21. Christophe Cornut's Homepage Harvard. Arithmetic of elliptic curves; Complex multiplication, Heegner and CM points; Kolyvagin conjectures and congruences. http://abel.math.harvard.edu/~cornut/

Christophe Cornut Science Center Harvard University One Oxford Street Cambridge, MA 02138, USA Department of Mathematics Office: SciCen 322 Tel: (617) 495 9560 Email: cornut@math.harvard.edu Mathematics Thesis (french): ps.gz Mazur's Conjecture through Ratner's theorem (english): dvi ps pdf Mazur's Conjecture through André-Oort's Conjecture (french): dvi ps pdf Teaching 21a (Fall). 21a (Spring) 129 (Spring) Personal Schedule Vita What I like What I look like ... Gabrielle and Manon I am looking for a baby-sitter: Tuesdays and Thursdays from 11.30 to 12.30am. Last update: February 11, 2002

22. Conjectures, Focus On Geometry, Curriculum Press, 1997 conjectures ( Focus on Geometry, Curriculum Press, 1997) Chapter 3. C1 If a point is on the perpendicular bisector of a segment, then it is equally distant from the endpoints (Perpendicular Bisector http://www.ocean.k12.wa.us/ilwacohi/mathDpt/Lewis/conjectures.htm

Conjectures Focus on Geometry , Curriculum Press, 1997) Chapter 3 C-1 If a point is on the perpendicular bisector of a segment, then it is equally distant from the endpoints (Perpendicular Bisector Conjecture). (pg 139) C-2 If a point is equally distant from the endpoints of a segment, then it is on the perpendicular bisector of the segment (Converse of the Perpendicular Bisector Conjecture). (pg 140) C-3 The shortest distance from a point to a line is measured along the perpendicular from the point to the line (Shortest Distance Conjecture). (pg 143) C-4 If a point is on the bisector of an angle, then it is equally distant from the sides of the angle (Angle Bisector Conjecture). (pg 147) C-5 The measure of each angle of an equilateral triangle is 60 . (pg 148) C-6 The three angle bisectors of a triangle are concurrent. (pg 155) C-7 The three perpendicular bisectors of a triangle are concurrent. (pg 155) C-8 The three altitudes (or the lines through the altitudes) of a triangle are concurrent. (pg 155) C-9 The circumcenter of a triangle is equally distant from the triangle’s three vertices. (pg 156)

23. Future Directions In Algorithmic Number Theory Some of the conjectures and open problems motivated by the PRIMES is in P papers, compiled at the AIM. http://aimath.org/WWN/primesinp/

Future directions in algorithmic number theory This web page highlights some of the conjectures and open problems concerning Future directions in algorithmic number theory. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Lecture Notes Agrawal: Primality Testing Agrawal: Finding Quadratic Nonresidues Bernstein: Proving Primality After Agrawal-Kayal-Saxena ... Remarks on Agrawal's Conjecture

24. Sir Karl Popper Sir Karl Popper. Science conjectures and Refutations. Mr. Turnbull had predicted evil consequences, . . . and was now doing the best http://cla.calpoly.edu/~fotoole/321.1/popper.html

Sir Karl Popper Science: Conjectures and Refutations Mr. Turnbull had predicted evil consequences, . . . and was now doing the best in his power to bring about the verification of his own prophecies. ANTHONY TROLLOPE When I received the list of participants in this course and realized that I had been asked to speak to philosophical colleagues I thought, after some hesitation and consultation, that you would probably prefer me to speak about those problems which interest me most, and about those developments with which I am most intimately acquainted. I therefore decided to do what I have never done before: to give you a report on my own work in the philosophy of science, since the autumn of1919 when I first began to grapple with the problem, "When should a theory be ranked as scientific?" or "Is there a criterion for the scientific character or status of a theory?" The problem which troubled me at the time was neither, "When is a theory true?"nor, "When is a theory acceptable?" My problem was different. I wished to distinguish between science and pseudo-science;

25. Least Primitive Root Of Prime Numbers Empirical and statistical results showing the smallest base required to prove a number is prime. Includes theory and conjectures. http://www.ieeta.pt/~tos/p-roots.html

