Gerd Faltings, amesi ɖo kpe Mordell ƒe nususugblɔ dzi lae xɔ Abel ƒe Nunana

Dzidzedzekpɔkpɔ Ŋkuɖodzi aɖe le Akɔntabubu me

Norwaytɔwo ƒe Dzɔdzɔmeŋutinunya Kple Lɛtanyawo ƒe Suku tsɔ ƒe 2024 ƒe Abel Nunana, si nye bubu gãtɔ kekeake siwo woxɔna le akɔntabubu me la dometɔ ɖeka, na Nufialagã Gerd Faltings si le Max Planck ƒe Akɔntabubu Dɔwɔƒe. Kafukafu xɔŋkɔ sia de dzesi Faltings ƒe akpa si wòwɔ le xexlẽdzesiwo ŋuti nufiafia kple akɔntabubu ƒe geometry me si de to eye wòtrɔ ame, eye wòɖe dzesi wue nye eƒe kpeɖodzi yeye si wòɖo le ƒe 1983 me ɖe Mordell ƒe nususugblɔa ŋu. Ƒe bla nanewoe nye sia la, kuxi sia nɔ tsitre abe kuxi dziŋɔ aɖe ene, si tɔtɔ akɔntabubu ƒe susu gãtɔwo dometɔ aɖewo. Menye ɖeko Faltings ƒe dzidzedzekpɔkpɔ kpɔ nya ɣaɣla vevi aɖe gbɔ ko o, ke eʋu numekuku ƒe mɔnu yeyewo kura hã, si na dɔwɔnu sẽŋuwo na akɔntanyala siwo woatsɔ aku Diophantin ƒe sɔsɔŋusẽwo ƒe xexeame katã si me kɔ la me.

Seɖoƒemanɔsitɔ ƒe Taming: Nukae nye Mordell ƒe Nususugblɔ?

Be ame nase Faltings ƒe dɔa ƒe vevienyenye gɔme la, ele be wòase kuxi si gbɔ wòkpɔ la ƒe nɔnɔme gɔme gbã. Louis Mordell ye do susua ɖa le ƒe 1922 me, eye nususugblɔ sia ku ɖe agbɔsɔsɔme ƒe sɔsɔŋusẽ ƒomevi aɖewo gbɔ kpɔnu ŋu—vevietɔ, esiwo ɖɔa ʋuʋudedi siwo ƒe nɔnɔme sesẽ aɖe (ƒomevi si lolo wu 1). Dzodzro bɔbɔe abe x2 + y2 = 1 (si ɖɔa gotagome) ƒe egbɔkpɔnu siwo me susu le sɔ gbɔ seɖoƒemanɔmee. Gake Mordell susui be le fli siwo gɔme sese sesẽ wu, siwo nye "ƒomevi kɔkɔtɔwo" gome—kpɔ donut alo nane si gɔme sese sesẽ wu gɔ̃ hã ƒe anyigba le susu me—la, nusi to vovo na emae nye nyateƒe. Egblɔe ɖi be egbɔkpɔnu siwo me susu le ƒe xexlẽme seɖoƒe koe ate ŋu anɔ sɔsɔŋusẽ mawo tɔgbe me. Faltings ƒe kpeɖodzi ɖo kpe nukpɔsusu sia dzi, si ɖee fia be akɔntabubu ƒe nɔnɔme na ʋuʋudedi sesẽ siawo menye liƒo si seɖoƒe meli na o, si nye gbemelã, ke boŋ enye domenyinyi si me teƒe tɔxɛwo ƒe xexlẽme seɖoƒe li na, si dzi woate ŋu akpɔ ŋusẽ ɖo.

Tɔtrɔ Kpata ƒe Dɔwɔnuwo: Arakelov ƒe Nufiafia Kple Edzi

Faltings meɖo kpe Mordell ƒe nususugblɔ dzi to mɔnu xoxowo zazã me o; etrɔ asi le dɔa ŋu to yeyewo toto vɛ me. Eƒe kpeɖodzia nye susu siwo tso xexlẽdzesiwo ŋuti nufiafia kple akɔntabubu ƒe nɔnɔmetatawo me ƒe ƒuƒoƒo gã aɖe, si ɖe dzesi wue nye eƒe Arakelov nufiafia ƒe ŋgɔyiyi. Dɔwɔɖoɖo sia ɖea mɔ na akɔntanyalawo be woasrɔ̃ nu tso xexlẽdzesiwo ƒe agblewo (akɔntabubu ƒe afisi) kple dɔwɔwɔ ƒe agblewo (geometry ƒe nuto) ŋu le mɔ ɖeka nu, si wɔa tɔdzisasrã nyuie le akɔntabubu ƒe anyigbagã gã eve dome. Esi Faltings tsɔ geometrimɔnu sẽŋuwo va akɔntabubu ƒe xexeame la, ena nukpɔsusu yeye kura va su ame si ku ɖe kuxi siwo li tso gbaɖegbe ke ŋu. Eƒe mɔnu yeyea lɔ nukpɔsusuwo abe:

