Extra Form
강연자 김병찬
소속 서울과학기술대학교
date 2015-04-02

To explain Ramanujan's integer partition function congruences, Dyson's rank and Andrews-Garvan's crank have been introduced. The generating functions for these two partition statistics are typical examples of mock Jacobi forms and Jacobi forms, and have been scorches of numerous researches in number theory and combinatorics. In particular, studying how their distributions differ is one of main themes in the theory of partitions. In this talk, we introduce recent results on their distributions with emphasizing on roles of q-series, combinatorial methods, and modular forms.

첨부 '1'
  1. Green’s function for initial-boundary value problem

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

  3. 07Apr
    by 김수현
    in 수학강연회

    On the distributions of partition ranks and cranks

  4. Q-curvature in conformal geometry

  5. Zeros of the derivatives of the Riemann zeta function

  6. Geometry, algebra and computation in moduli theory

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

  8. High dimensional nonlinear dynamics

  9. What is model theory?

  10. Essential dimension of simple algebras

  11. Restriction theorems for real and complex curves

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

  13. Deformation spaces of Kleinian groups and beyond

  14. Idempotents and topologies

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

  16. Existence of positive solutions for φ-Laplacian systems

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

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

  19. Random conformal geometry of Coulomb gas formalism

  20. Categorification of Donaldson-Thomas invariants

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