Academic Information

Research Interests Employment/Education Writings Talks Seminars Teaching Conferences Miscellany Math Links Quick Links: MNCAT MathSciNet JStor NUMDAM ArXiv:NT/AG

Research Interests


Employment and Education

My professional activities have been partially supported by the following grants and fellowships: Any opinions, findings, and conclusions or recommendations expressed in the supported works are those of mine and my collaborators, and do not necessarily reflect the views of the funding organizations.

Writings

  1. Closed immersions of toroidal compactifications of Shimura varieties, preprint.
  2. Logarithmic Riemann–Hilbert correspondences for rigid varieties, with Hansheng Diao, Ruochuan Liu, and Xinwen Zhu, submitted.
  3. Nearby cycles of automorphic étale sheaves, II, with Benoît Stroh, Cohomology of Arithmetic Groups: On the Occasion of Joachim Schwermer's 66th birthday, Bonn, Germany, June 2016, Springer Proceedings in Mathematics & Statistics, vol. 245, pp. 83–106, Springer International Publishing, 2018, doi:10.1007/978-3-319-95549-0_4.
  4. An example-based introduction to Shimura varieties, to appear in the proceedings of the ETHZ Summer School on Motives and Complex Multiplication.
  5. Cohomology of automorphic bundles, Proceedings of the Seventh International Congress of Chinese Mathematicians, Volume I, Advanced Lectures in Mathematics, vol. 43, pp. 303–325, International Press, 2019.
  6. Algebraic tori as degenerations of abelian varieties, with Junecue Suh, Mathematika 64 (2018), no. 2, pp. 303–329, doi:10.1112/S0025579317000420.
  7. Compactifications of subschemes of integral models of Shimura varieties, with Benoît Stroh, Forum Math. Sigma 6 (2018), e18, 105 pp., doi:10.1017/fms.2018.20.
  8. Nearby cycles of automorphic étale sheaves, with Benoît Stroh, Compos. Math. 154 (2018), no. 1, pp. 80–119, doi:10.1112/S0010437X1700745X. Errata.
  9. Vanishing theorems for coherent automorphic cohomology, Res. Math. Sci. 3 (2016), article no. 39, 43 pp., doi:10.1186/s40687-016-0085-6. Erratum. (MATLAB codes for computing vanishing degrees available upon request.)
  10. Compactifications of splitting models of PEL-type Shimura varieties, Trans. Amer. Math. Soc. 370 (2018), no. 4, pp. 2463–2515, doi:10.1090/tran/7088. Erratum.
  11. Integral models of toroidal compactifications with projective cone decompositions, IMRN 2017 (2017), no. 11, pp. 3237–3280, doi:10.1093/imrn/rnw123. Errata.
  12. Boundary strata of connected components in positive characteristics, an appendix to Families of nearly ordinary Eisenstein series on unitary groups by Xin Wan, Algebra Number Theory 9 (2015), no. 9, pp. 1955–2054, doi:10.2140/ant.2015.9.1955.
  13. Compactifications of PEL-type Shimura varieties in ramified characteristics, Forum Math. Sigma 4 (2016), e1, 98 pp., doi:10.1017/fms.2015.31. Errata.
  14. Higher Koecher's principle, Math. Res. Lett. 23 (2016), no. 1, pp. 163–199, doi:10.4310/MRL.2016.v23.n1.a9.
  15. Relative cohomology of cuspidal forms on PEL-type Shimura varieties, with Benoît Stroh, Algebra Number Theory 8 (2014), no. 8, pp. 1787–1799, doi:10.2140/ant.2014.8.1787.
  16. On the rigid cohomology of certain Shimura varieties, with Michael Harris, Richard Taylor, and Jack Thorne, Res. Math. Sci. 3 (2016), article no. 37, 308 pp., doi:10.1186/s40687-016-0078-5, in the Special Collection in Honor of Robert F. Coleman.
  17. Compactifications of PEL-type Shimura varieties and Kuga families with ordinary loci, World Scientific Publishing Co., Singapore, 2018. Errata. (For the preprint version missing the preface, see here.)
  18. Geometric modular forms and the cohomology of torsion automorphic sheaves, Fifth International Congress of Chinese Mathematicians, AMS/IP Studies in Advanced Mathematics, vol. 51, part 1, pp. 183–208, American Mathematical Society and International Press, 2012.
  19. Vanishing theorems for torsion automorphic sheaves on general PEL-type Shimura varieties, with Junecue Suh, Adv. Math. 242 (2013), pp. 228–286, doi:10.1016/j.aim.2013.04.004. Errata.
  20. Dual BGG complexes for automorphic bundles, with Patrick Polo, Math. Res. Lett. 25 (2018), no. 1, pp. 85–141, doi:10.4310/MRL.2018.v25.n1.a5.
  21. Vanishing theorems for torsion automorphic sheaves on compact PEL-type Shimura varieties, with Junecue Suh, Duke Math. J. 161 (2012), no. 6, pp. 1113–1170, doi:10.1215/00127094-1548452. Errata.
  22. Liftability of mod p cusp forms of parallel weights, with Junecue Suh, IMRN 2011 (2011), no. 8, pp. 1870–1879, doi:10.1093/imrn/rnq145.
  23. Elevators for degenerations of PEL structures, Math. Res. Lett. 18 (2011), no. 5, pp. 889–907, doi:10.4310/MRL.2011.v18.n5.a7. Errata.
  24. Comparison between analytic and algebraic constructions of toroidal compactifications of PEL-type Shimura varieties, J. Reine Angew. Math. 664 (2012), pp. 163–228, doi:10.1515/CRELLE.2011.099. Errata.
  25. Toroidal compactifications of PEL-type Kuga families, Algebra Number Theory 6 (2012), no. 5, pp. 885–966, doi:10.2140/ant.2012.6.885. Errata.
  26. Arithmetic compactifications of PEL-type Shimura varieties, London Mathematical Society Monographs, vol. 36, Princeton University Press, Princeton, 2013. Errata.
  27. Arithmetic compactifications of PEL-type Shimura varieties, Ph.D. thesis, Harvard University, May 20, 2008.
    1. Official double-spaced version submitted to Harvard University (for electronic publication on the ProQuest Dissertations & Theses Database).
    2. Single-spaced version compiled on May 21, 2008. (Almost identical to the above document.)
    3. Errata.
    4. Most recent revision (single-spaced) or (densely-spaced). (Corrections to typos and minor mistakes are incorporated at the time of compilation.) WARNING: The numbering of results in these documents are different from the official version. Nevertheless, it is consistent with that in the book published (see above) in London Mathematical Society Monographs. Please refer to that book.
  28. Moduli schemes of elliptic curves, M.S. thesis, National Taiwan University, Jun 15, 2001. (The electronic document for this is no longer available.)

