AG Activities in ChinaAlgebraic geometry activities in Beijing and throughout China.
http://www.alggeom.org/
2018Sat, 29 Sep 2018 06:25:14 -0700
http://www.alggeom.org/blog/2018
http://www.alggeom.org/blog/2018<p><em>10th Meeting, September 29, 2018, Tsinghua</em></p><h3><p>Ahmed Abbes (CNRS & IHÉS)</p></h3><p><em>The p-adic Simpson correspondence</em></p><p>The p-adic Simpson correspondence, initiated by Gerd Faltings in 2005, aims at describing all p-adic representations of the fundamental group of a proper smooth variety over a p-adic field in terms of linear algebra - namely Higgs bundles. My lecture will be an introduction to this topic. I will focus on the approach that I developed with Michel Gros relying on a new family of period rings built from the torsor of deformations of the variety over a universal p-adic thickening defined by J.-M. Fontaine.</p><h3><p>Daxin Xu (Caltech)</p></h3><p><em>Generalized Kloosterman sheaves and their p-adic variants</em></p><p>I will first review the relationship between the classical Bessel equation and the classical Kloosterman sum. Such a relation can be regarded as an instance of the geometric Langlands correspondence for GL2. I will then explain the recent generalizations of this story for arbitrary reductive groups, based on the works by Frenkel-Gross, Heinloth-Ngo-Yun, and X. Zhu. In the end, I will discuss some joint work in progress with X. Zhu, where we study the p-adic aspect of this theory.</p><p><em>11th Meeting, October 17, 2018, CAS</em></p><h3><p>Constantin Shramov (Steklov Institute)</p></h3><p><em>Finite groups of birational selfmaps of surfaces</em></p><p>I will speak about finite groups acting by birational automorphisms of surfaces. In particular, we will consider surfaces over function fields. One of our important observations here is that for a smooth geometrically rational surface S, either it is birational to a product of a projective line and a conic (so that S is rational provided that it has a point), or finite subgroups of its birational automorphism group are bounded. I will also discuss some particular types of surfaces with interesting automorphism groups, including Severi-Brauer...<a href=http://www.alggeom.org/blog/2018>Read More</a>2017Fri, 13 Oct 2017 23:16:58 -0700
http://www.alggeom.org/blog/2017
http://www.alggeom.org/blog/2017<p><em>9th Meeting, October 14, 2017, BICMR, PKU</em></p><h3><p>Kevin Tucker (UIC)</p></h3><p><em>Bertini theorems for F-signature</em></p><p>In characteristic zero, it is well known that multiplier ideals and log terminal singularities satisfy Bertini-type theorems for hyperplane sections. In characteristic p > 0, the analogous statements for test ideals are more complicated: while F-regular singularities satisfy Bertini, the test ideal does not. In this talk, I will describe joint work with Karl Schwede and Javier Carvajal-Rojas showing that the F-signature – a numerical invariant of singularities that detects F-regularity – satisfies the relevant Bertini statements for hyperplane sections. In particular, one can view this as a generalization of the corresponding results for F-regularity.</p><h3><p>Roberto Svaldi (Cambridge)</p></h3><p><em>Log birational boundedness of Calabi-Yau pairs</em></p><p>I will discuss new results towards the birational boundedness of Calabi-Yau pairs. Recent work in the minimal model program suggests that pairs with trivial log canonical class should satisfy some boundedness properties.</p><p>I will show that 4-dimensional Calabi-Yau pairs which are not birational to a product are indeed log birationally bounded. This implies birational boundedness of elliptically fibered Calabi-Yau manifolds with a section, in dimension up to 5. This is joint work with Gabriele Di Cerbo.</p><h3><p>Xuanyu Pan (AMSS, CAS)</p></h3><p><em>Cycles on Fano manifolds</em></p><p>In this talk, I will give a survey about cycles on Fano manifolds including a recent joint work with Cristian Minoccheri. The philosophy is that the positivity of the tangent bundle implies the simplicity of the cycle relations. At the end of this talk, I will talk about some speculation on 1-cycles on Fano manifolds.</p><a href=http://www.alggeom.org/blog/2017>Read More</a>2016Fri, 04 Mar 2016 19:57:32 -0800
