Emma Previato

Emma Previato
	;
Umumiy maʼlumotlar
Tavalludi	29-noyabr 1952; Badia Polesine
Vafoti	29-iyun 2022; Boston
Qardosh loyihalar
	Vikipediyadagi maqola Vikimaʼlumotlar sahifasi Vikiombordagi tasvirlar

Emma Previato (1952-yil 29-noyabr – 2022-yil 29-iyun) — Italiyada tugʻilgan, AQSHlik matematik. Algebraik geometriya va xususiy hosilali differensial tenglamalar sohasida ixtisoslashgan. U 2012-yilda Amerika Matematika Jamiyatining a’zoligiga saylangan.

Iqtiboslar

Teta funksiyalarining tabiati differensial tenglama va duallikka borib taqaladi. Ikki oʻzgaruvchi orasidagi oʻzaro bogʻliqlik hamon sirli boʻlib qolmoqda. Davrlar panjarasi tufayli, teta funksiyasi bir vaqtning oʻzida algebraik geometriyaning eng qudratli obyektlaridan biri hisoblanadi. Egri chiziqlar nazariyasining (Riman sirtlari) koʻplab klassik matematikasi aynan shu algebraik jihatdan kelib chiqqan. Asosiy gʻoya — egri chiziq ustidagi chiziqli qatlamlarning moduli fazosini asosiy qutblangan Abel xilma-xilligi sifatida talqin qilishdir. Uning oʻz-oʻziga duallik xususiyatidan foydalanish ikki oʻzgaruvchini ta’minlaydiki, ularning dualligi KP (Kadomtsev-Petviashvili) prototip boʻlgan qator nolineer xususiy hosilali differensial tenglamalarni (PDE) chiziqlilashtirishga xizmat qiladi^[1].

The nature of theta functions comes down to a differential equation and a duality. The interplay between the two variables is still something of a mystery (to this writer). By virtue of the lattice of periods, the theta function is at the same time one of the most powerful objects of algebraic geometry. Much classical mathematics of curve theory (Riemann surfaces) is derived using this algebraic aspect. The key idea is to interpret the moduli space of line bundles over the curve as a principally polarized abelian variety. Exploitng its self-dual property provides two variables whose duality establishes a linearization of the class of non-linear PDEs that have KP as a prototype.

1980-yillarning boshida kiritilgan ayrim mexanik tizimlarning Algebraik toʻliq integrallanuvchanligi (ACI) tushunchasi algebraik egri chiziq (yoki hali kamroq oʻrganilgan yuqori oʻlchamli xilma-xilliklar) ustidagi golomorf vektor qatlamlarining moduli fazolarini oʻrganishga katta turtki berdi. „Duallik“ning bir qancha koʻrinishlari har ikkala nazariyada ham katta qiziqish uygʻotdi. Biroq, 2-jinsli (genus-2) egri chiziqlarning oʻziga xos goʻzal xususiyati boʻlgan bir misol mavjud. Ushbu qaydda ACIning „universal“ sinfiga, ya’ni (umumlashtirilgan) Xitchin (Hitchin) tizimlariga tegishli boʻlgan oʻsha misol, Nyusted hamda Narasimxan-Ramanan dasturiga muvofiq, moduli fazolarini proyektiv modellar orqali oʻrganish va Kleynning kvadratik kompleksi klassik geometriyasi nuqtai nazaridan talqin qilinadi^[2].

The notion of Algebraic Complete Integrability (ACI) of certain mechanical systems, introduced the early 1980s, has given great impetus to the study of moduli spaces of holomorphic vector bundles over an algebraic curve ... several notions of 'duality' have been the object of much interest in both theories. There is one example, however, that appears to be a beautiful isolated feature of genus-2 curves. In this note such example, which belongs to a 'universal' class of ACIs, namely (generalized) Hitchin systems, is interpreted in the setting of the classical geometry of Klein's quadratic complex, following the Newstead and Narasimhan-Ramanan programme of studying moduli spaces through projective models.

Ushbu iqtibos Emma Previatoning (yoki unga zamondosh bo'lgan matematik ayolning) ilmiy karerasidagi ijtimoiy va professional qiyinchiliklar hamda ustoz-shogirdlik (mentoring) an'analarining ahamiyati haqidagi fikrlarini aks ettiradi. 1970-yillarda STEM sohalarida (fan, texnologiya, muhandislik va matematika) ayollarning o'rni juda kam bo'lgan davrdagi tajribalar bu yerda bayon etilgan.

