**Zu Chongzhi Mathematics Research Seminar**

**Date and Time (China standard time): **Monday, November 20, 3:00-4:00 pm

**Location: **IB 1050

**Zoom: **976 0269 6045;** Passcode: **dkumath

**Title**: Lp estimates of orthogonal projections, dual Furstenberg problem, and discretized sum-product

**Speaker**: Bochen Liu

**Bio**: Bochen Liu is an associated professor in the math department of Southern University of Science and Technology, whose research interests are harmonic analysis, geometric measure theory, and combinatorics.

**Abstract**:

L2 estimates of orthogonal projections are classical in geometric measure theory. In this talk we shall discuss about recent progress on Lp estimates. Then we come up with a dual version of the Furstenberg problem and introduce some partial results. We also find that, compared with general sets, Cartesian products have better Lp-behavior. This leads to improvement on some discretized sum-product estimates. This is joint work with Longhui Li.