Institute of Mathematics
Academia Sinica
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Research Fellow |   Yu, Chia-Fu
Contact Information
  • chiafu$\color{red}{@}$math.sinica.edu.tw
  • +886 2 2368-5999 ext. 628
  • +886 2 2368-9771

Research Interests
  • Arithmetic Algebraic Geometry
  • Representation Theory
Links
Education
  • Ph.D. University of Pennsylvania (1999)
  • M.S. University of Pennsylvania (1997)
  • B.S. National Taiwan University (1992)
Work Experience
  • Research Fellow Academia Sinica, Taiwan 2009 - Present
  • Associate Research Fellow Academia Sinica, Taiwan 2004 - 2009
  • Visiting Assistant Professor National Center of Theoretic Sciences (NCTS), Taiwan 2002 - 2003
  • Ritt Assistant Professor Columbia University 1999 - 2004
Research Descriptions

Dr. Yu's research area are number theory, arithmetic geometry and representation theory. In particular, he is interested in the geometry of Shimura varieties and their applications in representation theory.

Selected Publications
Publications
  1. "Jiangwei Xue and Chia-Fu Yu, Optimal spinor selectivity for quaternion orders." , arXiv:2207.12736, 18 pp. To appear in J. Number Theory , 2022.
  2. "Pei-Xin Liang, Yasuhiro Oki, Hsin-Yi Yang, Chia-Fu Yu and Jianing Li, On Tamagawa numbers of CM tori." , arxiv:2109.04121v3, 38 pp. To appear in Algebra & Number Theory , 2023.
  3. "Chia-Fu Yu, Japanese Dedekind domains are excellent" , Taiwanese J. Math. , 26 (3), 483-500, 2022.
  4. "Jia-Wei Guo, Nai-Heng Sheu and C.-F. Yu, Class numbers of CM algebraic tori, CM abelian varieties and components of unitary Shimura varieties." , Nagoya Math Journal. , 245, 74-99, 2022.
  5. "Jiangwei Xue and C.-F. Yu, Polarized simple superspecial abelian surfaces with real Weil numbers: a survey." , Proceedings of RIMS Conference ``Theory and Applications of Supersingular Curves and Supersingular Abelian Varieties'', RIMS K\^oky\^uroku Bessatsu. , B90, 39-57, 2022.
  6. "Jiangwei Xue, Chia-Fu Yu, Yuqiang Zheng, On superspecial abelian surfaces over finite fields III." , Res. Number Theory. , 8 (1.9), 1-22, 2022.
  7. "Yasuhiro Terakado and Chia-Fu Yu, Hecke eigensystems of automorphic forms (mod $p$) of Hodge type and algebraic modular forms." , Math Ann. , 382 (1-2), 69-102, 2022.
  8. "C.-F. Yu, Reduction of the moduli schemes of abelian varieties with definite quaternion multiplication." , Annales de l'Institut Fourier (Grenoble), 76 pp. , 71 (2), 539-613, 2021.
  9. "Xu Shen, Chia-Fu Yu, Chao Zhang, EKOR strata for Shimura varieties with parahoric level structure." , Duke Math. J. , 170 (14), 3111-3236, 2021.
  10. "Valentijn Karemaker, Fuetaro Yobuko and Chia-Fu Yu, Mass formula and Oort's conjecture for supersingular abelian threefolds." , Adv. in Math. 386 (2021), 107812 , 1-52, 2021.
  11. "Qun Li, Jiangwei Xue and C.-F. Yu, Unit groups of maximal Orders in totally definite quaternion algebras over real quadratic fields." , Trans. Amer. Math. Soc. , 374 (8), 5349-5403, 2021.
  12. "Chun-Yi Lin and Chia-Fu Yu, Dieudonn\'e determinants and subgroups of general linear groups over division rings revisited." , Bull. Inst. Math. Acad. Sin. (N.S.) , 16 (1), 21-47, 2021.
  13. "Jiangwei Xue and C.-F. Yu, On superspecial abelian surfaces and type numbers of totally definite quaternion algebras," , Indiana Univ. Math. J. , 70 (2), 783-810, 2021.
  14. "J. Xue and C.-F. Yu, On counting certain abelian varieties over finite fields." , Acta Math. Sinica (Engl. Ser.) 37 (2021), no. 1, 205--228. , 37 (1), 205-228, 2021.
