René Schoof

René Schoof
Schoof at Oberwolfach, 2009
Born
René J. Schoof

(1955-05-08) 8 May 1955 (age 69)
Den Helder, Netherlands
NationalityDutch
Alma materUniversity of Amsterdam
Scientific career
FieldsMathematics
InstitutionsUniversity of Rome Tor Vergata
Doctoral advisorHendrik W. Lenstra Jr.

René Schoof (born 8 May 1955 in Den Helder)[1] is a mathematician from the Netherlands who works in number theory, arithmetic geometry, and coding theory.

He received his PhD in 1985 from the University of Amsterdam with Hendrik Lenstra (Elliptic Curves and Class Groups).[1][2] He is now a professor at the University Tor Vergata in Rome.[3]

In 1985, Schoof discovered an algorithm which enabled him to count points on elliptic curves over finite fields in polynomial time.[4] This was important for the use of elliptic curves in cryptography, and represented a theoretical breakthrough, as it was the first deterministic polynomial time algorithm for counting points on elliptic curves. The algorithms known before (e.g. the baby-step giant-step algorithm) were of exponential running time. His algorithm was improved by A. O. L. Atkin (1992) and Noam Elkies (1990).

He obtained the best-known result extending Deligne's Theorem for finite flat group schemes to the non-commutative setting, over certain local Artinian rings. His interests range throughout Algebraic Number Theory, Arakelov theory, Iwasawa theory, problems related to the existence and classification of Abelian varieties over the rationals with bad reduction in one prime only, and algorithms.

In the past, René has also worked with Rubik's cubes by creating a common strategy in speedsolving used to set many world records known as F2L Pairs, in which the solver creates four 2-piece "pairs" with one edge and corner piece which are each "inserted" into F2L slots in the CFOP method to finish the first two layers of a 3x3x3 Rubik's cube. This strategy is also used for all cubes of higher order (4x4x4 and up) in the Reduction, Yau, and Hoya methods if CFOP is used for their 3x3x3 stages.

He also wrote a book on Catalan's conjecture.[5]

See also

Some publications

  • Counting points of elliptic curves over finite fields, Journal des Théories des Nombres de Bordeaux, No. 7, 1995, 219–254, pdf
  • With Gerard van der Geer, Ben Moonen (editors): Number fields and function fields – two parallel worlds, Birkhäuser 2005
  • Finite flat group schemes over Artin rings, Compositio Mathematica, v. 128 (2001), 1–15
  • Catalan's Conjecture, Universitext, Springer, 2008

References

  1. ^ a b R.J. Schoof, 1955 - at the University of Amsterdam Album Academicum website
  2. ^ René Schoof, Mathematics Genealogy Project
  3. ^ R. Schoof's homepage, University Tor Vergata
  4. ^ René Schoof: Elliptic curves over finite fields and the calculation of square roots mod p, Mathematics of Computation, No. 44, 1985, 483–494.
  5. ^ Schoof, René (2010). Catalan's Conjecture. Universitext. London: Springer. ISBN 9781848001855. LCCN 2008933674.

Read other articles:

Marise Payne

Senator The HonourableMarise PaynePayne pada 2019 Menteri Luar Negeri AustraliaMasa jabatan28 Agustus 2018 – 23 Mei 2022Perdana MenteriScott Morrison PendahuluJulie BishopPenggantiPenny WongMenteri WanitaMasa jabatan29 Mei 2019 – 23 Mei 2022Perdana MenteriScott Morrison PendahuluKelly O'DwyerPenggantiKaty GallagherMenteri PertahananMasa jabatan21 September 2015 – 28 Agustus 2018Perdana MenteriMalcolm TurnbullScott Morrison PendahuluKevin AndrewsPenggantiChrist...

 

 

Ovulo (gamete)

Questa voce o sezione sull'argomento riproduzione non cita le fonti necessarie o quelle presenti sono insufficienti. Puoi migliorare questa voce aggiungendo citazioni da fonti attendibili secondo le linee guida sull'uso delle fonti. Un ovulo, da una illustrazione del Gray Uno spermatozoo mentre penetra la parete di un ovulo L'ovulo o cellula uovo è il gamete femminile generato dal sistema riproduttivo femminile. Deriva dall'ovocita primario, la cellula uovo in uno stadio di maturazione...

 

 

Thomas Gresham

English merchant and financier (1519–1579) For his great-nephew of the same name, see Thomas Gresham (died 1630). SirThomas GreshamPortrait of Thomas Gresham, aged approximately 41. From the collection of the Rijksmuseum.BornThomas Gresham the Elderc. 1519London, EnglandDied21 November 1579(1579-11-21) (aged 59–60)London, EnglandResting placeSt Helen's Church, Bishopsgate, London, EnglandNationalityBritishEducationGonville and Caius College, CambridgeOccupation(s)Merchant, financierK...

