Yi Ouyang, Postdoctoral Fellow

• Education

  • I got both my BS and MS degrees from the Department of Mathematics at the University of Science and Technology of China, the youngest of the most prestigious universities in China and the proudest of all. You can find some information about my undergraduate study from our class homepage Class 8901.
    
  • In 1995, I spent a year at Department of Mathematics of the Ohio State University.
    
  • My four years study(1996-2000) at Department of Mathematics of the University of Minnesota ended up with my Ph.D degree in June 2000 under the instruction of Professor Greg William Anderson.
  
  

• Research

  My specialty is algebraic number theory and arithmetic geometry. More specifically, I apply cohomological tools to study the arithmetic properties of number fields. One topic I am studying is the universal norm distributions, which appears quite often in the theory of cyclotomic fields, elliptic curves and modular curves. I determined the group cohomology of some universal norm distributions and used the results to study the Kolyvagin recursions in Euler systems. The other topic I am studying is about the Mordell-Weil group and Selmer group of an abelian variety in number fields, in particular, in a tower of unramified extensions. I am also participating activities in the GANITA lab. I am interested in the theoretical part of cryptography based on abelian varieties.
  
  You may find more information about my work here:
  • AMS Coversheet (.dvi and .pdf )
  • Curriculum Vitae ( .dvi and .pdf ).
  • Past Research (.dvi and .pdf ).
  • Current Research interest ( .dvi and .pdf )
  • Publications:
    • Riemann-Hurwitz formula in basic $Z_S$-extension (with Fei Xu), Acta Arith. 81.1(1997), 1-10.
    • The group cohomology of universal ordinary distribution and its applications, Thesis, University of Minnesota, 2000 ( .dvi and .pdf ).
    • The group cohomology of universal ordinary distribution, J. reine. angew. Math. 537(2001), 1--32.
    • The universal norm distribution and Sinnott's index formula, Proceedings of AMS Vol. 130(2002), No.8, 2203-2213.
    • A note on the cyclotomic Euler systems and the double complex method (with Greg Anderson), to appear, Canadian Journal of Mathematics ( .dvi and .pdf ).
    • On the universal norm distribution, submitted, 2002 ( .dvi and .pdf ).
    • The universal Kolyvagin recursion implies the Kolyvagin recursion, submitted, 2002 ( .dvi and .pdf ).
  
  

• Other Math Links

  • My thesis advisor Professor Greg W. Anderson.
  • Professor Kumar Murty and the GANITA lab.
  • IHES , a great place I visited in January-June 2001.
  • Number theory on the web.
  • Algebraic Number Theory Archives.
  • e-Math and MathSciNet.
  • arXiv.org e-Print archive-Mathematics.
  • Mathematics Information Servers(Cool stuff in Math!).
  
  

• Teaching in Erindale College

  • MAT498 : Topics in Mathematics, Spring 2002.
  • MAT448: Algebra, Fall 2002.
  
  

• Other information:

  • Some non-mathematical Links I visit frequently.
  • A poem for the (good. sad?) old days.