Professor Xiang Fang

Contact

• Email: xfang@nycu.edu.tw
• Tel: ext. 56449
• Fax: +886-3-5724679
• Address: Department of Applied Mathematics, National Yang Ming Chiao Tung University,1001 Ta Hsueh Road, Hsinchu, Taiwan 30050, ROC

Teaching

• Fall Semester, 2025：
  • Probability Theory
  • Calculus A (I)
• Spring Semester, 2025：

Vitae

• Education
  • Ph.D. Texas A&M University
• Research Areas
  • Probability, Functional Analysis, Complex Analysis, Fractal
• Positions, Honors and Awards
  【Positions】

  1. Professor, National Yang Ming Chiao Tung University, 2024 - present
  2. Professor, National Central University, 2013 - 2024
  3. Associate Professor, Kansas State University, 2010 - 2013
  4. Assistant Professor, Kansas State University, 2005 - 2010
  5. Assistant Professor, University of Alabama, 2003 - 2005
  6. Visiting Assistant Professor, University of Florida, 2002 - 2003
  7. (Sabbatical leave) National Central University, 2011-2012

  【Honor and Awards】

  1. 2017 University Teaching Excellence Award, National Central University
  2. 08/2018 - 07/2019 【教育部大專院校教學實踐研究計劃】關於高等微積分教學的新嘗試
  3. 08/2014 - 07/2024 Mentor for Math Team of the Science Class, Wu-Ling Senior High School, Taoyuan

Selected Publications

(A)   Refereed Papers：

1. Hilbert polynomials and Arveson's curvature invariant, Journal of Functional Analysis, 198(2003), no. 2, 445-464.
2. Samuel multiplicity and the structure of Fredholm operators, Advances in Mathematics, 186(2004), no. 2, 411{437.
3. Invariant subspaces of the Dirichlet space and commutative algebra, J. Reine Angew Math., 569(2004), 189{211.
4. The Fredholm index of quotient Hilbert modules, Mathematical Research Letters, 12(2005) 911-920.
5. The Fredholm index of a pair of commuting operators, Geom. Funct. Anal. (GAFA), Vol.16.2 (2006), 367-402.
6. Canonical operator models over Reinhardt domains, Taiwanese Journal of Mathematics, Vol. 11.1, (2007) 75-94.
7. Additive Invariants on the Hardy space over the bidisk, Journal of Functional Analysis, Vol. 253 (2007) 359-372.
8. Estimates of Koszul homogoloy groups, Journal of Functional Analysis, , Vol. 255 (2008) 1-12.
9. The Fredholm index of a pair of commuting operators, II, Journal of Functional Analysis, Vol. 256 (2009) 1669-1692.
10. (With G. Cheng) An additive formula for Samuel multiplicities on Hilbert spaces of analytic functions, Journal of Functional Analysis, Vol. 260 (2011) 2027-2042.
11. (With G. Cheng) A generalization of the cellular indecomposable property via ber dimension, Journal of Functional Analysis, Vol. 260 (2011) 2964-2985.
12. (With G. Cheng) On the cellular indecomposable property of semi-Fredholm operators, Chin. Ann. Math. Ser. B Vol. 33 (2012) 903-908.
13. (With L. Chen and G. Cheng) Fiber dimension for invariant subspaces, Journal of Functional Analysis Vol. 268 (2015) 2621-2646.
14. (With Z. Wang) Two weight inequalities for the Bergman projection with doubling measures, Taiwanese Journal of Mathematics, Vol. 19 (2015) 919-926.
15. (With G. Cheng, Z. Wang and J. Yu) The hyper-singular cousin of the Bergman projection, Trans. Amer. Math. Soc. Vol. 369 (2017), no. 12, 8643-8662.
16. (With G. Cheng and S. Zhu) Random weighted shifts, Journal of Functional Analysis, Vol. 277 (2019), no. 2, 452{521.
17. (With T. Pham) A sucient condition for random zero sets of Fock spaces Archiv der Mathematik, Vol. 117 (2021), 291{304.
18. (With G. Cheng and C. Liu) A Littlewood-type theorem for random Bergman functions, Int. Math. Res. Not., Vol. 2022, Issue 14 (2022), 11056-11091.
19. (With G. Cheng, K. Guo and C. Liu) A Gaussian version of Littlewood's theorem on random power series Proc. Amer. Math. Soc., Vol. 150, number 8 (2022) 3525-3536.
20. (With T. Pham) Two problems on random entire functions in Fock spaces Canadian Journal of Mathematics Vol. 75 no. 4 (2023) 1176{1198. https://doi.org/10.4153/S0008414X22000372
21. (With K. Guo and Z. Wang) Composition operators on the Bergman space with quasiconformal symbols Journal of Geometric Analysis. 38 pages. Vol. 33 (4). Article number: 125 (2023)
 

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