Least primitive root of prime numbers Least prime primitive root of prime numbers Least base necessary to prove the primality of a number Introduction Results References Links ... [Up] Introduction Let p be a prime number. Fermat's little theorem states that a^(p-1) mod p=1 (a hat (^) denotes exponentiation) for all integers a between and p-1 . A primitive root of p is a number r such that any integer a between and p-1 can be expressed by a=r^k mod p , with k a nonnegative integer smaller that p-1 . If p is an odd prime number then r is a primitive root of p if and only if for all prime divisors q of p-1 . If a number r can be found that satisfies these conditions, then p must be a prime number. In fact, it is possible to relax the above conditions in order to prove that p is prime ; it is sufficient to find numbers denotes the variable r with index k such that and (r_k)^(p-1) mod p=1 for all prime divisors of p-1 (these conditions guarantee the existence of a primitive root of p A famous conjecture of Emil Artin [3, problem F9] states that if a is an integer other than or a perfect square, then the number

26. Belmont Club Sunday, September 21, 2003. Reader responses to The Three conjectures. posted by wretchard Permalink 1231 PM Zulu. Postscript to the Three conjectures. http://belmontclub.blogspot.com/2003_09_01_belmontclub_archive.html

Belmont Club History and history in the making Tuesday, September 30, 2003 Treason Dan Darling at Regnum Crucis wonders about the comparatively high percentage of suspected traitors at the Guantanamo Bay detention facility. "We now have at least three moles at Gitmo (which isn't all that large a facility), I don't think it's all that implausible to suspect that they might have been working together" that is, two translators and one Muslim chaplain. To put that number in perspective, there are 80 translators at Guantanamo and 12 Muslim chaplains in the US Armed Services. Although the high percentage of suspects among chaplains (as compared to translators) is affected by the small sample size and the unfortunate choice of the institutions chosen to supply the chaplains, the situation among the translators is also disturbing given that one of the suspects was already "a supply clerk before being pressed into service as a translator at Guantanamo Bay" . And there may be more. Gen. Peter Pace, vice chairman of the Joint Chiefs of Staff, said, "we don't presume that the two we know about is all there is to it"

27. Rational And Integral Points On Higher-dimensional Varieties Some of conjectures and open problems, compiled at AIM. http://aimath.org/WWN/qptsurface2/

Rational and integral points on higher dimensional varieties This web page highlights some of the conjectures and open problems concerning Rational and integral points on higher dimensional varieties. If you would like to print a hard copy of the whole outline, you can download a dvi postscript or pdf version. Lecture Notes Colliot-Thelene 1: Rational points on surfaces with a pencil ... Colliot-Thelene 2: Rational points on surfaces with a pencil ... de Jong: Rationally Connected Varieties ... Miscellaneous Photos The individual participant contributions may have problems because converting complicated TeX into a web page is not an exact science. The dvi, ps, or pdf versions are your best bet.

28. FRANCO MORETTI - CONJECTURES ON WORLD LITERATURE Africa. For the first time, the prospect of a morphology of global letters? FRANCO MORETTI. conjectures ON WORLD LITERATURE. Nowadays http://www.newleftreview.com/NLR23503.shtml

HOME ABOUT NLR SUBSCRIPTIONS RENEWALS ... New Left Review 1, January-February 2000 Nearly two hundred years ago, Goethe announced the imminence of a world literature. Here Franco Moretti offers a set of hypotheses for tracking the birth and fate of the novel in the peripheries of Europe, in Latin America, Arab lands, Turkey, China, Japan, West Africa. For the first time, the prospect of a morphology of global letters? FRANCO MORETTI CONJECTURES ON WORLD LITERATURE Weltliteratur Manifesto Weltliteratur : after all, the literature around us is now unmistakably a planetary system. The question is not really what how . What does it mean, studying world literature? How do we do it? I work on West European narrative between 1790 and 1930, and already feel like a charlatan outside of Britain or France. World literature? categories conceptual interconnection of problems problem World literature: one and unequal I will borrow this initial hypothesis from the world-system school of economic history, for which international capitalism is a system that is simultaneously

29. The UnMuseum - The Pharos Lighthouse Account of the findings of an expedition to discover the lighthouse, along with its history and conjectures on its interior design, by Lee Krystek in his Museum of Unnatural Mystery. http://www.unmuseum.org/pharos.htm

