»ã±¨±êÌâ (Title)£ºÀëÉ¢»·ÃæÌصãÖµµÄ¶à³ÁÐÔ£¨Eigenvalue mutiplicities of discrete torus£©

»ã±¨ÈË (Speaker)£º ÕÔÓÀÇ¿ ¸±½ÌÊÚ£¨Î÷ºþ´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê8ÔÂ29ÈÕ(Öܶþ) 10:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿F309

Ô¼ÇëÈË(Inviter)£ºÃ«Ñ©·å ½ÌÊÚ

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»ã±¨ÌáÒª£ºAbstract£º It is well known that the standard flat torus T^2=R^2/Z^2 has arbitrary large Laplacian-eigenvalue multiplicies. Consider the discrete torus C_N * C_N with the discrete Laplacian operator; we prove, however, its eigenvalue multiplicities are uniformly bounded for any N, except for the eigenvalue one when N is even. Our main tool to prove this result is the beautiful theory of vanishing sums of roots of unity. In this talk, we will give a brief introduction to this theory and outline a proof of the uniformly boundedness multiplicity result. This is a joint work with Bing Xie and Yigeng Zhao.