Recent Development on the Geometry of the Teichmuller and Moduli Spaces of Riemann Surfaces and Polarized Calabi-Yau Manifolds

TL;DR

This paper surveys recent advances in the geometric understanding of Teichmuller and moduli spaces for Riemann surfaces and Calabi-Yau manifolds, highlighting new results in their structure and properties.

Contribution

It presents new findings on the geometry of these moduli spaces, expanding current knowledge and techniques in the field.

Findings

New geometric properties of Teichmuller spaces

Insights into the structure of moduli spaces of Calabi-Yau manifolds

Recent results on the curvature and metric properties

Abstract

We survey our recent new results on the geometry of Teichmuller and moduli spaces of Riemann surfaces and Calabi-Yau manifolds.