《Math Colloquium 第319期》Bernhard Schmidt 教授：哈达玛差集六十年的历程
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- 题目: 哈达玛差集六十年的历程
- 主讲人：Bernhard Schmidt 教授 @ Nanyang Technological University
- 时间：2026年10月22日 16:30-17:30
- 地点：M1001, College of Science Building
主讲人简介
Bernhard Schmidt is a Professor in the Division of Mathematical Sciences, School of Physical and Mathematical Sciences, at Nanyang Technological University, Singapore. He received his Diploma from Justus-Liebig-Universität Gießen in 1992, his PhD from Universität Augsburg in 1995, and his Habilitation from Augsburg in 2001, and was a postdoctoral researcher at Caltech in 1998–99. He joined NTU in 2005 and has been a full Professor since 2018. His research is in algebraic design theory, in particular difference sets, Hadamard and weighing matrices, finite geometry, and character sums over cyclotomic fields; he is known for the field descent method for cyclotomic integers. He received the Kirkman Medal of the Institute of Combinatorics and its Applications in 1997 and serves on the editorial board of Designs, Codes, and Cryptography.
讲座简介
A Hadamard matrix is a square matrix with entries ±1 whose rows are mutually orthogonal. Such matrices play a central role in combinatorics, coding theory, and signal processing, and whether they exist for every order divisible by 4 is a famous open problem. Hadamard difference sets are their group-theoretic counterpart: subsets D of a group G of order 4u² such that every non-identity element of G arises exactly u² − u times as a “difference” dd′⁻¹ with d, d′ ∈ D. They yield Hadamard matrices with G as a symmetry group. The question of which groups contain them has driven six decades of research linking combinatorics, algebraic number theory, and finite geometry. Since the 1960s, this search has produced a series of beautiful constructions, together with strong restrictions on which groups can contain Hadamard difference sets. I will retrace these developments, from the pioneering work of Menon and Turyn to surprising results in 2026. The talk is aimed at a general mathematical audience; no background in design theory is assumed.
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