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THÔNG TIN TOÁN HỌC Tháng 7 Năm 2008 Tập 12 Số 2

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THÔNG TIN TOÁN HỌC Tháng 7 Năm 2008 Tập 12 Số 2 Hội Toán Học Việt Nam THÔNG TIN TOÁN HỌC Tháng 7 Năm 2008 Tập 12 Số 2 Lưu hành nội bộ Th«ng Tin To¸n Häc to¸n häc. Bµi viÕt xin göi vÒ toµ so¹n. NÕu bµi ®−îc ®¸nh m¸y tÝnh, xin göi kÌm theo file (chñ yÕu theo ph«ng ch÷ unicode, • Tæng biªn tËp: hoÆc .VnTime). Lª TuÊn Hoa • Ban biªn tËp: • Mäi liªn hÖ víi b¶n tin xin göi Ph¹m Trµ ¢n vÒ: NguyÔn H÷u D− Lª MËu H¶i B¶n tin: Th«ng Tin To¸n Häc NguyÔn Lª H−¬ng ViÖn To¸n Häc NguyÔn Th¸i S¬n 18 Hoµng Quèc ViÖt, 10307 Hµ Néi Lª V¨n ThuyÕt §ç Long V©n e-mail: NguyÔn §«ng Yªn [email protected] • B¶n tin Th«ng Tin To¸n Häc nh»m môc ®Ých ph¶n ¸nh c¸c sinh ho¹t chuyªn m«n trong céng ®ång to¸n häc ViÖt nam vµ quèc tÕ. B¶n tin ra th−êng k× 4- 6 sè trong mét n¨m. • ThÓ lÖ göi bµi: Bµi viÕt b»ng tiÕng viÖt. TÊt c¶ c¸c bµi, th«ng tin vÒ sinh ho¹t to¸n häc ë c¸c khoa (bé m«n) to¸n, vÒ h−íng nghiªn cøu hoÆc trao ®æi vÒ ph−¬ng ph¸p nghiªn cøu vµ gi¶ng d¹y ®Òu ®−îc hoan nghªnh. B¶n tin còng nhËn ®¨ng © Héi To¸n Häc ViÖt Nam c¸c bµi giíi thiÖu tiÒm n¨ng khoa häc cña c¸c c¬ së còng nh− c¸c bµi giíi thiÖu c¸c nhµ Chào mừng ĐẠI HỘI TOÁN HỌC VIỆT NAM LẦN THỨ VII Quy Nhơn – 04-08/08/2008 Sau một thời gian tích cực chuẩn bị, phát triển nghiên cứu Toán học của nước Đại hội Toán học Toàn quốc lần thứ VII ta giai đoạn vừa qua trước khi bước vào sẽ diễn ra, từ ngày 4 đến 8 tháng Tám tại Đại hội đại biểu. Đại hội đại biểu sẽ bầu ĐH Quy Nhơn. Đại hội Toán học Việt ra BCH khóa 6 để lãnh đạo Hội Toán Nam lần thứ VII bao gồm hai phần: Hội học. Hội được thành lập năm 1966. Cho nghị khoa học và Đại hội đại biểu Hội đến nay, lãnh đạo của các BCH khóa Toán học Việt Nam. Có tất cả 790 đại trước là: biểu đăng kí tham dự Hội nghị với 281 • Khóa 1 (1966 – 1988): Chủ tịch: GS báo cáo. Lê Văn Thiêm, Tổng thư kí: GS Các hội nghị Toán học toàn quốc đã Hoàng Tụy diễn ra trước đó là: HNTH toàn Miền • Khóa 2 (1988 – 1994): Chủ tịch: GS Bắc lần thứ 1 năm 1971, HNTH toàn Nguyễn Đình Trí, Tổng thư kí: GS Đỗ quốc lần thứ 2 năm 1977, HNTH toàn Long Vân quốc lần thứ 3 năm 1985, HNTH toàn • Khóa 3 + 4 (1994 - 1999 và 1999 – quốc