The Pharos. The Great Lighthouse at Alexandria In the fall of 1994 a team of archaeological scuba divers entered the waters off of Alexandria, Egypt. Working beneath the surface they searched the bottom of the sea for artifacts. Large underwater blocks of stone were marked with floating masts so that an Electronic Distance Measurement station on shore could obtain their exact positions. Global positioning satellites were used to further fix the locations. The information was then fed into computers to create a detailed database of the sea floor. Ironically, these scientists were using some of the most high-tech devices available at the end of the 20th century to try and discover the ruins of one of the most advanced technological achievements of the 3rd century, B.C.: The Pharos. It was the great lighthouse of Alexandria, one of the Seven Wonders of the Ancient World The story of the Pharos starts with the founding of the city of Alexandria by the Macedonian conqueror Alexander the Great in 332 B.C.. Alexander started at least 17 cities named Alexandria at different locations in his vast domain. Most of them disappeared, but Alexandria in Egypt thrived for centuries and continues even today.

30. RPO -- Edward Young : Conjectures On Original Composition (1759) conjectures on Original Composition (1759). {{Page i}} conjectures ON ORIGINAL COMPOSITION. Source Edward Young. conjectures on Original Composition. http://eir.library.utoronto.ca/rpo/display/displayprose.cfm?prosenum=16

31. A Performance Of Comus Introduction to the debut tracing verified facts and examining various conjectures as to staging and actors involved. http://www.mith.umd.edu/comus/final/ceperform.htm

A Performance History of Comus The masque was first performed on September 29, 1634, at Ludlow Castle in Wales, as part of a celebration honoring the installation of the Earl of Bridgewater as the Lord President of Wales. Although the Earl had been appointed to the position by Charles I in 1631, he had apparently been unable to actually move into Ludlow Castle, the official residence of the Lord President, until 1634. In midsummer 1634, however, he made a ceremonial visit to the castle itself and then to manors in the surrounding area. Travel journals suggest that the performance took place upon the Earl's subsequent return to the Castle, amid other entertainments centering around his appointment (Brown 33). The dating of the performance has occasioned much commment; September 29th is Michaelmas, a holiday honoring the angel St. Michael, and scholars have debated the extent to which the themes of the mask might be directly tied to the significance of the holiday. The inability to ascertain both exactly when Milton was writing the mask and exactly when the date of September 29th had been appointed as the date of performance makes such a link somewhat conjectural. The work does, however, manifest such themes as to suggest that Milton did intend for it to engage with the significance of the holiday (Creaser 114). The holiday "was associated with the election of new magistrates and governors" and traditions associated with the holiday often equated this "earthly governance" with heavenly or angelic protection (Brown 39). Thus the idea of the supernatural forces stepping in to protect the children in the mask would seem coherent with themes of Michaelmas Day.

32. Lømmelgård Veterinæroptik Byder Dem Velkommen A curious collection of absurd art, ludicrous language courses, crazy conjectures plus a weird weekly poem. http://www.sevaj.dk

Biograf Kro Poesirobot Forbrugeroplysning ... Malerier (Der er kommet en ny afstemning) A limited English translation is available (sidst opdateret 24 september 2003) kasper@sevaj.dk bulletin@sevaj.dk med ordet "Tilmeld" i emnelinjen. Eller nedfæld Deres emailadresse i nedenstående felt: Mere musik

33. Conjectures conjectures. To Realize One s Destiny is a Person s Only Obligation.. Paolo Coelho. Monday, May 24, 2004. Reactive Management. I was http://redcer.blogdrive.com/

C O N J E C T U R E S To Realize One's Destiny is a Person's Only Obligation.. -Paolo Coelho Tuesday, May 25, 2004 The Not So Fairy-Tale Ending One night, while working the Friday shift, the little princess was yelled at by several customers and even called " incompetent " because they had late fees which she was unable to take off (being a CSR and all- she was not given any real responsibility). Extremely peeved by the mean customer, the little princess began griping with a fellow employee about the low points of the job- finally complaining at while she handled 13% of the stores income, and outselling promotional bundles by at least 30 bundles, she was still being treated like shit by the company. Then, in the middle of the store on a Friday night, with the line stretching to the back of the store... the little princess burst into tears. Other employees, and even customers, tried to console her and told her, " if the job makes you feel this bad about yourself, you should just quit. They are taking advantage of you ". The little princess decided if she could not get a raise- she would indeed quit.

