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In this talk, I will present a proof a decomposition formula of Kazhdan-Lusztig basis for the elements in the lowest two-sided cell of an affine Weyl group. This formula can be used to determine the l...
Bernstein problem for affine maximal type hypersurfaces has been a core problem in affine geometry. A conjecture proposed firstly by Chern (Proc. Japan-United States Sem., Tokyo, 1977, 17-30) for enti...
I will talk about affine Grassmannians for the exceptional group of type G_2. This group can be given as automorphisms of octonion algebras. I consider all maximal parahoric subgroups in G_2, and give...
In this talk, we are mainly concerned with invariant geometric flows in affine-related geometries including centro-equiane, centro-affine, affine and affine-symplectic geometries. First, we show that ...
Let $k$ be a field of characteristic 0 and let $C$ be the a smooth affine curve over $k$. We will first discuss applications of strong approximation to the theory of integral quadratic forms over $C$....
The mod p points of a Shimura variety have a conjectural description called the Langlands-Rapoport conjecture. In accordance with the conjecture, Rapoport defined (generalized) affine Deligne-Lusztig ...
A natural family of affine cubic surfaces arises from SL(2)-characters of the 4-holed sphere and the 1-holed torus. The ideal locus is a tritangent plane which is generic in the sense that the...
A Margulis spacetime is a complete affine 3-manifold M with nonsolvable fundamental group. Associated to every Margulis spacetime is a noncompact complete hyperbolic surface S. We show that eve...
This paper is the sequel to The radiance obstruction and par- allel forms on a;ffne manifolds (lYans. Amer. Math. Soc. 286 (1984), 629 649) which introduced a new family of secondary characteristi...
A manifold M is affine if it is endowed with a distinguished atlas whose coordinate changes are locally affine. When they are locally linear M is called radiant. The obstruction to radiance is a o...
Those groups r which act properly discontinuously and aillnely on II?’ with compact fundamental domain are classified. First it is shown that such a group f contains a solvable subgroup of finite ...
TWO EXAMPLES OF AFFINE MANIFOLDS     AFFINE MANIFOLDS  affine       2015/9/29
An affine manifold is a manifold with a distinguished system of affine coordinates, namely, an open covering by charts which map homeomorphically onto open sets in an affine space E such that on ov...
It is well known that the real cohomology of a compact Riemannian manifold M is isomorphic to the algebra of its harmonic forms. When M is a fiat Riemannian manifold, i.e. a Euclidean manifold, a ...
This paper studies ane Deligne-Lusztig varieties in the ane ag manifold of a split group. Among other things, it proves emptiness for certain of these varieties, relates some of them to those fo...

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