ƒe nyawo
• Arakelov Nukpɔsusu: Akɔntabubu ƒe ɖoɖowo ƒe "nuwɔwɔ ɖekae" nana be woatsɔ awɔ geometric intuition ŋudɔ.
• Faltings' Height: Mɔ deŋgɔ aɖe si dzi woato "dzidze" akɔntabubu ƒe nusiwo ƒe sesẽme.
• Seɖoƒe ƒe Dɔwɔnuwo: Mɔnu yeye siwo woatsɔ aɖo kpe edzi be egbɔkpɔnu ƒe hatsotso aɖewo seɖoƒe li na.

Dɔwɔnu sia sẽ ŋu ale gbegbe be menye ɖeko wòkpɔ Mordell ƒe nususugblɔa gbɔ ko o, ke ewɔ akpa aɖe hã le Andrew Wiles ƒe kpeɖodzi mlɔeba le Fermat ƒe Nukpɔsusu Mamlɛa ŋu.

ƒe nyawo "Teƒe siwo me susu le ƒe xexlẽme le ƒome ƒe fli si lolo wu ɖeka dzi la seɖoƒe li na." — Gerd Faltings ƒe Nyagɔmeɖegbalẽ (Mordell ƒe Nususugblɔ)

Nuwɔwɔ pɛpɛpɛ kple Ŋusẽ: Nusɔsrɔ̃ na Egbegbe Asitsatsa

Gerd Faltings ƒe ŋutinya nye ɖaseɖiɖi sẽŋu aɖe le ŋusẽ si ɖoɖo nyuitɔ ƒe amesinɔnɔ kpɔna ɖe ame dzi ŋu. Abe alesi Arakelov ƒe nufiafia na ɖoɖo si hiã be woatsɔ akpɔ kuxi aɖe si dze abe womate ŋu akpɔ egbɔ o ene gbɔ ene la, nenema ke egbegbe dɔwɔƒewo hiã dɔwɔɖoɖo sesẽ aɖe be woatsɔ akpɔ woawo ŋutɔ ƒe kuxi sesẽwo gbɔe. Mɔnu si me mama le si zãa nyatakakagbalẽvi siwo me kadodo aɖeke mele o, kadodomɔnu, kple dɔa dzi kpɔkpɔ ƒe dɔwɔnuwo naa nɔnɔme si me zitɔtɔ le si me taɖodzinu siwo woatsɔ awɔ dɔe la buna le. Afi siae nuƒolanɔƒe si wɔ ɖeka abe Mewayz ene va zua nu vevi aɖe le. Mewayz wɔa dɔ abe modular business OS ene, eƒoa dɔ veviwo nu ƒu—tso dɔa dzikpɔkpɔ kple CRM dzi va ɖo ganyawo dzi kpɔkpɔ dzi—zu ɖoɖo ɖeka si wɔ ɖeka. Abe alesi Faltings ƒe akɔntabubu ƒe ɖoɖoa na ɖoɖo va kuxi aɖe si dze abe zitɔtɔ ene gbɔ ene la, Mewayz hea eme kɔ nyuie eye wòwɔa dɔ nyuie le asitsatsa ƒe dɔwɔnawo me, si wɔnɛ be kplɔlawo te ŋu léa fɔ ɖe aɖaŋunu yeyewo dodo ɖe ŋgɔ ŋu tsɔ wu be woatsɔ woƒe susu aɖo dɔdzikpɔkpɔ ƒe gazazãwo ŋu. To dɔwɔnuwo kple nyatakakawo ƒoƒo ƒu ɖekae me la, asitsaha ate ŋu aɖo nusi sɔ pɛpɛpɛ kple gɔmesese ƒe seƒe si ne menye nenema o la, manya wɔ o, si atrɔ kuxi sesẽwo woazu sɔsɔŋuɖoɖo siwo dzi woate ŋu akpɔ wo gbɔ le.

