Click on any of the [ 6] items below.

My mother's autobiography and vita items are now password protected. Should you desire access, I will ask my siblings if you fall within their guidelines. For those with username/password, click here vitalist-mmc.html.
Rainbow Line

1. Complete vita record back to the beginning of my career, up to 12/10/10. For just a chronological list of research papers see vitachron: vitafull12-10-10.pdf

2. Chronological list of research (and related) papers. Most of the later items end with mysite/precise_location (ex. mysite/paplist-mt). That is, on my site this is in a pdf file in the directory ~/paplist-mt. Add .html and expand mysite to (ex. to get an html listing including: data for this paper; a URL to an html file expanding on the paper; and a URL to the pdf file. I'm slowly (as of 10/13/07) including most of the papers in this format. vitachron.pdf

3. Quick Bio. A Bio intended for the lay audience, a brief history of Mike Fried's scientific career, starting from undergraduate school: Quickbio.pdf

4. Short vita accompanying a recent NSF Proposal: NSFvitaMT-RIGP-STC-0701342.pdf

5. Enhancing the teacher as an Evaluative Resource. Summary of the need for assessment technology in order that classroom topics of one class will effect those of another: teach_vita.pdf

6. explainingMyResearch: The path from the solution of Schur's conjecture and Davenport's Problem to finding appropriate spaces on which to generalize Serre's Open Image Theorem. The html file is the topics, the pdf file a version of the references.

  1. Prelude on Topics and Methods
  1. Davenport's Problem guided early developments
    1. Primitive covers, Arithmetic vs Geometric monodromy and Exceptionality:
    2. Davenport and permutation representations vs group representations:
    3. The tools for describing Davenport pairs over number fields:
  2. The B(ranch)C(ycle)L(emma) and Br(aid)A(ction)
    1. Branch cycles and Nielsen Classes of covers:
    2. Dragging a cover by its branch points:
    3. The BCL and Moduli of covers in a Nielsen class:
    4. Inner versus absolute Nielsen classes:
    5. Geometric/Arithmetic Monodromy of Hurwitz Space covers:
  3. The Genus zero problem and covers in positive characteristic
    1. The Guralnick/Thompson Genus 0 Problem:
    2. Exceptional positive characteristic covers:
    3. Extending Grothendieck's Theorem to Wild Ramification:
  4. Serre's OIT, exceptional Covers and the Branch Bound Conjecture
    1. Modular curves as Hurwitz spaces:
    2. Aspects of the Open Image Theorem:
    3. Modular curves form a Frattini system:
    4. Involution realizations of dihedral groups:
    5. IV.e. Rational function applications using the OIT:
    6. IV.f. Conclusions on A-G dihedral-related monodromy:
  5. Galois Sratification and Poincarè series
    1. Galois Stratifications:
    2. Projective groups, and PAC and Projective Fields:
    3. Poincarè series with Cohomology coefficients:
  6. Presentations of GQ from transitive BrA
    1. An equivalent to the Regular Inverse Galois Problem:
    2. Perfect groups and the L(ift)I(invariant):
    3. Conway-Fried-Parker-Voelklein and Harbater-Mumford components:
    4. Quotients of the Absolute Galois Group:
  7. The inverse Galois problem generalizes modular curve thinking
    1. The Universal Frattini Cover:
    2. The Modular Tower conjecture:
    3. Cusps and Explicit Tower Levels:
    4. Invariants that distinguish Tower Level components:
    5. Four systems of Nielsen classes:
  8. Concluding Remarks on "Field Arithmetic"
    1. Hilbert's Irreducibility Theorem:
    2. Properties of fields and understanding the Algebraic Numbers:
    3. Hilbert Irreducibility and Weil's Decomposition Theorem:
    4. The still mysterious and often forgotten Solvable Closure, Qsol, of Q:
    explainingMyResearch.html %-%-% explainingMyResearch.pdf