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
15/07/26, Hội nghị, hội thảo:
Hình học tôpô và các chủ đề liên quan
13/10/26, Hội nghị, hội thảo:
International Workshop on Optimization, Variational Analysis, and Control Theory
09/11/26, Hội nghị, hội thảo:
Workshop on singularities and related topics (Conference in memory of Professor Lê Dũng Tráng)
Xuất bản mới
Le Thi Hong Hanh,
Dương Trọng Luyện,
Nguyễn Minh Trí,
Nontrivial Solutions to Boundary Value Problems for Semilinear $\Delta ^{\alpha ,\beta }_{\alpha _1,\beta _1}$-Differential Equations,
Analysis and PDE in Developing Countries, Trends in Mathematics (TM, volume 17) (2026) pp 27–35, Birkhäuser/Springer, Cham, 2026 ISBN: 978-3-032-14210-8; 978-3-032-14211-5
Adam Czornik,
Đoàn Thái Sơn,
Nguyễn Thị Thu Sương,
Pole Placement Theorem for Linear Measurable Time-Varying Control Systems with Single Input,
SIAM Journal on Control and Optimization, Vol. 64, Iss. 4 (2026)
Đinh Nho Hào,
Maxim Shishlenin,
Van Ba Cong,
Stable Numerical Solution to Multi-dimensional Nonlinear Inverse Heat Conduction Problems via Artificial Neural Networks,
Lobachevskii Journal of Mathematics, Volume 47, pages 1213–1232 (2026)