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siam.org

Society for Industrial and Applied Mathematics (SIAM) is an international community of 14,000+ individual members. Almost 500 academic, manufacturing, research and development, service and consulting organizations, government, and military organizations worldwide are institutional members. SIAM was incorporated in 1952 as a nonprofit organization to convey useful mathematical knowledge to other professionals who could implement mathematical theory for practical, industrial, or scientific use.

ima.umn.edu

Earth sciences student Elise Palecek will compete internationally this winter in Alpine Luge.

math.psu.edu

penn state eberly college of science ecos dean tracy langkilde

numerics.kaust.edu.sa

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nonlinearstudies.com

nonlinear studies international journal

projecteuclid.org

In this paper we study the relative Chow and $K$-stability of toric manifolds. First, we give a criterion for relative $K$-stability and instability of toric Fano manifolds in the toric sense. The reduction of relative Chow stability on toric manifolds will be investigated using the Hibert-Mumford criterion in two ways. One is to consider the maximal torus action and its weight polytope. We obtain a reduction by the strategy of Ono [34], which fits into the relative GIT stability detected by Székelyhidi. The other way relies on $\mathbb{C}^*$-actions and Chow weights associated to toric degenerations following Donaldson and Ross-Thomas [13, 36]. In the end, we determine the relative $K$-stability of all toric Fano threefolds and present counter-examples which are relatively $K$-stable in the toric sense but which are asymptotically relatively Chow unstable.