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.


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.


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)
Lechao Xiao

Department of Mathematics
David Rittenhouse Lab.
209 South 33rd Street
Philadelphia, PA 19104-6395.

Office: DRL 3N4C
Email: xle at math.upenn.edu

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