  15. "Jianing Li and Chia-Fu Yu, The Chevalley-Gras formula over global fields," , J. Theor. Nombres Bordeaux , 32, 525-543, 2020.
  16. "C.-F. Yu, C.-L. Chai and F. Oort, Stratifying Lie strata of Hilbert modular varieties." , Taiwanese J. Math. , 24 (6), 1307-1352, 2020.
  17. "C.-F. Yu, A note on supersingular abelian varieties." , Bull. Inst. Math. Acad. Sin. (N.S.) , 15 (1), 9-32, 2020.
  18. "J. Xue, T.-C. Yang and C.-F. Yu, On superspecial abelian surfaces over finite fields II." , J. Math. Soc. Japan , 72 (1), 303-331, 2020.
  19. "Jiangwei Xue and Chia-Fu Yu, On counting certain principally polarized superspecial abelian surfaces over $\mathbb{F}_p$" , Proceedings of ``Automorphic forms, automorphic representations and related topics'', RIMS K\^oky\^uroku(数理解析研究所講究録), 2136, 146-159 , 2020.
  20. "C.-F. Yu, Chow's theorem for semi-abelian varieties and bounds for splitting fields of algebraic tori" , Acta Math. Sin. (Engl. Ser.) , 35 (9), 1453-1463, 2019.
  21. "J. Xue, T.-C. Yang and C.-F. Yu, Supersingular abelian surfaces and Eichler's class number formula" , Asian J. Math. , 23 (4), 651-680, 2019.
  22. "Qun Li, Jiangwei Xue and C.-F. Yu, Reduced unit groups in totally definite quaternion algebras over real quadratic fields." , Proceedings of ``Automorphic forms, automorphic representations and related topics'', RIMS K\^oky\^uroku(数理解析研究所講究録) , 2100, 80-93, 2019.
  23. "C.-F. Yu, On arithmetic of the superspecial locus" , Indiana Univ. Math. J. , 67 (4), 1341-1382, 2018.
  24. "C.-F. Yu, On fields of definition of components of Siegel supersingular locus" , Proc. Amer. Math. Soc. , 145 (12), 5053-5058, 2017.
  25. "C.-F. Yu, Notes on locally free class groups." , Bull. Inst. Math. Acad. Sin. (N.S.) , 12 (2), 125-139, 2017.
  26. "C.-F. Yu, Abelian varieties over finite fields as basic abelian varieties." , Forum Math. , 29 (2), 489-500, 2017.
  27. "C.-F. Yu, On existence and density of the ordinary locus of certain Shimura varieties." , Proceedings of the 6th International Congress of Chinese Mathematicians, ALM , 36, 361-379, 2017.
  28. "J. Xue, T.-C. Yang and C.-F. Yu, On superspecial abelian surfaces over finite fields." , Doc. Math. , 21, 1607-1643, 2016.
  29. "J. Xue, T.-C. Yang and C.-F. Yu, Numerical invariants of totally imaginary quadratic ${\mathbb Z}[\sqrt{p}]$-orders." , Taiwanese J. Math. , 20 (4), 723-741, 2016.
  30. "C.-F. Yu, On non-emptiness of basic loci of Shimura varieties." , MFO Workshop on Reductions of Shimura Varieties.~Math. F.~Oberwolfach Report No. 39/2015 , 2016.
  31. "Fu-Tsun Wei and C.-F. Yu, Class numbers of definite central simple algebras over global function fields." , Int. Math. Res. Not. , 2015 (11), 3525-3575, 2015.
  32. "J. Xue and C.-F. Yu, Endomorphism algebras of factors of certain hypergeometric Jacobians." , Trans. Amer. Math. Soc. , 367, 8071-8106, 2015.
  33. "C.-F. Yu, A Note on the Mumford-Tate conjecture for CM abelian varieties" , Taiwanese J. Math. , 19, 1073-1084, 2015.
  34. "C.-F. Yu, Variants of mass formulas for definite division algebras." , J. Algebra , 422, 166-186, 2015.
  35. "T.-C. Yang and C.-F. Yu, Monomial, Gorenstein and Bass orders." , J. Pure Appl. Algebra. , 219, 767-778, 2015.
