**SMS scnews item created by Martina Chirilus-Bruckner at Wed 6 Aug 2014 1517**

Type: Seminar

Distribution: World

Expiry: 13 Aug 2014

**Calendar1: 22 Aug 2014 1430-1530**

**CalLoc1: Carslaw Lect. 275**

Auth: martinac@como.maths.usyd.edu.au

### Joint Colloquium

# Higgs-de Rham flow in the non-abelian p-adic Hodge theory and a p-adic analogue of the uniformization theory of a hyperbolic Riemann surface

### Kang Zuo

Date:

** Fri, 22/08/2014 - 2:30pm **

Location:

** (Carslaw Lect. 275, Sydney Uni) **

Speaker:

** Kang Zuo**

Title:

**Higgs-de Rham flow in the non-abelian p-adic Hodge theory and a p-adic analogue of the uniformization theory of a hyperbolic Riemann surface **

Abstract:

The notion " Higgs-de Rham flow" over schemes X/W(k) over the ring of Witt vectors of
finite field k of characteristic p introduced in a recent paper by Lan-Sheng-Zuo has found some interesting applications in arithmetic geometry. Higgs-de Rham flow induces a correspondence between semistable graded Higgs bundles with $c_i=0$ and crystalline representations of the algebraic fundamental group of the generic fibre of $X,$ an p-adic analogue of the well known correspondence between polystable graded Higgs bundles of $c_i=0$ and polarized complex variation of Hodge structures. In my lecture I shall talk about application of Higgs-de Rham flow on uniformization of hyperbolic p-adic curves, which is closely related to S. Mochizuki's p-adic Teichmueller thoery. This is a joint work with Lan-Sheng-Yang.

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