LGBT employment discrimination in the United States

Map of states that have sexual orientation and gender identity discrimination prohibited in public and/or private employment via state statute, executive order, regulation, and/or case law. Note: Employment discrimination based on sexual orientation or gender identity is also prohibited under federal law.   Sexual orientation and gender identity discrimination prohibited in public and private employment   Gender identity discrimination prohibited in public and private empl...

 

 

Sturt Stony Desert

Desert in central-Eastern Australia Sturt Stony DesertSturt's Stony, StonyPosition of Sturt Stony Desert in AustraliaGeographyCountryAustraliaStateSouth Australia, QueenslandCoordinates27°S 140°E / 27°S 140°E / -27; 140  Sturt Stony Desert (previously Sturt's Stony Desert) is an area in the north-east of South Australia, far south western border area of Queensland and the far west of New South Wales. It was named by Charles Sturt in 1844, while he was trying ...

 

 

Secondo triumvirato

Disambiguazione – Se stai cercando il triumvirato argentino, vedi Secondo triumvirato (Argentina). Secondo triumvirato è il nome che gli storici danno all'alleanza stipulata tra Ottaviano Augusto, Marco Antonio e Marco Emilio Lepido, in carica dal 26 novembre del 43 a.C. alla fine del 33 a.C.[1] Indice 1 Nomenclatura 2 Antefatto 3 La lex Titia 3.1 I tre uomini del triumvirato 4 Lo scontro con i cesaricidi e Sesto Pompeo 4.1 Battaglia di Filippi 4.2 La sconfitta degli ultimi pompei...

Joseph H. Outhwaite

American politician Joseph Hodson OuthwaiteMember of the U.S. House of Representativesfrom OhioIn officeMarch 4, 1885 – March 3, 1895Preceded byGeorge L. ConverseSucceeded byDavid K. WatsonConstituency13th district (1885–1891)9th district (1891–1893)12th district (1893–1895)3rd Dean of Moritz College of LawIn office1905–1907Preceded byWilliam F. HunterSucceeded byGeorge W. Rightmire Personal detailsBorn(1841-12-05)December 5, 1841Cleveland, OhioDiedDecember 9, 1...

 

 

Hou Yu-ih

Ini adalah nama Tionghoa; marganya adalah Hou. Hou You-yi侯友宜Hou sebagai Wali Kota New Taipei Wali Kota New TaipeiPetahanaMulai menjabat 25 Desember 2018PendahuluEric ChuPenggantiPetahanaMasa jabatan20 Oktober 2015 – 18 Januari 2016(pelaksana jabatan)WakilChen Shen-hsienPendahuluEric ChuPenggantiEric ChuWakil Walikota New Taipei CityMasa jabatan18 Januari 2016 – 28 Februari 2018WalikotaEric ChuPendahuluDiri sendiriPenggantiPetahanaMasa jabatan25 Desember 2010...

 

 

Jim Harbaugh

American football player and coach (born 1963) American football player Jim HarbaughHarbaugh with Michigan in 2018Los Angeles ChargersPosition:Head coachPersonal informationBorn: (1963-12-23) December 23, 1963 (age 60)Toledo, Ohio, U.S.Height:6 ft 3 in (1.91 m)Weight:215 lb (98 kg)Career informationHigh school:Palo Alto (Palo Alto, California)College:Michigan (1982–1986)NFL draft:1987 / Round: 1 / Pick: 26Career history As a player: Chicago ...

2020年夏季奧林匹克運動會波蘭代表團

2020年夏季奥林匹克运动会波兰代表團波兰国旗IOC編碼POLNOC波蘭奧林匹克委員會網站olimpijski.pl（英文）（波兰文）2020年夏季奥林匹克运动会（東京）2021年7月23日至8月8日（受2019冠状病毒病疫情影响推迟，但仍保留原定名称）運動員206參賽項目24个大项旗手开幕式：帕维尔·科热尼奥夫斯基（游泳）和马娅·沃什乔夫斯卡（自行车）[1]闭幕式：卡罗利娜·纳亚（皮划艇）&#...

 

 

Dominika

Artikel ini bukan mengenai Republik Dominika. Persemakmuran DominikaCommonwealth of Dominican (Inggris) Bendera Lambang Semboyan: Après le Bondie, C'est la Ter(Kwéyòl: Setelah Tuhan adalah Dunia)Lagu kebangsaan: Isle of Beauty, Isle of SplendourIbu kota(dan kota terbesar)Roseau15°18′N 61°23′W / 15.300°N 61.383°W / 15.300; -61.383Bahasa resmiInggrisPemerintahanRepublik parlementer• Presiden Sylvanie Burton• Perdana Menteri Roosevelt Sk...