http://www.alggeom.org/blog/2016
http://www.alggeom.org/blog/2016<p><em>4th Meeting, March 5, 2016, AMSS, CAS</em></p><h3><p>Kang Zuo (Mainz)</p></h3><p><em>Periodic Higgs bundle in postive and mixed characteristic</em><br>I shall first explain briefly the notion "Higgs-de Rham flow" on a smooth quasiprojective scheme X/W(k) and the induced p-adic correspondence between the category of crystalline representations of the etale fundamental group of the generic fibre of X and the category of periodic Higgs bundles on X. As an application we construct an absolute irreducible rank-2 crystalline representation of the etale fundamental group of a so-called canonical lifted hyperbolic curve via the uniformization Higgs bundle, which should be regarded as a p-adic analogue of Hitchin-Simpson's uniformization theorem on complex hyperbolic curves via uniformization Higgs bundles. This talk is based on my joint papers with Lan, Sheng and Yang.</p><h3><p>Hui-Wen Lin (NTU)</p></h3><p><em>Quantum cohomology under smooth blow-ups along complete intersection centers</em><br>I would like to consider the Dubrovin (flat) connection on TH(X) and analyze its behavior under various maps including complete intersection imbedding and projective bundle maps. The essential mathematical tools are the corresponding Quantum Lefschetz Hyperplane Theorem and the Quantum Leray-Hirsch Theorem. By combining these two theorems, I can discuss an application on smooth blow-ups along complete intersection centers and succeed in determining a blow-up formula of quantum cohomology.</p><h3><p>Chin-Lung Wang (NTU)</p></h3><p><em>Simple flips and quantum cohomology</em><br>I will present a recent joint work with Yuan-Pin Lee and Hui-Wen Lin on on quantum cohomology rings under simple ordinary flips. There is a natural decomposition of quantum rings which refines the decomposition of motives. In contrast to the case of flops, where analytic continuation exists, the new phenomenon appeared here is the irregularity of the Dubrovin connections along the kernel factor under...<a href=http://www.alggeom.org/blog/2016>Read More</a>2015Sat, 09 May 2015 20:37:25 -0700
http://www.alggeom.org/blog/2015
http://www.alggeom.org/blog/2015<p><em>1st Meeting, May 10, 2015, BICMR, PKU</em></p><h3><p>Hélène Esnault (FU Berlin)</p></h3><p><em>Entropy of automorphisms on surfaces in positive characteristic</em><br>We shall review the notion of entropy in this context and show the existence of automorphisms of maximal entropy, the logarithm of a degree 22 Salem number, on a supersingular K3 surface, which thus does not lift to characteristic zero. (Based on joint work with V. Srinivas, K. Oguiso and K. Oguiso-X. Yu).</p><h3><p>Lawrence Ein (UIC)</p></h3><p><em>Asymptotic syzygies</em><br>We discuss joint work with Robert Lazarsfeld on asymptotic syzgies. We discuss our work on the gonality conjecture, which says that one can determine the gonality of a smooth curve X of genus g from the shape of the minimal resolution of the section ring of a line bundle L on X, when degree of L is sufficiently large. We also plan to discuss the shape of the minimal resolution of the section ring of (X, L), where X is a smooth projective variety of dimension n and L is a sufficiently positive line bundle on X.</p><p><em>2nd Meeting, September 26, 2015, AMSS, CAS</em></p><h3><p>Xin Lv (Mainz) on behalf of Kang Zuo</p></h3><p><em>On finiteness of CM jacobians of smooth hyperelliptic curves and superelliptic curves</em></p><p>Coleman’s conjecture predicts that for g sufficiently large there exists at most finitely many smooth complex projective curves of genus g (up to isomorphism) whose jacobians are CM abelian varieties. Based on the recent work by Tsimerman on the solution of André-Oort conjecture and my recent joint works with Ke Chen and Xin Lv on Oort conjectue for hyperelliptic curves and superelliptic curves we show Coleman’s conjecture holds true for those two cases.</p><h3><p>Kwokwai Chan (CUHK)</p></h3><p><em>Scattering diagrams and deformation theory</em></p><p>Given a Calabi-Yau manifold equipped with a Lagrangian torus fibration, we introduce a DGLA via Witten deformation, which is mirror to the...<a href=http://www.alggeom.org/blog/2015>Read More</a>