Papers By R. E. Borcherds Including proof of the Moonshine Conjecture (TeX, DVI, PDF). http://math.berkeley.edu/~reb/papers/
Extractions: tex dvi pdf A monster Lie algebra? (with J. H. Conway , L. Queen and N. J. A. Sloane .) Adv. Math. 53 (1984) 75-79. tex dvi pdf The Leech lattice and other lattices, Ph.D. thesis (Cambridge, 1985). tex dvi pdf The Leech lattice, Proc. Royal Soc. London A398 (1985) 365-376. tex dvi pdf Vertex algebras, Kac-Moody algebras and the monster, Proc.Nat. Acad. Sci. U.S.A. 83 (1986), 3068-3071. tex dvi pdf Automorphism groups of Lorentzian lattices, J.Alg. Vol 111, No. 1, Nov 1987, pp. 133-153. tex dvi pdf Generalized Kac-Moody algebras, J.Alg. Vol 115, No. 2, June 1988, p. 501-512. tex dvi pdf The 24-dimensional odd unimodular lattices. Sphere packings, lattices, and groups, by J.H. Conway and N. J. A. Sloane , chapter 17 (p. 421-430.) (This does not include the table of such lattices, which can be extracted from table -4 of "The Leech lattice and other lattices". ) tex dvi pdf The cellular structure of the Leech lattice. (with J. H. Conway and L. Queen) Sphere packings, lattices, and groups, by J.H. Conway and N. J. A. Sloane
Dynamical Complexity And Regularity Dynamic laws are classified and conjecture that the regular laws cannot produce organic structures is discussed. http://www.iscid.org/papers/Johns_DynamicalComplexity_020102.pdf
Louis De Branges: Home Professor of Mathematics at Purdue University. Contact information, papers on the Bieberbach Conjecture, the Riemann Hypothesis, and related topics. http://www.math.purdue.edu/~branges/
Lehmer's Problem That the Mahler measure of an algebraic number is bounded away from 1. Pages by Michael Mossinghoff, UCLA. http://www.cecm.sfu.ca/~mjm/Lehmer/lc.html
Extractions: Derrick Henry Lehmer, 1933 Mahler's measure of a polynomial f is defined to be the absolute value of the product of those roots of f which lie outside the unit disk, multiplied by the absolute value of the coefficient of the leading term of f . We denote it M f Lehmer's problem , sometimes called Lehmer's question, or Lehmer's conjecture, asks if there exists a constant C f with integer coefficients and M f M f C "We have not made an examination of all 10th degree symmetric polynomials, but a rather intensive search has failed to reveal a better polynomial than "All efforts to find a better equation of degree 12 and 14 have been unsuccessful." Despite extensive searches, Lehmer's polynomial remains the world champion. This page summarizes what is known today about Lehmer's problem. It includes descriptions of algorithms, histories of searches performed, and various lists of polynomials with small measure. Computational Aspects of Problems on Mahler's Measure , a talk for a short graduate course at the PIMS Workshop on Mahler's Measure of Polynomials , Simon Fraser University, June 2003. (
Yukie, Akihiko Tohoku University. Geometric invariant theory, Zeta functions for prehomogeneous vector spaces, Applications to the Oppenheim conjecture. http://www.math.tohoku.ac.jp/~yukie/
Benne De Weger Eindhoven University of Technology. Diophantine problems, ABC conjecture. http://www.win.tue.nl/~bdeweger/
Conjecture - Definition In mathematics, a conjecture is a mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or http://www.wordiq.com/definition/Conjecture
Extractions: In mathematics , a conjecture is a mathematical statement which has been proposed as a true statement, but which no one has yet been able to prove or disprove. Once a conjecture has been proven, it becomes known as a theorem , and it joins the realm of known mathematical facts. Until that point in time, mathematicians must be extremely careful about their use of a conjecture within logical structures. Conjectural means presumed to be real, true, or genuine, mostly based on inconclusive grounds (cf. hypothetical ). The term was used by Karl Popper , in the context of scientific philosophy. Contents showTocToggle("show","hide") 1 Famous conjectures 4 Undecidable conjectures Until its proof in 1995, the most famous of all conjectures was the mis-named Fermat's last theorem - this conjecture only became a true theorem after its proof. In the process, a special case of the Taniyama-Shimura conjecture , itself a longstanding open problem, was proven; this conjecture has since been completely proven. Other famous conjectures include: The Langlands program is a far-reaching web of ' unifying conjectures ' that link different subfields of mathematics, e.g.
Mike Knapp's Home Page Loyola College. Diagonal forms, Artin s conjecture. Papers, preprint, thesis. http://evergreen.loyola.edu/mpknapp/www/
Extractions: Welcome to my home page. I'm glad you stopped by! I am currently an associate professor in the mathematical sciences department at Loyola University (formerly Loyola College) in Baltimore. I came here in August 2003 from the University of Rochester , where I taught and did research for three years. Before that, I was a student at the University of Michigan , earning my Ph.D. under the direction of Trevor Wooley My research interests are in number theory. One of the main reasons why I like number theory is that there are so many questions which any junior high school student can understand, but nobody in the world knows how to answer. If you are interested, you can check out my research description above. My personal research is unfortunately not on one of the questions that are really easy to state, but I have tried to write it so that it's not too hard to understand. I hope that I have succeeded. If you're interested in reading a more detailed account of my work, please read either my research statement and NSF grant application on the professional items page or my papers and preprints.
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