 Research Interests 1: Additive Combinatorics 2: Harmonic Analysis 3: Geometric Measure Theory Publication List 1: A slight improvement to Korenblum's constant ( J. Math. Anal. Appl. 337 ( 2008), no. 1, 464-465.) 2: Matrices whose norm are determined by their actions on decreasing sequences (with CP Chen and HW Huang , Canadian J. Math. 60 (2008), no. 3, 520-531. ) 3: Garaev's inequality in finite fields not of prime order (with Nets Katz, Online J. Anal. Comb. no. 3 (2008)) 4: A slight improvement to Garaev's sum product estimate (with Nets Katz, Proc. Amer. Math. Soc. 136 (2008), no. 137, 2499-2504. ) 5: Quantitative sum product estimates on different sets ( Electron. J. Combin. 15 (2008), no. 1, #40 ) 6: On the sum product estimates and two variables expanders ( Publicacions Matemàtiques, 54 ( 2010) no. 1 ) 7: Sum product phenomenon in fields not of prime order ( Rocky. Mount. J. Math, to appear ) 8: An extension of Bourgain and Garaev’s sum product estimate ( Acta Arith. 135 (2008), no. 4, 351-356.) 9: On the size of the set A(A+1) ( with M. Garaev, Math. Z. 263 (2009), no 94. ) 10: Fourier analysis and expanding phenomena in finite fields ( with D. Hart and L. Li, submitted ) 11: Algebraic methods in sum-product phenomena ( submitted ) |  I am a fifth year PhD student in the Department of Mathematics at Indiana University Bloomington. ( email: shenc@indiana.edu) Curriculum Vitae (Click to View) (Click to Download) Useful links MathSciNet Math at arXiv AMS Terry Tao |