**VIASM Annual Meeting **is a regular activity of Vietnam Institute for Advance Study in Mathematics, to be organized once a year.

**Time:** 20/7 – 21/7/2013

**Venue: **Lecture hall, Vietnam Institute for Advance Study in Mathematics (VIASM)

7-th floor, Ta Quang Buu Library, in HUST’s campus; 1 Dai Co Viet street, Hanoi.

Organizers: Ngo Bao Chau (Univ. of Chicago – VIASM); Phung Ho Hai (Institute of Mathematics, Hanoi); Tran Thi Bich Diep (VIASM); Nguyen Ngoc Khoi (VIASM); Ngo Thien Nga (VIASM); Nguyen Ngoc Tuan (VIASM).

VIASM will invite highly reputed mathematicians to deliver lecturers on central topics of contemporary mathematics. The lecturers will provide the audience with most interested problems in their research fields, main ideas and main results. The lectures will be published in a special issue of Acta Mathematica Vietnamica.

The following scientists have agreed to deliver their lectures at VIASM Annual Meeting 2013:

- John Coates, Cambridge University, UK
- Dương Hồng Phong, Columbia University, USA
- Takeshi Saito, University of Tokyo, Japan
- Vasudevan Srinivas, Tata Institute, India
- Gan Wee Teck, National University of Singapore

**Registration:**

VIASM cordially invites all interested colleagues to participate VIASM Annual Meeting 2013. There will be no conference fee. For online registration, please go to: http://viasm.edu.vn/activities/am2013/registration?lang=en

You can also send an email attached a registration form to: am2013@viasm.edu.vn

**Deadlines for registration:** May 31, 2013.

**Financial support: ** VIASM will provide full accommodation for a limited number of young scientists and Ph.D, graduate students not coming from Hanoi to participate the Annual Meeting. A partial travel expense inside Vietnam could be also provided. To apply for the financial support please send an application form to VIASM at the email address mentioned above.

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Program

Saturday, July 20, 2013

Morning

7h45 – 8h30: Registration

8h30-8h45: Tea break

8h45-10h15: Lecture “Non-linear heat flows in complex geometry” presented by Professor Duong H. Phong

10h15-10h30: Tea break

10h30-12h00: Lecture “Recent Progress in the Gross-Prasad Conjecture” presented by Professor Gan Wee Teck.

Afternoon

14h00-14h15: Tea break

14h15-15h45: Lecture “The monodromy weight conjecture and perfectoid spaces” presented by Professor Takeshi Saito

15h45-16h00: Tea break

16h00: Round table discussion on the next meeting

Sunday, July 21, 2013

Morning

8h30-8h45: Tea break

8h45-10h15: Lecture “The Tate conjecture for K3 surfaces” presented by Professor Vansudevan Srinivas

10h15-10h30: Tea break

10h30-12h00: Lecture “Congruent Numbers” presented by Professor John Coates

Contents

1. Prof. John Coates – Cambridge University, UK

Title: Congruent Numbers

Abstract:

“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. Prof. Gan Wee Teck – National University of Singapore

Title: Recent Progress in the Gross-Prasad Conjecture

Abstract:

“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. Prof. Dương Hồng Phong – Columbia University, USA

Title: Non-linear heat flows in complex geometry

Abstract:

“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. Prof. Takeshi Saito – University of Tokyo, Japan

Title: The monodromy weight conjecture and perfectoid spaces

Abstract:

“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. Prof. Vasudevan Srinivas – Tata Institute, India

Title: The Tate conjecture for K3 surfaces

Abstract:

“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.”