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Exploring the Invisible College: A Case Study of Singularity Theory in Mathematics

This research study delves into the intellectual structure and social processes of Singularity Theory research in mathematics, using methods such as author co-citation analysis, social network analysis, and ethnography of communication. It examines the role of collegiality and international research institutes in fostering invisible college activity, the co-authorship and collaboration patterns in Singularity Theory, and provides insights into the growth of knowledge within this field. The study concludes with recommendations for future research directions, including comparative studies with other communities and exploring alternative information use environments.

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Exploring the Invisible College: A Case Study of Singularity Theory in Mathematics

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  1. Revisiting the Invisible College:A Case Study of the Intellectual Structure and Social Process of Singularity Theory Research in Mathematics Alesia Zuccala University of Toronto

  2. Research Problem and Context • The structure versus social process problem concerning the invisible college (Lievrouw, 1990) • Why choose Singularity Theory for the case study?

  3. Invisible College Definition • An invisible college is a set of interacting scholars or scientists who share similar research interests concerning a subject specialty, who often produce publications relevant to this subject and who communicate both formally and informally with one another to work towards important goals within the subject even though they may belong to geographically distant research affiliates.

  4. Fig. 1.2. Structurationally informed value-added model for the study of scientific organizations.

  5. Research Methods • Author Co-citation Analysis • Social Network Analysis • Ethnography of Communication • All methods focus on relational systems and complement one another in an overlapping analysis

  6. Three Parts to the Research: 3) Collegiality and the International Research Institute’s Role in Fostering Invisible College Activity 1) The Intellectual Structure of Singularity Theory Invisible College 2) Co-authorship and Collaboration in Singularity Theory

  7. 63% connectivity Fig. 4.2. ACA map of 75 Singularity Theory authors (1974-2000).

  8. Fig. 4.5. National research groups or "schools" in Singularity Theory (1974-2000).

  9. Network density= .10 Fig. 5.1. Co-author map of 75 Singularity Theorists (1974-2000).

  10. Network density = .52 Fig. 6.1. Collegial map of 75 Singularity Theory authors (1970-2000).

  11. QAP Correlation Collegiality data: Co-citation data: Co-authorship data:

  12. Fig. 6.2. Isaac Newton Institute for Research in Mathematical Sciences

  13. ACA as an Evaluation Tool? Fig. 6.6. ACA-Social Network mapping of Workshop on Singularity Theory and Its Applications to Quantum Field Theory (1974-2000).

  14. Conclusions • Singularity Theory and the “branching model” of knowledge growth. • Author Co-citation Analysis in connection with the invisible college model ‘themes’ leads to an “aerial view” of a subject and a “ground level” exploration into a community’s social history.

  15. Future Directions • Comparative studies with other communities using the same invisible college model? • Further research with alternative Information Use Environments (e.g., Virtual Institute Networks)?

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