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Events for November 20, 2017 from General and Seminar calendars

Geometry Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 628

Speaker: Zheng Zhang, TAMU

Title: On the moduli space of pairs consisting of a cubic threefold and a hyperplane

Abstract: The period map is a powerful tool for studying moduli spaces, and has been applied successfully to abelian varieties, K3 surfaces, cubic threefolds/fourfolds, and hyper-Kahler manifolds. However, for some interesting moduli problems (e.g. moduli spaces for pairs of varieties) there might be no obvious way to construct periods. Joint with R. Laza and G. Pearlstein, we construct a period map for cubic pairs consisting of a cubic threefold and a hyperplane using a variation of the construction by Allcock, Carlson and Toledo (which allows us to encode a cubic pair as a “lattice polarized” cubic fourfold). The main result is that the period map induces an isomorphism between a GIT model of the moduli of cubic pairs and the Baily-Borel compactification of some locally symmetric domain.

Probability Seminar

Time: 3:00PM - 4:00PM

Location: BLOC 220

Speaker: Jiayan Ye, TAMU

Title: Continuity of cheeger constant in super-critical percolation

Abstract: Abstract: We consider the super-critical bond percolation on $Z^d$ with $d \geq 3$ and $p > p_c(Z^d)$. In particular, we study the subgraphs of $C_{\infty} \cap [-n, n]^d$ with minimal cheeger constant, where $C_{\infty}$ is the unique infinite open cluster on $Z^d$. Recently, Gold proved that the subgraphs converge to a deterministic shape almost surely. We prove that this deterministic shape is Hausdrorff - continuous in the percolation parameter $p$. This is joint work with Eviatar Procaccia.