Cristian S. Calude氏、Elena Calude氏 講演会のお知らせ
参加申込: 不要
[ 講演内容 ]
◆15時00分~16時00分
講演題目: The complexity of mathematical problems
講演者: Cristian S. Calude (University of Auckland, NZ) and
Elena Calude (Massey University, NZ)
講演要旨:
Evaluating (or even guessing) the degree of complexity of an open
problem, conjecture or mathematically proven statement is not an
easy task not only for beginners, but also for the most experienced
mathematicians.
Is there a (uniform) method to evaluate, in some objective way,
the difficulty of a mathematical statement or problem? The question
is not trivial because mathematical problems can be so diverse.
But, is there any indication that all, or most, or even a large part
of mathematical problems have a kind of "commonality" allowing a
uniform evaluation of their complexity? How could one compare a
problem in number theory with a problem in complex analysis, a
problem in algebraic topology or a theorem in dynamical systems?
Surprisingly enough, such "commonalities" do exist for many
mathematical problems. One of them is based on the possibility
of expressing the problem in terms of (very) simple programs
reducible to a (natural) question in theoretical computer science,
the so-called "halting problem". A more general "commonality"
can be discovered using the inductive type of computation, a
computation more general the Turing computability. As a consequence,
uniform approaches for evaluating the complexity of a large class
of mathematical problems/conjectures/statements can be, and
have been, developed. This talks reviews current progress and
some open problems.
◆16時30分~17時30分
講演題目: The Kochen-Specker theorem and quantum randomness
講演者: Cristian S. Calude (University of Auckland, NZ)
講演要旨:
The Kochen-Specker theorem shows the impossibility for a hidden
variable theory to consistently assign values to certain (finite) sets
of observables in a way that is noncontextual and consistent with
quantum mechanics. If we require noncontextuality, the consequence
is that many observables must not have pre-existing definite values.
However, the Kochen-Specker theorem does not allow one to
determine which observables must be value indefinite. In this talk we
present an improvement on the Kochen-Specker theorem which
allows one to actually locate observables which are provably value
indefinite. Various technical and subtle aspects relating to this formal
proof and its connection to quantum mechanics are discussed. This
result is then utilized for the proposal and certification of a dichotomic
quantum random number generator operating in a three-dimensional
Hilbert space.
(通訳なし)
連絡先:中央大学研究開発機構准教授 只木孝太郎