141. Papers By R. E. Borcherds Including proof of the Moonshine Conjecture (TeX, DVI, PDF). http://math.berkeley.edu/~reb/papers/

PDF, dvi and plain TeX files of papers and preprints by R. E. Borcherds 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

142. 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

143. 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/

Department of Mathematics About Us Faculty Emeritus Faculty ... Home Louis de Branges Home Papers Publications PhD: Cornell University 1957 Title: Edward C. Elliott Distinguished Professor of Mathematics Professional Interests: complex analysis, Fourier analysis, functional analysis Office: MATH 800 Phone: Email: Homepage: http://www.math.purdue.edu/~branges/ Home Papers Publications Department of Mathematics, Purdue University 150 N. University Street, West Lafayette, IN 47907-2067 Phone: (765) 494-1901 - FAX: (765) 494-0548 Contact the Webmaster West Lafayette, IN 47907 USA, 765-494-4600 An equal access/equal opportunity university Contact the Webmaster to address accessibility issues.

144. 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

Lehmer's Problem f x x r a x r-1 a r where the a 's are integers, such that the absolute value of the product of those roots of f 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 x x x x x x x x "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. Talks on Lehmer's Problem and Mahler's 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. (

145. 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/

Home page of Akihiko Yukie Japanese About myself Birthdate, Birthplace: Born on August 1, 1957 in Kofu Yamanashi Japan Kofu is a city about 80 miles west of Tokyo. The climate is similar to that of Oklahoma. It is surrounded by mountains and one of them is Mt. Fuji. Mt. Fuji is about 1 hour and half from Kofu Family: Married to Miho Yukie with two daughters Mayu (5 years old) and Tomomi (2 years old) Education: Ph. D. Harvard University 1986 BS University of Tokyo 1980 Employment: Professor Tohoku University 1999- Associate Professor OSU 1995-1999 Assistant Professor OSU 1989-1995 Guest Professor at SFB 170 Goettingen Germany 1990-1991 Member of Institute for Advanced Study Princeton 1989-1990 Visiting Assistant Professor OSU 1987-1989 Tamarkin Assistant Professor Brown University 1985-1987 Mathematical interest: Geometric Invariant Theory, Zeta functions for prehomogeneous vector spaces. Applications to the Oppenheim conjecture. Lectures on rational orbit decompositions of prehomogeneous vector spaces Anyone who wants the lecture note of my course on prehomogeneous vector spaces can copy its gzipped ps file course.ps.gz

146. Benne De Weger Eindhoven University of Technology. Diophantine problems, ABC conjecture. http://www.win.tue.nl/~bdeweger/

147. Machiel Van Frankenhuijsen -- Official Web Site Utah Valley University. Hyperbolic spaces and the ABC conjecture. http://research.uvu.edu/machiel/

Home Classes Downloads Bibliography Curriculum Vitae ... Contact Information Machiel van Frankenhuijsen Machiel van Frankenhuijsen is an Associate Professor at Utah Valley University Here you will find: information about the classes I teach. a complete and up-to-date bibliography that points to downloadable papers. downloadable programs. information about the State Math Contest To get in touch with Machiel van Frankenhuijsen, see the Contact section.

148. 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

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 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 2 Counterexamples 3 Use of conjectures in conditional proofs 4 Undecidable conjectures Famous 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: There are no odd perfect numbers Goldbach's conjecture The twin prime conjecture The Collatz conjecture The Riemann hypothesis P NP The Poincaré conjecture The abc conjecture The Langlands program is a far-reaching web of ' unifying conjectures ' that link different subfields of mathematics, e.g.

149. Mike Knapp's Home Page Loyola College. Diagonal forms, Artin s conjecture. Papers, preprint, thesis. http://evergreen.loyola.edu/mpknapp/www/

Michael Knapp Mathematical Sciences Department Loyola College 4501 North Charles Street Baltimore, MD 21210-2699 Office: Knott 301e Office Hours: Monday 11-12 Wednesday 1-2 (Math 252 ONLY) Wednesday 2-3 (Math 447 ONLY) Friday 11-12 Or by appointment. Phone: (410)-617-2382 Email: mpknapp (at) loyola.edu Research Description (Non-technical) Papers and Preprints Undergraduate Research Math 252 Webpage Math 252 Webwork Page ... Links 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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