34. The Riemann Hypothesis Some of the conjectures and open problems concerning RH, compiled by the AIM. http://aimath.org/WWN/rh/

The Riemann Hypothesis This web page highlights some of the conjectures and open problems concerning The Riemann Hypothesis. Click on the subject to see a short article on that topic. If you would like to print a hard copy of the entire web page, you can download a dvi postscript or pdf version. What is an $L$-function? Terminology and basic properties Functional equation Euler product ... Anecdotes about the Riemann Hypothesis

35. Inside The Circle Of Summertime.. Offers thoughts on alternative realms, soulful conjectures, poetry and philosophy. http://www.omnarayan.com

36. Nature Publishing Group ERROR, There has been an error while processing your request. In most cases, this is an isolated incident that can be overcome by http://www.nature.com/cgi-taf/DynaPage.taf?file=/nature/journal/v423/n6936/full/

37. Independent On Sunday Minister's Aides Are Pro-hunt Campaigners Jo Dillon, political correspondent. Concerns and conjectures about how the final Government Bill and voting will play out. http://www.independent.co.uk/story.jsp?story=333421

38. E-Library Of Science A collection of Ebooks on Smarandache functions, sequences, problems, conjectures, geometries, neutrosophic logic, and paradoxes. http://www.gallup.unm.edu/~smarandache/Ebooks-otherformats.htm

E-Library of Science E-books of Mathematics E-books of Philosophy E-Books of Physics Smarandache Function, book series ( Vol. 1 , edited by R. Muller; Vol. 2-3, Vol. 4-5, Vol. 6 Smarandache Notions, book series ( Vol. 7 Vol. 8 Vol. 9 Vol. 10 ... Vol. 14 new E-Books of Mathematics Smarandache Algebraic Structures, book series by W. B. Vasantha Kandasamy: ( Vol. I: Groupoids Vol. II: Semigroups Vol. III: Semirings, Semifields, and Semivector Spaces Vol. IV: Loops ... Comments and Topics on Smarandache Notions and Problems, by Kenichiro Kashihara Applications of Smarandache Function, Prime and Coprime Functions [ English Espanol ], by Sebastian Martin Ruiz Only Problems, not Solutions! Proposed Problems of Mathematics, Vol. II [Romanian, French, English] Probleme Compilate Rezolvate de Geometrie ... Metode de Calcul in Analiza Matematica [Romanian] Collected Papers ( Vol. I Vol. II Vol. III Randomness and Optimal Estimation in Data Sampling, by M. Khoshnevisan, S. Saxena, H. P. Singh, S. Singh, F. Smarandache ... Analysis of Social Aspects of Migrant Labourers Living with HIV/AIDS Using Fuzzy Theory and Neutrosophic Cognitive Maps, by W. B. Vasantha Kandasamy, F. Smarandache; translation of the Tamil interviews by M. Kandasamy new Geometric Theorems, Diophantine Equations, and Arithmetic Functions, by Jozsef Sandor

39. Meteorits conjectures sobre la seva proced¨ncia. Efectes de l'impacte. Amb simulacions i gr fics diversos. http://www.xtec.es/recursos/astronom/craters/

Meteorits D'on venen els meteorits? Quins efectes pot produir un meteorit quan cau a la Terra? Imatges: A STRONOMY i National Geographic

40. Analogies And Conjectures AskWhy! Publications Holy Bibble Click to get more bibble! Speculation at the fringes of history and science. Is it unlikely but, on the evidence, not impossible? http://www.askwhy.co.uk/analogiesandconjectures/

Speculation at the fringes of history and science. Is it unlikely but, on the evidence, not impossible? Or quite likely but lacking sound evidence? Or even likely but ignored because of prejudice. email us your fringe ideas. Contents Updated: Thursday, May 10, 2001 Tuesday, 30 March 2004 Act of God by Graham Phillips: Book review (13 KB) Was America a Phoenician Colony Puzzles of History Kaspar Hauser Is the Pope Human? ... Christian Test Speak! Speak! You got nothing to say? S Tino Nikos Contents

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