Associate Professor in Mathematics
Department of Mathematics
University of Georgia
Athens, GA 30606
Email: weiwei d0t wu@uga do/t edu
Carnation, Lily, Lily, Rose
John Singer Sargent
I was born in Guangzhou, China, and got my B.S. in Mathematics at Peking University , Beijing, China in 2006. In 2012, I accomplished my Ph.D. degree in Mathematics at the University of Minnesota under the supervision of Professor Tian-Jun Li.
My research interests lie in symplectic geometry and topology, including Floer theories, homological mirror symmetry, symplectomorphism groups, topology of Lagrangian submanifolds. Recently I also got interested in some problems in C1-generic dynamical systems.Here is my CV.
- 14. Spherical twists and Lagrangian spherical manifolds
We study Dehn twists along Lagrangian submanifolds that are finite quotients of spheres. We decribe the induced auto-equivalences to the derived Fukaya category and explain its relation to twists along spherical functors. A new phenomenon is observed in this type of auto-equivalence: they decompose into spherical twists in characteristic zero, and yields completely new auto-equivalences in non-zero characteristics.
- 13. Symplectic rational G-surfaces and equivariant symplectic cones.
We give characterizations of a finite group G acting symplectically on a rational surface (\CP^2 blown up at two or more points). In particular, we obtain a symplectic version of the dichotomy of G-conic bundles versus G-del Pezzo surfaces for the corresponding G-rational surfaces, analogous to a classical result in algebraic geometry.
- J. Differ. Geom., to appear
arXiv:1708.07500. Slides (IBS-Pohang) (with Weimin Chen, Tian-Jun Li)
- 12. Symplectic −2 spheres and the symplectomorphism group of small rational 4-manifolds.
We study both connected components and fundamental groups of the symplectomorphism groups for small rational surfaces. Especially, when the rational surface has Euler characteristic eight, we computed the symplectic mapping class groups for all symplectic forms, and related them to braid groups on a sphere.
- 11. Dehn twists exact sequences through Lagrangian cobordism.
We give a new point of view to various long exact sequences in the symplectic literature. In particular, we interpret them as a direct consequence of a clean surgery construction and Biran-Cornea's Lagrangian cobordism theory. This is a "mirror" construction of the Fourier-Mukai construction of spherical/projective twists in algebraic geometry. We also obtained a Floer-theoretic description of Lagrangian projective twists, confirming a mirror conjecture of Huybrechts and Thomas. Besides these, we introduced a "bottleneck formulation" to immersed Lagrangian cobordisms, and a new simple algebraic technique which is very handy at computing connecting maps coming from cobordisms in certain cases.
- Compositio Math. 154(12), 2485-2533. Journal link,
arXiv:1509.08028, Slides (IAS). (with Cheuk-Yu Mak) [+]
- 10. Gauged Floer homology and spectral invariants.
We established the spectral theory in the gauged Floer setting. Entov-Polterovich's quasi-morphism and quasi-state theories were defined in this case. As applications, we obtained a weak Arnold conjecture in arbitrary toric manifolds without appealing to virtual techniques, and also [+]ed the class of superheavy Lagrangians.
- 9. Equivariant split generation and mirror symmetry of special isogenous tori.
We established the homological mirror symmetry for a class of symplectic tori called the "special isogenous tori". Also we showed by Orlov's criterion on the $B$-side, that the derived Fukaya category is a complete invariant in this class of symplectic tori. The main technical ingredient is a generalization of Abouzaid's generation criterion to an equivariant version when a free finite group action is present; some classical results of lattice quotients in rigid analytic geometry were also employed.
- 8. Stability and existence of surfaces in symplectic 4-manifolds with b+=1.
We completely classified the homology class of smooth and symplectic (-4)-spheres in rational and ruled surfaces, and established the existence of ADE-plumbing of Lagrangian spheres under minimal assumption. Two main technical innovations were made: we extended part of Opshtein-Mcduff's non-generic Gromov-Witten technique to more complicated non-generic configurations, and we introduced a "tilted transport" to construct symplectic submanifolds.
- J. Reine Angew. Math. (Crelle's Journal), 2018 (742), 115-155., Journal link, arXiv:1407.1089
, Slides (UMass).
(with J. Dorfmeister and T.-J. Li.) [+]
- 7. Symplectormophism groups of non-compact manifolds,
orbifold balls, and a space of Lagrangians.
J. Symp. Geom.
- Selecta Math. (N.S.), 20 (2014), no. 1, 261-283. Journal Link,
arXiv 1211.5952. (with M. S. Borman and T.-J. Li) [+]
- Acta Math. Sin. (Engl. Ser.) 28 (2012), no. 1, 121-132. Journal Link,
arXiv:1509.08128. (with T.-J. Li) [+]
- Dehn twists along Lagrangian spherical space forms. (with C.Y. Mak)
- Finite symplectic symmetries and orbifold cohomology. (with L. Amorim, S.C. Lau)
- Donaldson hypersurfaces in orbifold theory. (with G. Xu)
- Detecting Non-displaceable fibers in toric degenerations , preliminary version.
This paper is subsumed by "Spherical Lagrangians via ball packings and symplectic cutting". However, it still contains some preliminary results that is not contained in the aforementioned paper.
- Slides for a talk in CIRGET (joint Geometry seminar in Montreal city), summarizing some main results of my work in symplectic 4-manifolds (2, 3, 4, 6, 8 in the publication list), with emphasis on the relations to symplectic packing problems.