  36. "J. Xue and C.-F. Yu, Abelian varieties without a prescribed Newton polygon reduction." , Proc. Amer. Math. Soc. , 143 (6), 2339-2345, 2015.
  37. "H. Wang, J. Xue and C.-F. Yu, Fixed points and homology of superelliptic Jacobians." , Math. Z. , 278, 169-189, 2014.
  38. "C.-F. Yu, Notes on density of the ordinary locus" , Bull. Inst. Math. Acad. Sin. (N.S.) , 9, 711-733, 2014.
  39. "S.-C. Shih, T.-C. Yang and C.-F. Yu, Embeddings of fields into simple algebras over global fields." , Asian J. Math. , 18, 365-386, 2014.
  40. "C.-F. Yu, Shuffle structures on KR strata." , MFO Workshop on Reductions of Shimura Varieties. Math. F. Obwerwolfach Report No. 32/2012 , 1995-1999, 2013.
  41. "C.-F. Yu, Characteristic polynomials of central simple algebras." , Taiwanese J. Math. , 17 (1), 351-359, 2013.
  42. "C.-F. Yu, Endomorphism algebras of QM abelian surfaces." , J. Pure App. Algebra. , 217, 907-914, 2013.
  43. "U. Goertz and C.-F. Yu, The supersingular locus in Siegel modular varieties with Iwahori level structure." , Math. Ann. , 353, 465-498, 2012.
  44. "C.-F. Yu, Embeddings of fields into simple algebras: generalizations and applications." , J. Algebra , 368, 1-20, 2012.
  45. "C.-F. Yu, On Hermitian forms over dyadic non-maximal local orders." , Pure Appl. Math. Q. , 8 (4), 1117-1146, 2012.
  46. "F.-T. Wei and C.-F. Yu, Mass formula of division algebras over function fields." , J. Number Theory , 132, 1170-1185, 2012.
  47. "C.-F. Yu, Superspecial abelian varieties over prime finite fields." , J. Pure and Appl. Algebra , 216, 1418-1427, 2012.
  48. "C.-F. Yu, On the existence of maximal orders." , Int. J. Number Theory , 7 (8), 2091-2114, 2011.
  49. "C.-F. Yu, Geometry of the Siegel modular threefold with paramodular level structure." , Proc. Amer. Math. Soc. , 139 (9), 3181-3190, 2011.
  50. "C.-F. Yu, Kottwitz-Rapoport strata of the Siegel moduli spaces." , Taiwanese J. Math. , 14, 2343-2364, 2010.
  51. "C.-F. Yu, On finiteness of endomorphism rings of abelian varieties" , Math. Res. Letters , 17, 357-370, 2010.
  52. "C.-F. Yu, Simple mass formulas on Shimura varieties of PEL-type." , Forum. Math. , 22 (3), 565-582, 2010.
  53. "U. G\"ortz and C.-F. Yu, Supersingular Kottwitz-Rapoport strata and Deligne-Lusztig varieties" , J. Inst. Math Jussieu , 9 (2), 357-390, 2010.
  54. "C.-F. Yu and J.-D. Yu, Mass formula for supersingular abelian surfaces." , J. Algebra , 322, 3733-3743, 2009.
  55. "C.-F. Yu, Irreducibility of the Hilbert-Blumenthal moduli spaces with parahoric level structure." , J. Reine Angew. Math. , 635, 187-211, 2009.
  56. "C.-F. Yu, An exact geometric mass formula." , Int. Math. Res. Not. , 2008 (113), 1-11, 2008.
  57. "C.-F. Yu, Irreducibility and $p$-adic monodromies on the Siegel moduli spaces." , Adv. Math. , 218, 1253-1285, 2008.
  58. "C.-F. Yu, Leaves on Shimura varieties." , Proceedings of the ICCM , II, 630-661, 2007.
  59. "C.-F. Yu, Construction of Galois covers of curves with groups of ${\rm SL_2}$-type." , C. R. Acad. Sci. Paris S{\'e}r. I. Math , 345, 77-80, 2007.
  60. "C.-F. Yu, The supersingular loci and mass formulas on Siegel modular varieties. Doc. Math. 11 (2006), 449 -- 468" , 2006.
  61. "C.-F. Yu, On the slope stratification of certain Shimura varieties. Math. Z. 251 (2005), 859 --873." , 2005.