Talks (Selection)

(Talks given in reading seminars are not listed.)

  1. 2020 Winter School on Geometry and Arithmetic of Shimura Varieties, Morningside Center of Mathematics, Mar 2–6, 2020.
  2. Closed immersions of toroidal compactifications of Shimura varieties, Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, May 31, 2019.
  3. Cohomology of Shimura varieties and Hodge–Tate weights:
    1. The Legacy of Élie Cartan, Tsinghua Sanya International Mathematics Forum, Dec 16–20, 2019.
    2. NCTS Seminar on Arithmetic Geometry and Representation Theory (at Academia Sinica and National Taiwan University), Jan 4, 2019.
    3. Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Dec 21, 2018.
  4. De Rham comparison and Poincaré duality for rigid varieties:
    1. Workshop on Shimura Varieties, Representation Theory and Related Topics, Hokkaido University, Jul 15, 2019.
    2. International Congress of Chinese Mathematicians, Beijing, Jun 12, 2019.
    3. NCTS Seminar on Arithmetic Geometry and Representation Theory (at Academia Sinica and National Taiwan University), Jan 3, 2019.
    4. Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Dec 21, 2018.
  5. Logarithmic Riemann–Hilbert correspondences for rigid varieties (and applications to Shimura varieties):
    1. NCTS Seminar on Arithmetic Geometry and Representation Theory (at Academia Sinica and National Taiwan University), Dec 25, 2018.
    2. Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Dec 19, 2018.
    3. KIAS (Korea Institute for Advanced Study) Intensive Lecture Series, with Ruochuan Liu and Xinwen Zhu, Aug 6–10, 2018.
  6. Local systems over Shimura varieties: a comparison between two constructions:
    1. Princeton University / IAS Number Theory Seminar, Nov 14, 2019.
    2. Northwestern Number Theory Seminar, Nov 8, 2019.
    3. University of Chicago Number Theory Seminar, Nov 7, 2019.
    4. Harvard Number Theory Seminar, March 27, 2019.
    5. Arithmetic of Shimura Varieties, Oberwolfach, Jan 15, 2019. Extended abstract, to appear in Oberwolfach Reports.
    6. Annual Meeting of International Consortium of Chinese Mathematicians, National Taiwan University, Dec 28, 2018.
    7. Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Dec 19, 2018.
    8. Automorphic Forms, Representations of Lie Groups and Several Complex Variables, Hua Loo-Keng Center for Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Jul 13, 2018.
    9. The Joint International Meeting of the Chinese Mathematical Society and the American Mathematical Society, Fudan University, Jun 11, 2018.
    10. Arithmetic Geometry and Related Topics, Ehime University, Nov 22, 2017.
    11. Automorphic Forms and Arithmetic Seminar, Columbia University, Oct 13, 2017.
    12. Automorphic Forms and Representation Theory Seminar, Purdue University, Aug 24, 2017.
  7. Compactifications of subschemes of integral models of Shimura varieties:
    1. Workshop on Shimura Varieties, Representation Theory and Related Topics, Kyoto, Nov 25, 2016.
    2. Number Theory Seminar, Beijing International Center for Mathematical Research, Jan 14, 2016.
  8. Nearby cycles of automorphic étale sheaves:
    1. Caltech Number Theory Seminar, Sep 12, 2019.
    2. University of Chicago Number Theory Seminar, May 8, 2018.
    3. Northwestern Number Theory Seminar, May 7, 2018.
    4. Special Cycles on Shimura Varieties and Iwasawa Theory, Bernoulli Center, EPFL, Aug 29, 2017.
    5. Johns-Hopkins–University of Maryland Algebra & Number Theory Day, Apr 15, 2017.
    6. From Number Theory to Arithmetic Geometry, National Taiwan University, Dec 26, 2016.
    7. Conference on the Cohomology of Arithmetic Groups on the occasion of Joachim Schwermer's 66th birthday, MPI, Bonn, Jun 10, 2016.
