Modular Forms and Special Cycles on Shimura Curves.

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On arithmetic fundamental lemmas (2012, background): “Ever since the publication of [10], it has inspired a large amount of works in number theory (for example, [18, 25, 26, 30, 31], etc.”
Fourier transform and the global Gan–Gross–Prasad conjecture for unitary groups (2014, background): “Zhang in 1990’s, completed by Yuan–Zhang–Zhang ([54]) recently, and Kudla–Rapoport–Yang ([37]), Bruinier–Ono ([5]) in various prospectives.”
Integral canonical models for Spin Shimura varieties (2012, methodology): “ce L ⋄ ⊂F⊗Lcontaining L. The details can be found in §7. For low values of n, there are direct, moduli-theoretic ways to construct these integral canonical models. For the case of Shimura curves, cf. [KRY06], and for the case of certain HilbertBlumenthalsurfaces, cf. [DP94,KR99]. Moreover,there iswo”
Unearthing the visions of a master: harmonic Maass forms and number theory (2008, methodology): “This has inspired the extensive program of Kudla, Rapoport and Yang which relates Arakelov intersection numbers on Shimura varieties of orthogonal type to derivatives of Siegel-Eisenstein series and modular L-functions (for example, see [140], [141], [142]).”
Special cycles on unitary Shimura varieties I. Unramified local theory (2008, background): “We show that this length coincides with the derivative of a representation density for hermitian forms.”
Faltings heights of CM cycles and derivatives of L-functions (2008, unknown): “[24, 27, 34].”