Email: sgan7 [at] wisc [dot] edu

Office:  Van Vleck Hall 807

About me

I am a Van Vleck postdoc at University of Wisconsin-Madison starting in 2023 Fall. My mentors are Shaoming Guo and Andreas Seeger.

From 2018 to 2023, I was a PhD student at MIT advised by Larry Guth.  

From 2014 to 2018, I was an undergraduate student at Tsinghua University.

My research interests are Fourier analysis and related problems in geometric measure theory.

CV 

Research

[22] (with Shukun Wu) On local smoothing estimates for wave equations. arXiv:2502.05973

[21] Furstenberg set problem and exceptional set estimate in prime fields: dimension two implies higher dimensions. arXiv:2409.11637

[20] (with Mingfeng Chen, Shaoming Guo, Jonathan Hickman, Marina Iliopoulou, James Wright) Oscillatory integral operators and variable Schrödinger propagators: beyond the universal estimates.  arXiv:2407.06980

[19] Kakeya problem and projection problem for k-geodesics in Grassmannians. arXiv:2404.04290

[18] (with Shukun Wu) A weighted decoupling inequality and its application to the maximal Bochner-Riesz problem. to appear in Journal of Functional Analysis

[17] A Marstrand projection theorem for lines. Journal d'Analyse Mathématique

[16] Exceptional Set Estimate Through Brascamp–Lieb Inequality, IMRN.

[15] (with Larry Guth, Changkeun Oh) Restriction estimates for quadratic manifolds of arbitrary codimensions. arXiv:2308.06427

[14] Hausdorff dimension of unions of $k$-planes. arXiv:2305.14544

[13] Small cap square function estimates. to appear in Journal of Fourier Analysis and Applications.

[12] (with Paige Bright)Exceptional set estimates in finite fields. arXiv:2302.13193

[11] (with Shaoming Guo, Hong Wang) A restricted projection problem for fractal sets in $\mathbb{R}^n$. To appear in Cambridge Journal of Mathematics.

[10] (with Larry Guth, Dominique Maldague) An exceptional set estimate for restricted projections to lines in $\mathbb R^3$. The Journal of Geometric Analysis.

[9] (with Paige Bright) Exceptional set estimates for orthogonal and radial projections in $\mathbb R^n$, Annales Fennici Mathematici

[8] (with Shaoming Guo, Larry Guth, Terence Harris, Dominique Maldague, Hong Wang) On restricted projections to planes in $\mathbb R^3$, To appear in American Journal of Mathematics.

[7] (with Shukun Wu) Square function estimates for conical regions, To appear in Indiana University Mathematics Journal

[6] (with Changkeun Oh and Shukun Wu) A note on local smoothing estimates for fractional Schrödinger equations, Journal of Functional Analysis.

[5] (with Changkeun Oh and Shukun Wu) New bounds for Stein's square functions in higher dimensions, arXiv:2108.11567 

[4] (with Yuqiu Fu and Kevin Ren) An incidence estimate and a Furstenberg estimate for tubes in $\mathbb R^2$, Journal of Fourier Analysis and Applications.

[3] (with Yifan Jing and Shukun Wu) New bounds for Stein's square function in $\mathbb R^3$, Contemp. Math. Amer. Math. Soc.

[2] (with Alina Harbuzova) A sum-product estimate for well-spaced sets, arXiv:2010.01377

[1] (with Yuqiu Fu) On Kakeya maps with regularity assumptions, Mathematical Research Letters.