Winter School on Geomtry, 2018

Organizers:

HU, Jianxun  (Sun Yat-sen University)
LI, Changzheng (Sun Yat-sen University)

Speakers:

Arguz, Hulya      (Imperial College London)

Betancourt, Luis Nunez   (CIMAT)

Leung, Naichung Conan  (Chinese University of Hong Kong)

Mikhalkin, Grigory      (University of Geneva)

Zhang, Lei        (Freie Universitat Berlin)

Program:

Venue: Room 416 (New Math. Building)

Banquet: 18:00-20:00  (Jan. 5)

Title and Abstracts:

Title: Real Lagrangians in toric degenerations (by Hulya Arguz)

Abstract: One of the main tools of the Gross-Siebert program in mirror symmetry is toric degenerations constructed from integral affine manifolds with singularities. The real loci of such degenerations provide interesting examples of Lagrangians which conjecturally are amenable to algebraic-geometric versions of Floer theory. In this talk I will discuss how the topology of the real locus can be understood by means of affine geometry and by Kato-Nakayama spaces associated to log spaces. This talk reports on joint work with Bernd Siebert.

Title: Local cohomology and geometry (by Luis Nunez Betancourt)

Abstract: Since the introduction of local cohomology by Grothendieck, it has proven a powerful tool in commutative algebra and algebraic geometry. These lectures intend to give an introduction to local cohomology with a strong emphasis on topological aspects measured by it. In particular, we will discuss how to detect and measure connectedness with this algebraic tool.

Title: G2 Geometry (by Conan Leung)

Abstract: I will explain the geometry of G2 manifolds in these lectures.

Title: Tropical and real algebraic methods in symplectic geometry. (by Grigory Mikhalkin)

Abstract: We'll review some techniques linking tropical, real algebraic and symplectic geometries. This includes constructions of Lagrangian varieties from tropical cycles (in particular, recovering Givental's theorem on Lagrangian embeddability of connected sums of Klein bottles to C2) as well as some integrable systems responsible for certain planar real algebraic curves (generalizaing a theorem of Kenyon and Okounkov on rigid isotopy of simple Harnack curves).

Title: Neukirch-Uchida Theorem for Purely Inseparable Field Extensions. (by Lei Zhang)

Abstract: In this talk I would like to introduce my recent result with M. Romagny, F. Tonini on Neukirch-Uchida theorem for purely inseparable field extensions. I will start with the famous anabelian conjecture by A. Grothendieck which predicts that there is a class of schemes which are recognizable by their fundamental groups. This class of schemes are the conjectural "anabelian schemes". It is known under the name "Neukirch-Uchida Theorem" that the sprectrum of number fields are anabelian. Then I will introduce the notion of Nori-local gerbe and the local fundamental group, I will also introduce a Tannakian description of those and how those gerbes or group schemes classify the finite local torsors. In the end I will show that purely inseparable field extensions are anabelian under the local fundamental group schemes, that is, they are recognizable by their local fundamental group schemes.

Accommodations and Local information:

Hotels on campus:
　

SYSU hotel & Conference Center（中山大学学人馆）
　

Address: North gate of Sun Yat-sen University, Bingjiang Dong Road, Haizhu District, Guangzhou

Tel: 020-89222888                 Website: http://www.syskaifeng.com

Contact information:

Ms. YU, Jinyun 
Email: yujin250 AT 163.com 

Prof. LI, Changzheng 
Email: lichangzh AT mail.sysu.edu.cn

Phone: +86-20-84111738 
School of Mathematical, Sun Yat-sen University, No. 135, Xingang Xi Road, Haizhu, Guangzhou, 510275, China