Yu Xie

Research Assistant Professor

Notre Dame Instructor in Mathematics

B.S., China West Normal University, 1996
Ph.D., Purdue University, Indiana, 2009

Research Interests

My research interests are in commutative algebra and its interaction with algebraic geometry, computational and homological algebra. My current research focuses on the Noetherian rings and blowup algebras such as Rees algebras, associated graded rings and special fiber rings. I study their j-multiplicity, depth or Cohen-Macaulay property and reduction numbers. I also have interest about the Pl$\ddot{\mbox{u}}$cker formula and the degree of dual varieties. My research could lead to some interesting results in intersection theory.

Selected Publications

• Y. Xie.  Formulas for the multiplicity of graded algebras.  (in preparation)
• B.Z. Guo and Y. Xie.  A sufficient condition on Riesz basis with parentheses of non-self adjoint operator and application to a serially connected string systme under joint feedbacks.  SIAM J. Control Optim. 43 (2004/05), 1234-1252, MR2124271 (2005i:93050).
• B.Z. Guo and Y. Xie.  Basis property and stabilization of a translating tensioned beam through a pointwise control force.  Comput. Math. Appl,. 47 (2004), 1397-1409, MR2070993 (2005d:74023).
• B.Z. Guo and Y. Xie and X.Z. Hou.  On spectrum of a general Petrovsky type equation and Risz basis of N-connected beams with linear feedback at joints.  J. Dynam. Control Systems 10 (2004), 187-211, MR2051966 (2005c:93043).
• Y. Xie, J.Y. Li and F.L. Huang.  Asymptotic stability of C_0-semigroups in Banach spaces.  (Chinese) J. Sichuan University 35 (1998), 810-814, MR1681861 (2000b:47100).

Please direct questions and comments to: xie.14@nd.edu