  62. "C.-F. Yu, On the mass formula of supersingular abelian varieties with real multiplications" , J. Australian Math. Soc. , 78, 373-392, 2005.
  63. "C.-F. Yu, Irreducibility of Siegel moduli spaces with parahoric level structure" , Int. Math. Res. Not. , 48, 2593-2597, 2004.
  64. "C.-F. Yu and J. Yu, Mass formula for supersingular Drinfeld modules" , C. R. Acad. Sci. Paris S\'er. I Math , 338, 905-908, 2004.
  65. "C.-F. Yu, The isomorphism classes of abelian varieties of CM type" , J. Pure Appl. Algebra , 187, 305-319, 2004.
  66. "C.-F. Yu, On reduction of Hilbert-Blumenthal varieties" , Annales de l'Institut Fourier (Grenoble) , 53, 2105-2154, 2003.
  67. "C.-F. Yu, On the supersingular locus in Hilbert-Blumenthal 4-folds" , J. Algebraic Geom. , 12, 653-698, 2003.
  68. "C.-F. Yu, Lifting abelian varieties with additional structure. Math. Z. 242 (2002) 427--441." , 2002.
  69. "C.-F. Yu, On the supersingular locus of Hilbert-Blumenthal 4-folds, Thesis, University of Pennsylvania (1999), 76 pp" , 1999.

Lecture Notes
  1. (with C.-L. Chai) "Notes on Cartier theory, Barsotti-Tate groups, Hecke orbits and canonical coordinates, lectures presented in the 2004 AS-NCTS joint seminar on Arithmetic and Algebraic Geometry, Number Theory, and Representation Theory, 12/30-31/2004, 1/6-7/2005." , 2004.
  2. "Zeta functions of modular curves. NCTS Lecture Notes, 2003." , NCTS Lecture Notes , 2003.
  3. "Notes on Intersection cohomology, $L^2$-cohomology and $L$-functions of Hilbert-Blumenthal varieties (following the work of Brylinski and Labesse), NCTS Lecture Notes, 2002, 111 pp." , NCTS Lecture Notes , 111-, 2002.

Preprints
  1. "Fan-Yun Hung and Chia-Fu Yu, Class numbers of multinorm one tori." , arXiv:2307.11440, 21 pp. submitted. , 2023.
  2. "Jun-Hao Huang, Fan-Yun Hung, Pei-Xin Liang and Chia-Fu Yu, Computing Tate-Shafarevich groups of multinorm one tori of Kummer type" , arXiv:2211.11249, 17 pp, submitted. , 2023.
  3. "Yasuhiro Terakado and Chia-Fu Yu, Mass formulas and the basic locus of unitary Shimura varieties." , arXiv:2210.04054, 47 pp. Submitted. , 2022.
  4. "Chun-Yi Lin and Chia-Fu Yu, On the structure of unitary groups revisited." , Preprint July, 2022. 33 pp. Submitted. , 2022.
  5. "Tomoyoshi Ibukiyama, Valentijn Karemaker and Chia-Fu Yu, When is a polarised abelian variety determined by its $p$-divisible group?" , http://arxiv.org/abs/2205.13180v2, 39 pp. Submitted. , 2022.
  6. "Urs Hartl and Chia-Fu Yu, Arithmetic Satake compactifications and algebraic Drinfeld modular forms." , arXiv:2009.13934, 45 pp. Submitted. , 2022.
  7. "Jiangwei Xue and C.-F. Yu, Polarized simple superspecial abelian surfaces with real Weil numbers." , arXiv:2009.02729, 59 pp. , 2022.
  8. "Jiangwei Xue and Chia-Fu Yu, Trace formulas for the norm one group of totally definite quaternion algebras" , arXiv:1909.11858v3, 27 pp. Submitted. , 2022.
  9. "C.-F. Yu, A remark on Chevalley's ambiguous class number formulas" , arXiv:1412.1458. 3 pp. , 2018.
  10. "C.-F. Yu, Basic points in the moduli spaces of PEL-type." , MPIM-preprint 2005-113, 11 pp , 2005.
  11. "C.-F. Yu, Discrete Hecke orbit problems for Hilbert-Blumenthal varieties." , NCTS/TPE-Math Technical Report 2006-1, 20 pp , 1-20, 2006.
Director & Deputy Director