Vikiiqtibos (Wikiquote) uchun o'zbekcha tarjima:

Ayollar kamchilikni tashkil etgan 1970-yillarda voyaga yetgan matematik sifatida, men kasbiy e’tirofga erishgan kam sonli ayollar bilan kamdan-kam uchrashuvlarim chogʻida tajribaga asoslangan maslahatlar shaklida norasmiy ustozlik saboqlarini oldim; ularning hikmatli soʻzlari menga matonat bilan davom etish imkonini beruvchi muhim manba boʻldi. Men „Every Other Thursday“ (Daniell 2006) kitobidan ilhomlandim; u olimlar, universitet professorlari va ma’murlardan iborat bir guruh professional ayollarning yigirma besh yil davomida oyiga ikki marta uchrashib, maqsadlar qoʻyish, aloqalar oʻrnatish va bir-birlarining yutuqlarini kuzatib borish kabi aniq amaliyotlarni yoʻlga qoʻygani haqida hikoya qiladi. Men STEM sohasiga qiziqqan ayollar va qizlar uchun tizimli ustozlik namunalarini yanada koʻproq ko'rishdan ilhomlanaman^[3].

As a mathematician coming of age in the early years when women were underrepresented, namely the 1970s, I received informal mentoring in the form of experiential advice from rare encounters with females who had achieved professional recognition; their words of wisdom were substantive resources that allowed me to persevere. I am inspired by the book Every Other Thursday (Daniell 2006) which tells the story of a group of professional women ... establishing specific practices such as goal setting, networking, and checking on each other's progress. I am inspired to see more intentional examples of mentoring taking panel for women and girls interested in the STEM field.

Manbalar

↑ „Theta functions, old and new by Emma Previato“, The Ubiquitous Heat Kernel: AMS Special Session, the Ubiquitous Heat Kernel, October 2-4, 2003, Boulder, Colorado, Contemporary Mathematics, volume 398. American Mathematical Society, 2006 — 347–367-bet. DOI:10.1090/conm/398/07496. ISBN 9780821836989. edited by Jay Jorgensen & Lynn Walling
↑ „Chapter 11. Dualities on 𝒯^∗𝒮𝒰_X(2,𝒪_X) by Emma Previato“, Moduli Spaces and Vector Bundles. Cambridge University Press, 2009 — 367–387-bet. ISBN 9780521734714. edited by Steve B. Bradlow, Leticia Brambila-Paz, Oscar García-Prada, & Sundararaman Ramanan
↑ „Chapter 10. Mentoring Practices for Female Faculty: The Role of Professional Networks by Emma Previato“, Mentoring Away the Glass Ceiling in Academia: A Cultured Critique. Lexington Books, 10 June 2015. ISBN 9781498515313. p. 176 (edited by Brenda Marina; quote from pp. 175–176; See Every Other Thursday by Ellen Daniell.)

[1] „Theta functions, old and new by Emma Previato“, The Ubiquitous Heat Kernel: AMS Special Session, the Ubiquitous Heat Kernel, October 2-4, 2003, Boulder, Colorado, Contemporary Mathematics, volume 398. American Mathematical Society, 2006 — 347–367-bet. DOI:10.1090/conm/398/07496. ISBN 9780821836989. edited by Jay Jorgensen & Lynn Walling

[2] „Chapter 11. Dualities on 𝒯^∗𝒮𝒰_X(2,𝒪_X) by Emma Previato“, Moduli Spaces and Vector Bundles. Cambridge University Press, 2009 — 367–387-bet. ISBN 9780521734714. edited by Steve B. Bradlow, Leticia Brambila-Paz, Oscar García-Prada, & Sundararaman Ramanan

[3] „Chapter 10. Mentoring Practices for Female Faculty: The Role of Professional Networks by Emma Previato“, Mentoring Away the Glass Ceiling in Academia: A Cultured Critique. Lexington Books, 10 June 2015. ISBN 9781498515313. p. 176 (edited by Brenda Marina; quote from pp. 175–176; See Every Other Thursday by Ellen Daniell.)

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