 

 

رؤية ثنائية

مجال الرؤية لدى طائر الكيوي والمتميز بمجال رؤية ثنائي زاويته 11° ومجال أحادي 229° وزاوية عمياء سعتها 120°.[1] الرؤية الثنائية أو الرؤية بالعينين [2] (بالإنجليزية: Binocular vision)‏ في علم الأحياء هي نوع من الرؤية تملك فيها الحيوانات عينين قادرتين على إدراك صورة ثلاثية الأبعاد �...

جزر البهاما

  جزر البهاما (بالإنجليزية: Commonwealth of the Bahamas)‏[1]  جزر البهاماعلم جرز البهاما  جزر البهاماشعار جزر البهاما    الشعار الوطني(بالإنجليزية: Forward, Upward, Onward, Together)‏  النشيد:  نشيد جزر البهاما الوطني  الأرض والسكان إحداثيات 25°00′N 77°24′W / 25°N 77.4°W / 2...

 

 

Qin Shengxiang

Chinese admiral (born 1957) In this Chinese name, the family name is Qin. Qin Shengxiang秦生祥Political Commissar of the People's Liberation Army NavyIn officeSeptember 2017 – January 2022CommanderShen JinlongPreceded byMiao HuaSucceeded byYuan HuazhiDirector of the General Office of the Central Military CommissionIn officeOctober 2012 – August 2017Preceded byWang GuanzhongSucceeded byZhong Shaojun Personal detailsBornFebruary 1957 (age 67)Jianli, Hubei, Chi...

 

 

Underwater acoustic communication

Wireless technique of sending and receiving messages through water Example of multi-path propagation Underwater acoustic communication is a technique of sending and receiving messages in water.[1] There are several ways of employing such communication but the most common is by using hydrophones. Underwater communication is difficult due to factors such as multi-path propagation, time variations of the channel, small available bandwidth and strong signal attenuation, especially over lo...

Opalescent River

River tributary in New York, United States Opalescent RiverPainting of a flume in the Opalescent River by Alexander H. WyantLocationCountryUnited StatesStateNew YorkRegionAdirondacksCountyEssexPhysical characteristicsSourceLittle Marcy Mountain • locationAdirondack Mountains, New York, United States • elevation4,200 ft (1,300 m) Mouth  • coordinates44°01′05″N 74°03′10″W / 44.0181°N 74.0528°W...

 

 

Sculcoates power station

Former power station in Kingston upon Hull, East Riding of Yorkshire, England Sculcoates power stationCountryEnglandLocationKingston upon HullCoordinates53°45′49″N 00°20′42″W / 53.76361°N 0.34500°W / 53.76361; -0.34500StatusDecommissioned and demolishedConstruction began1896Commission date1898Decommission date1976Owner(s)Kingston upon Hull Corporation(1898–1948)British Electricity Authority(1948–1955)Central Electricity Authority(1955–1...

 

 

بانيو (فرنسا)

بانيو  شعار الاسم الرسمي (بالفرنسية: Bagneux)‏    الإحداثيات 48°47′52″N 2°18′45″E / 48.797777777778°N 2.3125°E / 48.797777777778; 2.3125 [1]  [2] تقسيم إداري  البلد فرنسا[3][4]  التقسيم الأعلى أو دو سين (1 يناير 1968–)  خصائص جغرافية  المساحة 4.19 كيلومتر مربع[1]...

Brandon Sanderson

Brandon Sanderson Brandon Sanderson (Lincoln, 19 dicembre 1975) è uno scrittore statunitense di letteratura fantasy. Indice 1 Biografia 1.1 Carriera 2 Caratteristiche e stile 2.1 Stile 2.2 Leggi di Sanderson 2.2.1 Prima legge di Sanderson 2.2.2 Hard Magic 2.2.3 Soft Magic 2.2.4 Seconda legge di Sanderson 2.2.5 Terza legge di Sanderson 2.2.6 Osservazioni critiche 3 Cosmoverso 3.1 Struttura del Cosmoverso 3.2 Storia del Cosmoverso 3.3 Collegamenti nel Cosmoverso 3.4 Hoid 3.5 Sviluppo della sag...

 

 

Kabupaten Manggarai

Untuk kegunaan lain, lihat Manggarai. Kabupaten ManggaraiKabupatenRumah Adat Niang Todo LambangMotto: Muku ca pu'u neka woleng curup teu ca ambo neka woleng lakoPetaKabupaten ManggaraiPetaTampilkan peta Kepulauan Sunda KecilKabupaten ManggaraiKabupaten Manggarai (Indonesia)Tampilkan peta IndonesiaKoordinat: 8°36′46″S 120°27′45″E / 8.612651°S 120.462584°E / -8.612651; 120.462584Negara IndonesiaProvinsiNusa Tenggara TimurIbu kotaRutengJumlah satuan ...