KAS, and R. KIRBY. “HANDLEBODY STRUCTURES FOR COMPLEX-SURFACES.” Memoirs of the American Mathematical Society 62, no. 350 (July 1986): 1–102.
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  - Harer, J. L. “The virtual cohomological dimension of the mapping class group of an orientable surface.” Inventiones Mathematicae 84, no. 1 (February 1, 1986): 157–76. https://doi.org/10.1007/BF01388737.
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  - Harer, J. “The second homology group of the mapping class group of an orientable surface.” Inventiones Mathematicae 72, no. 2 (June 1, 1983): 221–39. https://doi.org/10.1007/BF01389321.
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  - Harer, John. “Representing elements of π1M3 by fibred knots.” Mathematical Proceedings of the Cambridge Philosophical Society 92, no. 1 (July 1982): 133–38. https://doi.org/10.1017/s030500410005979x.
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  - Harer, J. “How to construct all fibered knots and links.” Topology 21, no. 3 (January 1, 1982): 263–80. https://doi.org/10.1016/0040-9383(82)90009-X.
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  - Casson, A. J., and J. L. Harer. “Some homology lens spaces which bound rational homology balls.” Pacific Journal of Mathematics 96, no. 1 (January 1, 1981): 23–36. https://doi.org/10.2140/pjm.1981.96.23.
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  - Harer, J. “On handlebody structures for hypersurfaces in ℂ³ and ℂP³.” Mathematische Annalen 238, no. 1 (February 1, 1978): 51–58. https://doi.org/10.1007/BF01351453.
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- Conference Papers
  - Tralie, C. J., P. Bendich, and J. Harer. “Multi-Scale Geometric Summaries for Similarity-Based Sensor Fusion.” In Ieee Aerospace Conference Proceedings, Vol. 2019-March, 2019. https://doi.org/10.1109/AERO.2019.8741399.
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  - Garagić, D., J. Peskoe, F. Liu, M. S. Claffey, P. Bendich, J. Hineman, N. Borggren, J. Harer, P. Zulch, and B. J. Rhodes. “Upstream fusion of multiple sensing modalities using machine learning and topological analysis: An initial exploration.” In Ieee Aerospace Conference Proceedings, 2018-March:1–8, 2018. https://doi.org/10.1109/AERO.2018.8396737.
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  - Tralie, C. J., A. Smith, N. Borggren, J. Hineman, P. Bendich, P. Zulch, and J. Harer. “Geometric cross-modal comparison of heterogeneous sensor data.” In Ieee Aerospace Conference Proceedings, 2018-March:1–10, 2018. https://doi.org/10.1109/AERO.2018.8396789.
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  - Bendich, P., E. Gasparovic, J. Harer, and C. Tralie. “Geometric models for musical audio data.” In Leibniz International Proceedings in Informatics, Lipics, 51:65.1-65.5, 2016. https://doi.org/10.4230/LIPIcs.SoCG.2016.65.
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  - Bendich, P., E. Gasparovic, J. Harer, and C. Tralie. “Geometric Models for Musical Audio Data.” In Proceedings of the 32st International Symposium on Computational Geometry (Socg), 2016.
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  - Bendich, P., E. Gasparovic, J. Harer, R. Izmailov, and L. Ness. “Multi-scale local shape analysis and feature selection in machine learning applications.” In Proceedings of the International Joint Conference on Neural Networks, Vol. 2015-September, 2015. https://doi.org/10.1109/IJCNN.2015.7280428.
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  - Rouse, D., A. Watkins, D. Porter, J. Harer, P. Bendich, N. Strawn, E. Munch, et al. “Feature-aided multiple hypothesis tracking using topological and statistical behavior classifiers.” In Proceedings of Spie the International Society for Optical Engineering, Vol. 9474, 2015. https://doi.org/10.1117/12.2179555.
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  - Edelsbrunner, Herbert, and John Harer. “Persistent homology - a survey.” In Surveys on Discrete and Computational Geometry: Twenty Years Later, edited by J. E. Goodman, J. Pach, and R. Pollack, 453:257-+. AMER MATHEMATICAL SOC, 2008.
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  - Bendich, Paul, David Cohen-Steiner, Herbert Edelsbrunner, John Harer, and Dmitriy Morozov. “Inferring Local Homology from Sampled Stratified Spaces.” In 48th Annual Ieee Symposium on Foundations of Computer Science (Focs’07). IEEE, 2007. https://doi.org/10.1109/focs.2007.45.
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  - Czumaj, Artur, and Christian Sohler. “Testing Expansion in Bounded-Degree Graphs.” In 48th Annual Ieee Symposium on Foundations of Computer Science (Focs’07). IEEE, 2007. https://doi.org/10.1109/focs.2007.33.
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Teaching & Mentoring
Recent Courses
- MATH 412: Topological Data Analysis 2019
- MATH 713: Topological Data Analysis 2019
- MATH 494: Research Independent Study 2018
Scholarly, Clinical, & Service Activities
Presentations & Appearances
Outreach & Engaged Scholarship
- Bass Connections Faculty Team Member. Data+. June 2016 - July 2016 2016
Service to the Profession
Service to Duke

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Education, Training, & Certifications

Duke Appointment History

Selected Grants

Industry Relationships

Selected Publications

Books

Academic Articles

Conference Papers

Recent Courses

Presentations & Appearances

Outreach & Engaged Scholarship

Service to the Profession

Service to Duke