Nugɔmesese Deto ƒe Domenyinu

Gerd Faltings ƒe Abel Nunana nye akɔntabubu ƒe gɔmesese deto ƒe agbemeŋkekewo katã ƒe azãɖuɖu. Menye nuwuƒe dzro aɖe koe wòɖo kpe Mordell ƒe nususugblɔa dzi o ke boŋ enye gɔmedzedze, si ʋã akɔntanyala ƒe dzidzimewo eye wòna míaƒe gɔmesese deto ɖe akɔntabubu ƒe gɔmeɖoanyi veviwo ŋu. Eƒe dɔa nye alesi nukpɔsusu ƒe ɖoɖo nyuitɔ tutu ate ŋu aʋu kuxi siwo nɔ anyi ƒe alafa ɖeka la gbɔ kpɔnu ƒe kpɔɖeŋu. Le xexlẽdzesiwo ŋuti nufiafia ƒe xexe si me susu mele o kple asitsatsa ƒe xexe ŋutɔŋutɔ siaa me la, gɔmeɖosea gakpɔtɔ le ɖeka: eme kɔ, ɖoɖowɔwɔ, kple ƒoƒo ɖekae nye nu vevi siwo ana woabi ɖe nusiwo sesẽ me eye woakpɔ emetsonu yeyewo.

Nyabiase Siwo Wobiana Enuenu

Dzidzedzekpɔkpɔ Ŋkuɖodzi aɖe le Akɔntabubu me

Norwaytɔwo ƒe Dzɔdzɔmeŋutinunya Kple Lɛtanyawo ƒe Suku tsɔ ƒe 2024 ƒe Abel Nunana, si nye bubu gãtɔ kekeake siwo woxɔna le akɔntabubu me la dometɔ ɖeka, na Nufialagã Gerd Faltings si le Max Planck ƒe Akɔntabubu Dɔwɔƒe. Kafukafu xɔŋkɔ sia de dzesi Faltings ƒe akpa si wòwɔ le xexlẽdzesiwo ŋuti nufiafia kple akɔntabubu ƒe geometry me si de to eye wòtrɔ ame, eye wòɖe dzesi wue nye eƒe kpeɖodzi yeye si wòɖo le ƒe 1983 me ɖe Mordell ƒe nususugblɔa ŋu. Ƒe bla nanewoe nye sia la, kuxi sia nɔ tsitre abe kuxi dziŋɔ aɖe ene, si tɔtɔ akɔntabubu ƒe susu gãtɔwo dometɔ aɖewo. Menye ɖeko Faltings ƒe dzidzedzekpɔkpɔ kpɔ nya ɣaɣla vevi aɖe gbɔ ko o, ke eʋu numekuku ƒe mɔnu yeyewo kura hã, si na dɔwɔnu sẽŋuwo na akɔntanyala siwo woatsɔ aku Diophantin ƒe sɔsɔŋusẽwo ƒe xexeame katã si me kɔ la me.

Seɖoƒemanɔsitɔ ƒe Taming: Nukae nye Mordell ƒe Nususugblɔ?

Be ame nase Faltings ƒe dɔa ƒe vevienyenye gɔme la, ele be wòase kuxi si gbɔ wòkpɔ la ƒe nɔnɔme gɔme gbã. Louis Mordell ye do susua ɖa le ƒe 1922 me, eye nususugblɔ sia ku ɖe agbɔsɔsɔme ƒe sɔsɔŋusẽ ƒomevi aɖewo gbɔ kpɔnu ŋu—vevietɔ, esiwo ɖɔa ʋuʋudedi siwo ƒe nɔnɔme sesẽ aɖe (ƒomevi si lolo wu 1). Dzodzro bɔbɔe abe x2 + y2 = 1 (si ɖɔa gotagome) ƒe egbɔkpɔnu siwo me susu le sɔ gbɔ seɖoƒemanɔmee. Gake Mordell susui be le fli siwo gɔme sese sesẽ wu, siwo nye "ƒomevi kɔkɔtɔwo" gome—kpɔ donut alo nane si gɔme sese sesẽ wu gɔ̃ hã ƒe anyigba le susu me—la, nusi to vovo na emae nye nyateƒe. Egblɔe ɖi be egbɔkpɔnu siwo me susu le ƒe xexlẽme si seɖoƒe li na koe ate ŋu anɔ sɔsɔŋusẽ mawo tɔgbe me. Faltings ƒe kpeɖodzi ɖo kpe nukpɔsusu sia dzi, si ɖee fia be akɔntabubu ƒe nɔnɔme na ʋuʋudedi sesẽ siawo menye liƒo si seɖoƒe meli na o, si nye gbemelã, ke boŋ enye domenyinyi si me teƒe tɔxɛwo ƒe xexlẽme seɖoƒe li na, si dzi woate ŋu akpɔ ŋusẽ ɖo.

