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| Wednesday, April 29, 2:30pm-3:30pm, MP3311 | Xiangdong Xie, Georgia Southern University | Barycent method in Geometry II |
| Wednesday, April 22, 2:30pm-3:30pm, MP3311 | Xiangdong Xie, Georgia Southern University | Barycent method in geometry |
| Wednesday, April 15, 2:30pm-3:30pm, MP3311 | Francois Ziegler, Georgia Southern University | Elements of Differential Geometry V |
| Wednesday, April 8, 2:30pm-3:30pm, MP3311 | Yi Lin, Georgia Southern University | Flux homomorphism in symplectic topology |
| Wednesday, April 1, 2:30pm-3:30pm, MP3311 | Francois Ziegler, Georgia Southern University | Elements of Differential Geometry IV |
| Wednesday, March 25, 2:30pm-3:30pm, MP3311 | Yi Lin, Georgia Southern University | Introduction to Hamiltonian Symplectomorphisms |
| Wednesday, February 25, 2:30pm-3:30pm, MP3311 | Francois Ziegler, Georgia Southern University | Elements of Differential Geometry III |
| Wednesday, February 18, 2:30pm-3:30pm, MP3311 | Xiangdong Xie, Georgia Southern University | Discrete groups acting on Symplectic manifolds III |
| Wednesday, February 11, 2:30pm-3:30pm, MP3311 | Francois Ziegler, Georgia Southern University | Elements of Differential Geometry II |
| Wednesday, February 4, 2:30pm-3:30pm, MP3311 | Xiangdong Xie, Georgia Southern University | Discrete groups acting on Symplectic manifolds II |
| Wednesday, January 28, 2:30pm-3:30pm, MP3311 | Francois Ziegler, Georgia Southern University | Elements of Differential Geometry |
| Wednesday, January 21, 2:30pm-3:30pm, MP3311 | Xiangdong Xie, Georgia Southern University | Discrete groups acting on Symplectic manifolds |
| Thursday, November 20, 5pm-6pm, MP3311 | Yi Lin, Georgia Southern University | An introduction to generalized complex geometry |
| Thursday, November 13, 5pm-6pm, MP3311 | Xiangdong Xie, Georgia Southern University | Ratner's orbit closure theorem. |
Wednesday, February 18, 2:30pm-3:30pm, MP 3311
Speaker: Xiangdong Xie, Georgia Southern UniversityAbstract:
This is the third talk of the series. I will introduce Gal-Kedra's cocycle and discuss its properties.
Wednesday, February 11, 2:30pm-3:30pm, MP 3311
Speaker: Francois Ziegler, Georgia Southern UniversityAbstract:
Today, continuing our exposition of differential calculus on numerical spaces we will 1) establish the key properties of the Lie bracket, then 2) introduce differential forms. Notes up to the point we stopped last time are available at http://math.georgiasouthern.edu/~fziegler/7999/.
Wednesday, February 4, , 2:30pm-3:30pm, MP 3311
Speaker: Xiangdong Xie, Georgia Southern UniversityAbstract:
This is the second talk of the series. I will first review the basics of group cohomology, then explain Gal-Kedra's strategy for proving Polterovich's theorem.
Wednesday, January 28, 2:30pm-3:30pm, MP 3311
Speaker: Francois Ziegler, Georgia Southern UniversityAbstract:
(First talk of a series, alternating with Xiangdong's on Wednesdays.) Differential geometry blends analysis, algebra, and topology. This gives the subject its power and appeal, but also a certain reputation of being difficult for outsiders to enter. In this series, we want to infirm this reputation by giving a leisurely introduction to the basics: the calculus of differential forms, vector fields, and group actions on numerical spaces and manifolds. We aim to take the shortest (connected) path to actually-used results, to minimize technicalities, and to give enough examples for comfort. Twin goals are to help make geometry seminars/colloquia more accessible, and to outline a possible strategy for adapting the upcoming graduate course to our students' background. All faculty and students with an interest or curiosity about geometry, should feel welcome to attend.
Wednesday, January 21, 2:30pm-3:30pm, MP 3311
Speaker: Xiangdong Xie, Georgia Southern UniversityAbstract:
This is the first of a series of talks. The ultimate goal(dream) of the talks is to combine the strengths of the faculty (including Francois, Yi and myself) and prove some new results about discrete groups acting on symplectic manifolds. We start by presenting a new proof by Gal and Kedra of Polterovich's theorem (that a finitely generated group acting effectively by Hamiltonian diffeomorphisms on closed symplectic hyperbolic manifolds have undistorted cyclic subgroups.) In this talk I will explain the algebraic ingredients of the proof: group cohomology and distortion of subgroups.
Friday, November 20, 5pm-6pm, MP 3311
Speaker: Yi Lin, Georgia Southern UniversityAbstract:
Generalized complex geometry was initiated by N. Hitchin a few years ago. It is a common generalization of both complex anf symplectic geometry and has turned out to be important in the recent development of string theory and theoretical high energy physics. In this talk, I will give a gentle introduction to some basic concepts in generalized complex geometry. if time permits, I will review some more recent developments.
Friday, November 13, 5pm-6pm, MP 3311
Speaker: Xiangdong Xie, Georgia Southern UniversityAbstract:
Ratner's theorems are important in geometry and topology, and also have important applications in number theory(say, the proof of Oppenheim conjecture on quadratic forms). Let $T=R^2/Z^2$ be the standard torus. Each one dimensional subspace H of R^2 acts by translations on R^2, and the orbits are lines parallel to H. This action projects down to an action on T. When H has rational slope, the orbits of H on T are circles. When H has irrational slope, the orbits of H on T are dense in T. In any case, the closure of each orbit is either T or a circle (the closure has NICE GEOMETRIC FORM). Ratner's orbit closure theorem is a far reaching generalization of the above observation, where R^2 is replaced by any Lie group, Z^2 is replaced by any lattice, and H is replaced by a subgroup of the Lie group generated by unipotent elements. The conclusion is the closure of every orbit has a "nice geometric form" used results, to minimize technicalities, and to give enough examples for comfort.(a homogeneous space admitting finite invariant measure).