Tonghai Yang

Benjamin Howard

This monograph treats one case of a series of conjectures by S. Kudla, whose goal is to show that Fourier of Eisenstein series encode information about the Arakelov intersection theory of special cycles on Shimura varieties of orthogonal and unitary type. Here, the Eisenstein series is a Hilbert modular form of weight one over a real quadratic field, the Shimura variety is a classical Hilbert modular surface, and the special cycles are complex multiplication points and the Hirzebruch-Zagier divisors. By developing new techniques in deformation theory, the authors successfully compute the Arakelov intersection multiplicities of these divisors, and show that they agree with the Fourier coefficients of derivatives of Eisenstein series.

Intersections of Hirzebruch–Zagier Divisors and CM Cycles

During Advent we think about a wondrous mystery: that God chose to become human and lived among us. The Savior of the world was born a vulnerable child. The king who will rule all of creation lies in a humble manger. The Wondrous Mystery invites readers to reflect on several paradoxes that make up the Advent season: light and darkness, peace and strife, solitude and community, simplicity and complexity. This daily Advent reader incorporates meditations from Weavings: A Journal of the Christian Spiritual Life. Writers include Barbara Brown Taylor, Henri J. M. Nouwen, Esther de Waal, Walter Wink, Sue Monk Kidd, Wendy M. Wright, and other voices from Weavings, which wove together the teachings and perspectives of some of the finest theologians and teachers of Christian spiritual formation. Compiler Ben Howard writes, "The glory of the Advent season is that it is irrational. It shows us a glimpse of the way that God turns the world and our expectations upside down. . . . In a season filled with the longest, darkest nights, we are told to wait for the coming of the most beautiful light.

Benjamin Howard

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