Tɔtrɔ Kpata ƒe Dɔwɔnuwo: Arakelov ƒe Nufiafia Kple Edzi

Faltings meɖo kpe Mordell ƒe nususugblɔ dzi to mɔnu xoxowo zazã me o; etrɔ asi le dɔa ŋu to yeyewo toto vɛ me. Eƒe kpeɖodzia nye nukpɔsusu siwo tso xexlẽdzesiwo ŋuti nufiafia kple algebra ƒe geometry me ƒe ƒuƒoƒo gã aɖe, si ɖe dzesi wue nye alesi wòto Arakelov nufiafia vɛ. Dɔwɔɖoɖo sia ɖea mɔ na akɔntanyalawo be woasrɔ̃ nu tso xexlẽdzesiwo ƒe agblewo (akɔntabubu ƒe afisi) kple dɔwɔwɔ ƒe agblewo (geometry ƒe nuto) ŋu le mɔ ɖeka nu, si wɔa tɔdzisasrã nyuie le akɔntabubu ƒe anyigbagã gã eve dome. Esi Faltings tsɔ geometrimɔnu sẽŋuwo va akɔntabubu ƒe xexeame la, ena nukpɔsusu yeye kura va su ame si ku ɖe kuxi siwo li tso gbaɖegbe ke ŋu. Eƒe mɔnu yeyea lɔ nukpɔsusuwo abe:

Nuwɔwɔ pɛpɛpɛ kple Ŋusẽ: Nusɔsrɔ̃ na Egbegbe Asitsatsa

Gerd Faltings ƒe ŋutinya nye ɖaseɖiɖi sẽŋu aɖe le ŋusẽ si ɖoɖo nyuitɔ ƒe amesinɔnɔ kpɔna ɖe ame dzi ŋu. Abe alesi Arakelov ƒe nufiafia na ɖoɖo si hiã be woatsɔ akpɔ kuxi aɖe si dze abe womate ŋu akpɔ egbɔ o ene gbɔ ene la, nenema ke egbegbe dɔwɔƒewo hiã dɔwɔɖoɖo sesẽ aɖe be woatsɔ akpɔ woawo ŋutɔ ƒe kuxi sesẽwo gbɔe. Mɔnu si me mama le si zãa nyatakakagbalẽvi siwo me kadodo aɖeke mele o, kadodomɔnu, kple dɔa dzi kpɔkpɔ ƒe dɔwɔnuwo naa nɔnɔme si me zitɔtɔ le si me taɖodzinu siwo woatsɔ awɔ dɔe la buna le. Afi siae nuƒolanɔƒe si wɔ ɖeka abe Mewayz ene va zua nu vevi aɖe le. Mewayz wɔa dɔ abe modular business OS ene, eƒoa dɔ veviwo nu ƒu—tso dɔa dzikpɔkpɔ kple CRM dzi va ɖo ganyawo dzi kpɔkpɔ dzi—zu ɖoɖo ɖeka si wɔ ɖeka. Abe alesi Faltings ƒe akɔntabubu ƒe ɖoɖoa na ɖoɖo va kuxi aɖe si dze abe zitɔtɔ ene gbɔ ene la, Mewayz hea eme kɔ nyuie eye wòwɔa dɔ nyuie le asitsatsa ƒe dɔwɔnawo me, si wɔnɛ be kplɔlawo te ŋu léa fɔ ɖe aɖaŋunu yeyewo dodo ɖe ŋgɔ ŋu tsɔ wu be woatsɔ woƒe susu aɖo dɔdzikpɔkpɔ ƒe gazazãwo ŋu. To dɔwɔnuwo kple nyatakakawo ƒoƒo ƒu ɖekae me la, asitsaha ate ŋu aɖo nusi sɔ pɛpɛpɛ kple gɔmesese ƒe seƒe si ne menye nenema o la, manya wɔ o, si atrɔ kuxi sesẽwo woazu sɔsɔŋuɖoɖo siwo dzi woate ŋu akpɔ wo gbɔ le.

Nugɔmesese Deto ƒe Domenyinu

Gerd Faltings ƒe Abel Nunana nye akɔntabubu ƒe gɔmesese deto ƒe agbemeŋkekewo katã ƒe azãɖuɖu. Menye nuwuƒe dzro aɖe koe wòɖo kpe Mordell ƒe nususugblɔa dzi o ke boŋ enye gɔmedzedze, si ʋã akɔntanyala ƒe dzidzimewo eye wòna míaƒe gɔmesese deto ɖe akɔntabubu ƒe gɔmeɖoanyi veviwo ŋu. Eƒe dɔa nye alesi nukpɔsusu ƒe ɖoɖo nyuitɔ tutu ate ŋu aʋu kuxi siwo nɔ anyi ƒe alafa ɖeka la gbɔ kpɔnu ƒe kpɔɖeŋu. Le xexlẽdzesiwo ŋuti nufiafia ƒe xexe si me susu mele o kple asitsatsa ƒe xexe ŋutɔŋutɔ siaa me la, gɔmeɖosea gakpɔtɔ le ɖeka: eme kɔ, ɖoɖowɔwɔ, kple ƒoƒo ɖekae nye nu vevi siwo ana woabi ɖe nusiwo sesẽ me eye woakpɔ emetsonu yeyewo.