The Ordered Multiplicity Inverse Eigenvalue Sequence Problem, Powers Of Graphs, And More!
Người báo cáo: Franklin H. J. Kenter (U.S. Naval Academy)
Time: 9:30 -- 11: 00, October 01, 2025
Venue: Room 612, A6, Institute of Mathematics-VAST
Abstract: Given a matrix pattern, one may ask: "What sets of eigenvalues are possible over all such matrices?'' This problem is very hard! A mild relaxation of this question considers the multiplicity sequence instead of the exact eigenvalues themselves. For instance, ``Given an $n times n$ matrix pattern and an ordered partition $(m_1, ldots, m_q)$ of $n$, is there a matrix with that pattern where the $i$-th distinct eigenvalue has multiplicity $m_i$?'' This is known as the ``ordered multiplicity inverse eigenvalue sequence problem''. Recent work has solved this problem for all symmetric matrix patterns up to size $6 times 6$.
In this talk, we develop methods using combinatorial optimization on networks to approach this otherwise linear-algebraic problem. We apply many different ``zero forcing'' techniques to simultaneously bound on sums of various multiplicities. Not only can we verify the result above in a more straight-forward manner, but we apply our techniques to more domains including skew-symmetric matrices, nonnegative matrices, among others. This is joint work with Jephian C.-H. Lin (National Sun Yat-sen University, Taiwan).
Tin tức nổi bật
Hoạt động tuần
Hội thảo sắp diễn ra
12/10/26, Hội nghị, hội thảo:
International School and Conference on Differential Equations
13/10/26, Hội nghị, hội thảo:
International Workshop on Optimization, Variational Analysis, and Control Theory
27/10/26, Hội nghị, hội thảo:
Phương trình vi phân và đạo hàm riêng trong Vật lý và Toán học
09/11/26, Hội nghị, hội thảo:
Workshop on singularities and related topics (Conference in memory of Professor Lê Dũng Tráng)
Xuất bản mới
Đỗ Duy Hiếu,
Block-pair edge community detection in bipartite networks via an adaptive spectral-modularity framework,
Computational and Mathematical Organization Theory, Volume 32, article number 31 (2026)
Nguyễn Thị Vân Hằng,
Felipe Lara,
Nguyễn Đông Yên,
Discontinuous strongly quasiconvex functions,
Journal of Optimization Theory and Applications 210 (2026), Paper No. 40, 18 pp.
Đoàn Thái Sơn,
Generic properties of the Lyapunov spectrum of compact operator cocycles on Hilbert spaces,
Journal of Mathematical Analysis and Applications, Article: 131103 Volume: Volume 566, Issue 2 (2027)