Cedarville University

http://www.cedarville.edu/academics/sciencemath/personalpages/ddf_www.htm

Cedarville University

Darrin D. Frey

Associate Professor of Mathematics, Department of Science and Math, Cedarville University

Address:

Office: Tyler 124
Phone: 937-766-7643
e-mail: freyd@cedarville.edu

If you are on the cedarville campus, you will get a fuller version of this page at  this location.  If you aren't local, then you can't get there.  Sorry!


Education

  • Ph.D. in Mathematics from the University of Michigan. My advisor at Michigan was Robert Griess. He is famous for constructing the monster simple group. I will say more about the monster below.
  • B.S. in Mathematics from the University of Nebraska. At Nebraska, I studied inverse semigroups under John Meakin.

Biography:

Mathematical Interests:

I am currently studying conjugacy of finite subgroups (particularly alternating groups and their central extensions) of exceptional complex Lie groups. 

If you would like to know more about my work in this area you can download my research summary either in DVI or Postscript format. (I'm working on these too). My thesis is now one volume (Volume 133 NO. 634) in the Memoirs of the AMS, and I have two other papers which have recently appeared in the Journal of Algebra.

I am also interested in learning about monstrous moonshine. Monstrous moonshine is a collection of extraordinary and unexpected facts about the monster simple group. First, I'll explain a little about the monster and then about moonshine.

The classification of finite simple groups says that any finite simple group is either a cyclic group of prime order, an alternating group of degree at least 5, a group of Lie type, or one of 26 simple groups that don't fall into any of the other (infinite) categories. These 26 groups are called "sporadic". Five of them were discovered in the 1860's by Mathieu and the other 21 were discovered between 1965 and 1975. Three of the latter type were discovered by University of Michigan faculty. The Higman-Sims group was discovered and constructed (in one day!) in 1968 by Don Higman of the U of M and Charles Sims of Rutgers University. It has 44,352,000 elements. The McLaughlin group was discovered by Jack McLaughlin in 1968. It has 898,128,000 elements. The monster group is the largest of the sporadic groups. It was discovered independently by Bernd Fischer and Robert Griess in 1973 and was constructed by Griess in 1980. The monster has 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000 elements. I have written a short introduction to monstrous moonshine which is aimed at non-algebraists. There are two parts to it, the first part introduces some background material, and the second part actually talks about moonshine. The material in what I have written uses material from the following sources very heavily and I want to give due credit:

  • I. M. Isaacs, Character Theory of Finite Groups, Academic Press, San Diego, 1976.
  • I. Frenkel, J. Lepowsky and A. Meurman, Vertex Operator Algebras and the Monster, Academic Press, San Diego, 1988.
  • E. Jurisich, Generalized Kac-Moody Lie algebras, free Lie algebras and the structure of the Monster Lie algebra, to appear in Journal of Pure and Applied Algebra, Nov., 1997.
  • Various issues of John Baez's This week's finds in mathematical physics
  • R. W. Gebert Introduction to Vertex Algebras, Borcherds Algebras and the Monster Lie Algebra to appear in International Journal of Modern Physics.

    • You can get these two files here in either DVI or Postscript format.  (Yes I am working on these too).
     

    Other interesting math sites:

    The American Mathematical Society
    This week's finds in mathematical physics
    The mathematics of Fermat's Last Theorem
    More about moonshine
    Tony Smith's homepage  I don't understand much on this page but it's interesting.  I would especially like to understand his D4-D5-E6-E7 Physics model.

    Christian sites:

  • I am a Christian and Cedarville is a Christian University.  Click here to see what I believe (this is Cedarville's doctrinal statement).  Below, I have put links to some good Christian sites on the Web.

    •  My home church in Lincoln, Nebraska
    Some other churches I have attended:
               Grace Bible Church in Ann Arbor, Michigan.
               Bethany Evangelical Free Church in LaCrosse, Wisconsin.
    My current church is Grace Baptist Church in Cedarville, Ohio.
    Other good sites:
    John MacArthur's Grace to You page
    Charles Stanley's In Touch   This site and Chuck Swindoll's site have their daily radio messages set up so you can listen to them from your computer.
    Chuck Swindoll's Insight for Living.
    An online bible
     

    Other interests:

  • I have a wife and three kids that I enjoy spending time with.
  • Nebraska Football.  (This is a different link than the one above).
  • Classical Music.  I am especially fond of Bach and Mozart.  The highlight is an interesting page on Bach that I found.
  • Old Italian Art. Here are a few of my favorite art, sculpture and architecture objects.  (These pictures don't show up because I am concerned about violating copyright laws.  Sorry!)

    • .  The cathedral of Florence and the baptistry.
    Below are the competition panels of the sacrifice of Isaac by Abraham that were submitted by Lorenzo Ghiberti and Filippo Brunelleschi in the competition to do the sculptures on the North Doors of the Baptistry of Florence. Brunelleschi's is on the left.  (Ghiberti won the competition.  Brunelleschi went on to greatness as well.  He was the architect who designed the dome for the cathedral of Florence).

    Below are the East doors of the Baptistry done by Lorenzo Ghiberti. They were called the Gates of Paradise by Michaelangelo.  One of the panels is shown in detail at the right.
  • Honda Automobiles, especially the Acura NSX.  I also follow Honda Racing


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