Цель коллоквиума – обсудить математические направления, интересные московскому и пекинскому научным сообществам, найти пересечения для их дальнейшего совместного развития, выделить темы для организации серии спецкурсов как в МГУ, так и в Пекинском университете.
Приглашаются все сотрудники, аспиранты и студенты, заинтересованные в сотрудничестве с представителями китайской математической школы.
Объявления о заседаниях будут появляться на следующей веб-странице: http://english.math.pku.edu.cn/conferences/242.html
Следующее заседание намечено на 12 июня 2020 (пятница), с 15:00 до 17:00 (время московское).
To join Zoom meeting:
https://zoom.com.cn/j/63647081382?pwd=Zy9DZkFMNDVBbEhGUmJra2gyRlFQZz09
Zoom ID：636 4708 1382
Password：705881
Lecture 1 – Slopes of modular forms and ghost conjecture of Bergdall and Pollack
Speaker：Prof. Xiao Liang （Beijing International Center for Math. Research ）
Time: 2020-06-12 20:00-21:00 Beijing time (15:00-16:00 Moscow time)
Abstract: In classical theory, slopes of modular forms are p-adic valuations of the eigenvalues of the Up-operator. On the Galois side, they correspond to the p-adic valuations of eigenvalues of the crystalline Frobenius on the Kisin's crystabelian deformations space. I will report on a joint work in progress in which we seems to have proved a version of the ghost conjecture of Bergdall and Pollack. This has many consequences in the classical theory, such as some cases of Gouvea-Mazur conjecture, and some hope towards understanding irreducible components of eigencurves. On the Galois side, our theorem can be used to prove certain integrality statement on slopes of crystalline Frobenius on Kisin's deformation space, as conjectured by Breuil-Buzzard-Emerton. This is a joint work with Ruochuan Liu, Nha Truong, and Bin Zhao.
Lecture 2 – Higher-dimensional Contou-Carrere symbols
Speaker：Prof. RAS Denis V. Osipov (Steklov Mathematical Institute of Russian Academy of Sciences)
Time: 2020-06-12 21:00-22:00 Beijing time (16:00-17:00 Moscow time)
Abstract: The classical Contou-Carrere symbol is the deformation of the tame symbol, so that residues and higher Witt symbols naturally appear from the Contou-Carrere symbol. This symbol was introduced by C. Contou-Carrere itself and by P. Deligne. It satisfies the reciprocity laws. In my talk I will survey on the higher-dimensional generalization of the Contou-Carrere symbol. The n-dimensional Contou-Carrere symbol naturally appears from the deformation of a full flag of subvarieties on an n-dimensional algebraic variety and it is also related with the Milnor K-theory of iterated Laurent series over a ring. The talk is based on joint papers with Xinwen Zhu (when n=2) and with Sergey Gorchinskiy (when n>2).