Thứ Bảy, 20/7/2013
Sáng
- 7h45 – 8h30: Đăng ký đại biểu
- 8h30-8h45: Tiệc trà
- 8h45-10h15: Bài giảng “Non-linear heat flows in complex geometry” bởi GS. Dương Hồng Phong (ĐH Columbia, Mỹ).
- 10h15-10h30: Tiệc trà giữa buổi
- 10h30-12h00: Bài giảng “The Tate Conjecture for K3 surfaces” bởi GS. Vansudevan Srinivas (Viện Tata, Ấn Độ).
Chiều
- 14h00-14h15: Tiệc trà
- 14h15-15h45: Bài giảng “The weight – monodromy conjecture and perfectoid spaces” bởi GS. Takeshi Saito (Đại học Tokyo, Nhật Bản).
- 15h45-16h00: Tiệc trà giữa buổi
- 16h00: Thảo luận bàn tròn về Hội thảo hàng năm 2014
Chủ Nhật, 21/7/2013
Sáng
- 8h30-8h45: Tiệc trà
- 8h45-10h15: Bài giảng “Recent progress in the Gross-Prasad Conjecture” bởi GS. Gan Wee Teck (Đại học Quốc gia Singapore).
- 10h15-10h30: Tiệc trà giữa buổi
- 10h30-12h00: Bài giảng “Congruent Numbers” bởi GS. John Coates (Đại học Cambridge, Anh).
Tóm tắt các bài giảng:
1. GS. John Coates – Đại học Cambridge, Anh
Tiêu đề: Congruent Numbers
Bản tóm tắt:
“The congruent number problem is the oldest unsolved major problem in number theory, and, in retrospect, the simplest and most down to earth example of the conjecture of Birch and Swinnerton-Dyer. After a brief description of the history of the problem, I shall discuss Y. Tian’s beautiful recent extension to composite numbers, with arbitrarily many prime factors, of Heegner’s original proof of the existence of infinitely many congruent numbers. I hope also to say a little at the end about possible generalizations of Tian’s work to other elliptic curves.”
2. GS. Gan Wee Teck – Đại học Quốc gia Singapore
Tiêu đề: Recent Progress in the Gross-Prasad Conjecture
Bản tóm tắt:
“I will discuss the local and global Gross-Prasad conjecture concerning the restriction of a representation or an automorphic form of a classical group to a smaller such group. In particular, I will discuss the resolution of the local conjecture by Waldspurger, Beuzart-Plessis and progress for the global conjecture due to Jacquet-Rallis, Wei Zhang, Yifeng Liu and Hang Xue. I will also mention a refinement of the global conjecture due to Ichino and Ikeda.”
3. GS. Dương Hồng Phong – Đại học Columbia, Mỹ
Tiêu đề: Non-linear heat flows in complex geometry
Bản tóm tắt:
“A fundamental result in complex geometry is the Uniformization Theorem, which asserts the existence of a metric of constant scalar curvature on complex curves. The analogue in higher dimensions would be the existence of a canonical metric, with or without singularities, as required by the underlying geometry. A powerful approach to the construction of such metrics is as fixed points of a non-linear heat flow. We discuss several such flows, including the Yang-Mills flow and the K\”ahler-Ricci flow, with emphasis on issues of long-time existence, convergence, or formation of singularities.”
4. GS. Takeshi Saito – Đại học Tokyo, Nhật Bản
Tiêu đề: The monodromy weight conjecture and perfectoid spaces
Bản tóm tắt:
“The monodromy weight conjecture is one of the main remaining open problems on Galois representations. It implies that the local Galois action on the l-adic cohomology of a proper smooth variety is almost completely determined by the traces. Peter Scholze proved the conjecture in many cases including smooth complete intersections in a projective space, using a new powerful tool in rigid geometry called perfectoid spaces. In the talk, I plan to sketch the main arguments of the proof after briefly introducing basic ingredients in the theory of perfectoid spaces.”
5. GS. Vasudevan Srinivas – Viện Tata, Ấn Độ
Tiêu đề: The Tate conjecture for K3 surfaces
Bản tóm tắt:
“The most important open questions in the theory of algebraic cycles are the Hodge Conjecture, and its companion problem, the Tate Conjecture. Both these questions attempt to give a description of those cohomology classes on a nonsingular proper variety which are represented by algebraic cycles, in terms of intrinsic structure which is present on the cohomology of such a variety (namely, a Hodge decomposition, or a Galois representation). For the Hodge conjecture, the case of divisors (algebraic cycles of codimen-sion 1) was settled long ago by Lefschetz and Hodge, and is popularly known as the Lefschetz (1; 1) theorem, though there is little general progress beyond that case. However, even this case of divisors is an open question for the Tate Conjecture, in general, even for divisors on algebraic surfaces. After giving an introduction to these problems, I will discuss the recent progress on the Tate Conjecture for K3 surfaces, around works of M. Lieblich and D. Maulik, F. Charles and K. Pera.”