Extra Form
강연자 지운식
소속 충북대학교
date 2011-04-14
We start with the famous Heisenberg uncertainty principle to give the idea of the probability in quantum mechanics. The Heisenberg uncertainty principle states by precise inequalities that the product of uncertainties of two physical quantities, such as momentum and position (operators), must be greater than certain (strictly positive) constant, which means that if we know one of the quantities more precisely, then we know the other one less precisely. Therefore, in quantum mechanics, predictions should be probabilistic, not deterministic, and then position and momentum should be considered as random variables to measure their probabilities.
In mathematical framework, the noncommutative probability is another name of quantum probability, and a quantum probability space consists of an -algebra of operators on a Hilbert space and a state (normalized positive linear functional) on the operator algebra. We study the basic notions in quantum probability theory comparing with the basic notions in classical (commutative) probability theory, and we also study the fundamental theory of quantum stochastic calculus motivated by the classical stochastic calculus.
Finally, we discuss several applications with future prospects of classical and quantum probability theory.
첨부 '1'
  1. An introduction to hyperplane arrangements

  2. Analysis and computations of stochastic optimal control problems for stochastic PDEs

  3. Analytic torsion and mirror symmetry

  4. Anomalous diffusions and fractional order differential equations

  5. Arithmetic of elliptic curves

  6. Averaging formula for Nielsen numbers

  7. Birational Geometry of varieties with effective anti-canonical divisors

  8. Brownian motion and energy minimizing measure in negative curvature

  9. Brownian motion with darning and conformal mappings

  10. Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras

  11. Categorification of Donaldson-Thomas invariants

  12. Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds

  13. Circular maximal functions on the Heisenberg group

  14. Class field theory for 3-dimensional foliated dynamical systems

  15. 07Nov
    by Editor
    in 수학강연회

    Classical and Quantum Probability Theory

  16. Cloaking via Change of Variables

  17. Codimension Three Conjecture

  18. Combinatorial Laplacians on Acyclic Complexes

  19. Compressible viscous Navier-Stokes flows: Corner singularity, regularity

  20. Conformal field theory and noncommutative geometry

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