Lechao Xiao

I have moved to Google Brain. Here is my new website.

I am a Hans Rademacher Instructor of Mathematics at the University of Pennsylvania. Starting from this July, I will be a research resident in Google Brain. I received my PhD from University of Illinois at Urbana-Champaign and my BA from Zhejiang University, Hangzhou, China. Here is my CV.

Research

My research area is Harmonic analyis: multilinear operators, oscillatory integrals, singular Radon-like transforms, time-frequency analysis and resolution of singularities; see my research statement for more details.

Publication

Higher decay inequalities for multilinear oscillatory integrals, with M. Gilula and P.T. Gressman, arXiv:1612.00050, submitted.

Endpoint estimates for one-dimensional oscillatory integral operators , arXiv:1602.05663, Adv. in Math., to appear.

Sharp Estimates for Trilinear Oscillatory Integrals and an Algorithm of Two-dimensional Resolution of Singularities, Rev. Mat. Ibero., 33, No. 1 (2017), 67-116.

Maximal Decay Inequalities for Trilinear Oscillatory Integrals of Convolution Type, with P.T. Gressman, J. Func. Anal., 271, No. 12 (2016), 3695 -3726.

Bilinear Hilbert Transforms Associated with Plane Curves, with J. Guo, J. of Geom. Anal., 26 (2016), no. 2, 967-995.

Uniform Estimates for Bilinear Hilbert Transforms and Bilinear Maximal Functions Associated to Polynomials, with X. Li, Amer. J. Math., 138, No. 4 (2016), 907-962.

Current teaching at Penn

2017 Spring	Math 313	Computational linear algebra
2016 Fall	Math 361	Advanced calculus II
2016 Fall	Math 240	Calculus III

Past teaching at Penn

2016 Spring	Math 360	Advanced calculus
2016 Spring	Math 104	Calculus I: active learning
2015 Fall	Math 410	Complex Analysis
2015 Spring	Math 313	Computational linear algebra
2014 Fall	Math 114	Calculus II
2014 Fall	Math 420	Differential Equations

Teaching at UIUC

2013 Fall	Math 231	Calculus II	(discusstion)
2013 Spring	Math 234	Calculus for business	(discusstion)
2012 Fall	Math 220	Calculus	(discusstion)