Learning seminar on Arithmetic Inner Product Formula

In this seminar, we want to understand the statement of arithmetic inner product formula conjecture and the idea of the proof.

2pm-4pm ET time, at 2-255 MIT.

Date	Title	Speaker	Notes
Sep23	Classical theta correspondence, Doubling method and Siegel-Weil formula	Julia Meng	notes
Sep30	Rallis inner product formula & central derivatives	Weixiao Lu	notes
Oct7	Arithmetic and geometric theta series	Ayan Nath	notes
Oct16 1-2:30pm at 2-361	Research talk: Comparison of absolute and relative unitary Rapoport-Zink spaces	Yu Luo	TBA
Oct21	Geometric Siegel-Weil formula and geometric inner product formula	Vijay Srinivasan	TBA
Oct28	Arithmetic intersection theory	Daniel Hu	notes
Nov4	Research talk: Semi-Lie arithmetic fundamental lemma for full spherical Hecke algebras	Evan Chen	TBA
Nov11	Research talk: On local newform theory for unramified odd unitary groups	Masao Oi	TBA
Nov18	Integral models and Arakelov theta series	Patrick Bieker	TBA
Nov25	Arithmetic Siegel-Weil formula and arithmetic inner product formula	Mikayel Mkrtchyan	TBA
Dec2	Beilinson-Bloch height pairing and local indices	Ryan Chen	TBA
Dec9	Sketch of proof of arithmetic inner product formula	Zeyu Wang	TBA

[BHKRY]J. Bruinier, B. Howard, S. Kudla, M. Rapoport and T. Yang, Modularity of generating series of divisors on unitary Shimura varieties. Asterisque,Diviseurs arithmetiques sur les varietes orthogonales et unitaires de Shimura(2020), no.421, 7-125.
[G-S90]H. Gillet and C. Soule, Arithmetic intersection theory. Inst. Hautes Etudes Sci. Publ. Math.(1990), no.72, 93-174.
[Kud04]S. Kudla, Special cycles and derivatives of Eisenstein series.Heegner points and Rankin L-series. 243-270. Math. Sci. Res. Inst. Publ., 49. Cambridge University Press, Cambridge, 2004.
[Li24]C. Li, Geometric and arithmetic theta correspondences. https://www.math.columbia.edu/~chaoli/IHES.pdf
[L-L21]C. Li and Y. Liu, Chow groups and L-derivatives of automorphic motives for unitary groups. Ann. of Math. (2)194(2021), no.3, 817-901.
[Liu11]Y. Liu, Arithmetic theta lifting and L-derivatives for unitary groups, I. Algebra Number Theory5(2011), no.7, 849-921.

[Bei87]A. A. Beilinson, Height pairing between algebraic cycles. $K$-theory, arithmetic and geometry (Moscow, 1984-1986), 1-25. Lecture Notes in Math., 1289. Springer-Verlag, Berlin, 1987.
[Dun22]N. C. Dung, Geometric Pullback Formula for Unitary Shimura Varieties. Thesis (Ph.D.)-Columbia University. ProQuest LLC, Ann Arbor, MI, 2022. 68 pp.
[Li92]J.-S. Li, Nonvanishing theorems for the cohomology of certain arithmetic quotients. J. Reine Angew. Math.428(1992), 177-217.
[Liu11a]Y. Liu, Arithmetic theta lifting and L-derivatives for unitary groups, II. Algebra Number Theory5(2011), no.7, 923-1000.