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Extra Form
강연자 국웅
소속 서울대학교
date 2013-10-10
The main topic of the talk is a determinantal formula for high dimensional tree numbers of acyclic complexes via combinatorial Laplace operators . This result is a generalization of Temperley's tree number formula for graphs, motivated by a simple (but not well-known) observation that Temperley's method uses combinatorial Laplacian  in dimension zero. The talk will begin with a brief survey of properties and applications of including network theory and topological data analysis. Towards the end, we will discuss a logarithmic version of the main formula of the talk and demonstrate intriguing applications of its generating function to various complexes that arise naturally in combinatorics.
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첨부 '1'
  1. Existence of positive solutions for φ-Laplacian systems

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

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

  4. Random conformal geometry of Coulomb gas formalism

  5. Categorification of Donaldson-Thomas invariants

  6. Noncommutative Surfaces

  7. The Shape of Data

  8. Topological Mapping of Point Cloud Data

  9. Structures on Persistence Barcodes and Generalized Persistence

  10. Persistent Homology

  11. Topological aspects in the theory of aperiodic solids and tiling spaces

  12. Subgroups of Mapping Class Groups

  13. Irreducible Plane Curve Singularities

  14. Analytic torsion and mirror symmetry

  15. Fefferman's program and Green functions in conformal geometry

  16. 최고과학기술인상수상 기념강연: On the wild world of 4-manifolds

  17. 정년퇴임 기념강연: Volume Conjecture

  18. Queer Lie Superalgebras

  19. Regularization by noise in nonlinear evolution equations

  20. A New Approach to Discrete Logarithm with Auxiliary Inputs

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