lần thứ 4 năm 1990, HNTH toàn 2004): Chủ tịch: GS Đỗ Long Vân, Việt Nam lần thứ 5 năm 1997 và HNTH Tổng thư kí: GS Phạm Thế Long toàn quốc lần thứ 6 năm 2002. Năm hội nghị đầu được tổ chức tại Hà Nội, còn • Khóa 5 (2004 – 2008): Chủ tịch: GS Hội nghị lần thứ 6 được tổ chức tại Huế. Phạm Thế Long, Tổng thư kí GS Lê Tuấn Đây là lần thứ hai, Hội nghị Toán học Hoa. Các ủy viên khác của BCH là: GS toàn quốc được tổ chức xa Hà Nội. Đại Nguyễn Hữu Anh (ĐHKHTN - ĐHQG Tp. hội được sự quan tâm đặc biệt của Bộ HCM): Phó CT, GS Nguyễn Quý Hỷ Khoa học và Công nghệ, Ủy ban nhân (ĐHKH TN - ĐHQG HN): Phó CT, GS dân tỉnh Bình Định và Viện Khoa học và Hà Huy Khoái (Viện Toán học): Phó CT, Công nghệ Việt Nam. GS Lê Ngọc Lăng (ĐH Mỏ - Địa chất): Phó CT, GS Nguyễn Văn Mậu (ĐHKHTN Các cơ quan tài trợ chính của Đại hội - ĐHQG HN): Phó CT, GS Lê Mậu Hải lần này là: Bộ Khoa học và Công nghệ (ĐHSP HN): Phó TTK, PGS Tống Đình (thông qua Chương trình nghiên cứu cơ Quỳ (ĐHBK HN): Phó TTK và các ủy bản), Đại học Quy Nhơn, Ủy ban nhân viên: GS Nguyễn Hữu Việt Hưng dân tỉnh Bình Định, Viện Khoa học và (ĐHKHTN - ĐHQG HN), GS Phan Quốc Công nghệ Việt Nam và Viện Toán học. Khánh (ĐH Quốc tế, ĐHQG Tp. HCM), Điều đặc biệt ở Đại hội lần này là lần PGS Lê Hải Khôi (Viện CNTT), GS Trần đầu tiên có sự kết hợp giữa Hội nghị và Văn Nhung (Bộ GD & ĐT), GS Lê Hùng Đại hội đại biểu Hội Toán học Việt Nam. Sơn (ĐHBK HN), GS Nguyễn Khoa Sơn Đây là Đại hội đại biểu lần thứ 6 của (Viện KH & CN VN), TS Nguyễn Thái Hội Toán học. Nhiệm vụ chính của Đại Sơn (ĐHSP Tp. HCM), GS Lê Văn Thuyết hội là đánh giá, tổng kết những thành tựu (ĐH Huế), GS Nguyễn Duy Tiến phát triển Toán học trong 4 năm qua, (ĐHKHTN-ĐHQG HN). đồng thời vạch ra đề cương phát triển Thông Tin Toán Học xin chào mừng Toán học trong 5 năm tới. Việc kết hợp và xin chúc Đại hội Toán học Toàn quốc với Hội nghị khoa học trước đó là một lần thứ 7 thành công tốt đẹp. cơ hội tốt để các đại biểu có một cái nhìn toàn diện và sâu sắc hơn về tình hình 1 E8 - mët d÷ luªn bòng nê é Ngåc Di»p (Vi»n To¡n håc) Email: [email protected] E8 l mët nhâm Lie °c bi»t, mët To¡n håc trong th¸ k¿ 19 ÷ñc chùng ¤i sè Lie °c bi»t, mët h» nghi»m °c ki¸n sü ra íi cõa l½ thuy¸t nhâm Lie bi»t, .... mët ch÷ìng tr¼nh t½nh to¡n v ¤i sè