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Extra Form
Lecturer Gunnar E. Carlsson
Dept. Stanford University
date Mar 27, 2014

Creating information and knowledge from large and complex data sets is one the fundamental intellectual challenges currently being faced by the mathematical sciences. One approach to this problem comes from the mathematical subdiscipline called topology, which is the study of shape and of its higher dimensional analogues. This subject has thrived as a field within pure mathematics, but the last fifteen years has seen the development of topological methods for studying data sets, which are modeled as point clouds or finite metric spaces. I will survey this work, with examples.


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  1. The classification of fusion categories and operator algebras

  2. Green’s function for initial-boundary value problem

  3. Mechanization of proof: from 4-Color theorem to compiler verification

  4. On the distributions of partition ranks and cranks

  5. Q-curvature in conformal geometry

  6. Zeros of the derivatives of the Riemann zeta function

  7. Geometry, algebra and computation in moduli theory

  8. Gromov-Witten-Floer theory and Lagrangian intersections in symplectic topology

  9. High dimensional nonlinear dynamics

  10. What is model theory?

  11. Essential dimension of simple algebras

  12. Restriction theorems for real and complex curves

  13. Recommendation system and matrix completion: SVD and its applications (학부생을 위한 강연)

  14. Deformation spaces of Kleinian groups and beyond

  15. Idempotents and topologies

  16. Recent progress on the Brascamp-Lieb inequality and applications

  17. Existence of positive solutions for φ-Laplacian systems

  18. Riemann-Hilbert correspondence for irregular holonomic D-modules

  19. Normal form reduction for unconditional well-posedness of canonical dispersive equations

  20. Random conformal geometry of Coulomb gas formalism

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