Lie nh÷ l mët t÷ìng tü li¶n khêng lç ¡ng ÷ñc nhi·u ng÷íi quan töc cõa lþ thuy¸t Galois. Elie Cartan t¥m. Möc ½ch cõa b i l giîi thi»u ¢ ÷a v o c¡c ma trªn c§u tróc cõa æi i·u v· tr÷íng hñp hy húu n y ¤i sè Lie, m ng y nay ÷ñc gåi l trong ¤i sè, trong tæpæ, trong cæng ma trªn Cartan. Nhí â m ng÷íi ta ngh» t½nh to¡n. x¥y düng ÷ñc h» nghi»m li¶n k¸t v sì ç Dynkin cho mët h¼nh dung v· c§u Thæng tin To¡n håc sè 3 Tªp 11, tróc cõa c¡c h» nghi»m li¶n quan. H» Th¡ng 9 n«m 2007, trong möc tin nghi»m công ÷ñc x¡c ành bði mët To¡n håc th¸ giîi, câ ÷a tin v· nhâm c§u tróc polytope cõa h» nghi»m. Lie E8 v nhúng i·u ang ÷ñc sü quan t¥m cõa giîi to¡n håc th¸ giîi. Trong bèi c£nh â, E8 ÷ñc bi¸t Ban Bi¶n tªp Thæng tin To¡n håc câ ¸n nh÷ nhúng èi t÷ñng to¡n håc °c °t h ng vi¸t b i chi ti¸t hìn v· c§u bi»t, c¡c c§u tróc li¶n quan mªt thi¸t tróc to¡n håc E8 °c bi»t n y. Chóng vîi nhau nh÷: nhâm Lie ìn °c bi»t, tæi hy vång ¡p ùng mët ph¦n þ muèn ¤i sè Lie ìn °c bi»t, h» nghi»m °c n y. Nhúng ëc gi£ quan t¥m chi ti¸t bi»t, v.v.... Nâ ÷ñc Whilhelm Killing hìn câ thº tham kh£o th¶m trong c¡c ÷a ra giúa nhúng n«n 1888 v 1890. t i li»u d¨n ð cuèi b i. W. Killing l mët nh to¡n håc câ nhi·u âng gâp trong lþ thuy¸t ph¥n 1 Ph¥n lo¤i c¡c nhâm lo¤i c¡c nhâm Lie v ¤i sè Lie ìn. Lie v ¤i sè Lie ¤i sè Lie e8 câ h¤ng (tùc l sè ìn v l g¼? chi·u cõa ¤i sè Lie con giao ho¡n cüc E8 ¤i) 8 v chi·u (nh÷ khæng gian v²ctì) l 248. C¡c v²ctì cõa h» nghi»m lªp 2 th nh mët l÷îi câ chi·u l 8. Nhâm ¤i sè Lie e8 câ ¤i sè Lie con so(16) c¡c ph²p ph£n x¤ t÷ìng ùng ch½nh l vîi 120 chi·u thüc v nâ câ 128 ph¦n nhâm Weyl cõa e8 công ch½nh l nhâm tû sinh thäa m¢n c¡c h» thùc Weyl- èi xùng cõa xuy¸n cüc ¤i t÷ìng ùng Majorana spinor cõa spin(16) cho t½ch v câ bªc l 696, 729, 600. Nhâm Lie Lie E8 l nhâm Lie ìn duy nh§t m biºu di¹n khæng t¦m th÷íng chi·u b² nh§t [Jij,Jk`] = δjkJi`−δj`Jik−δikJj`+δi`Jjk ch½nh l biºu di¹n phö hñp 248 chi·u çng thíi trong ch½nh ¤i sè Lie E8. 1 Nhâm Lie phùc , tùc l bao [Jij,Qa] = (γiγj − γjγi)abQb, (E8)C 4 phùc cõa nhâm Lie E8 thüc, câ sè chi·u thüc g§p æi, tùc l 496, m nâ còng vîi c¡c h» thùc cán l¤i (khæng kº câ 3 d¤ng thüc (real form) 248 chi·u ph£n-ho¡n tû) thüc l : [i j] [Qa,Qb] = γacγcbJij.
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