    8. Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Dec 18, 2015.
  9. Compactifications of splitting models of PEL-type Shimura varieties:
    1. 2016 Workshop on Number Theory, Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Aug 2, 2016.
    2. Journées arithmétiques à Lyon, June 12, 2015.
  10. Vanishing theorems for coherent automorphic cohomology:
    1. Group, Lie and Number Theory Seminar, University of Michigan, Oct 5, 2015.
    2. Frontiers in Serre's Modularity Conjecture: Torsion and Low Weights, Luxembourg, Jun 18, 2015.
    3. Arithmetic Geometry and Automorphic Representations, ESI, Vienna, May 20, 2015.
    4. Lie Theory Seminar, University of Minnesota, Twin Cities, Mar 27 and Apr 3, 2015.
  11. Higher Koecher's principle:
    1. Automorphic Forms, Shimura Varieties, Galois Representations and L-Functions (a workshop in honor of Michael Harris), MSRI, Dec 2, 2014. Video
    2. Stanford/AIM Number Theory Seminar, Nov 7, 2014.
    3. Lie Theory Seminar, University of Minnesota, Twin Cities, Oct 17 and 24, 2014.
    4. Pan Asia Number theory (ICM satellite conference), POSTECH, Pohang, South Korea, Aug 8, 2014.
  12. Compactifications of PEL-type Shimura varieties in ramified characteristics:
    1. Morningside Center of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Dec 18, 2015.
    2. p-adic Methods in the Theory of Classical Automorphic Forms, CRM, Montréal, Mar 12, 2015.
    3. University of Chicago Number Theory Seminar, Feb 24, 2015.
    4. Caltech Number Theory Seminar, Jan 15, 2015.
    5. NCTS/TPE Seminar on Arithmetic Geometry and Representation Theory (at Academia Sinica and National Taiwan University), July 28, 2014.
  13. An example-based introduction to Shimura varieties and their compactifications:
    1. Automorphic Forms, Representations of Lie Groups and Several Complex Variables, Hua Loo-Keng Center for Mathematical Sciences, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Jul 6, 2018.
    2. Motives and Complex Multiplication, Ascona, Switzerland, minicourse, Aug 15–17, 2016.
    3. Introductory Workshop: New Geometric Methods in Number Theory and Automorphic Forms, MSRI, 3 lectures, Aug 18–20, 2014. Videos: 1 2 3
    4. NCTS/TPE Seminar on Arithmetic Geometry and Representation Theory (at Academia Sinica and National Taiwan University), July 28, 2014.
  14. Galois representations for regular algebraic (cuspidal) automorphic forms/representations over CM fields:
    1. Number Theory–Representation Theory Seminar, University of Wisconsin, Madison, Mar 7, 2013.
    2. Number Theory Seminar, University of North Carolina, Chapel Hill, Mar 5, 2013.
    3. Arithmetic and Geometry, Hausdorff Trimester Program, Bonn, Jan 31 and Feb 1, 2013.
    4. Stanford/AIM Number Theory Seminar, Jan 18, 2013.
    5. University of Chicago Number Theory Seminar, Oct 9, 2012.
    6. Lie Theory Seminar, University of Minnesota, Twin Cities, Oct 5 and 12, 2012.
    7. NCTS/TPE Seminar on Arithmetic Geometry (at National Taiwan University), Aug 9, 2012.
    8. Workshop on the Arithmetic Geometry of Shimura Varieties, Representation Theory, and Related Topics, Sapporo, Jul 21, 2012.
  15. Compactifications of PEL-type Shimura varieties and Kuga families with ordinary loci:
    1. Arithmetic Algebraic Geometry, Paderborn, Oct 11, 2013.
    2. NCTS Seminar on Arithmetic Geometry and Representation Theory (at Academia Sinica and National Taiwan University), 8 lectures, Jul 23, 25, 29, and 31, 2013.
    3. International Congress of Chinese Mathematicians, Taipei, Jul 16, 2013.
    4. p-adic Modular Forms, L-functions, and Galois representations, UCLA, May 11, 2013.
    5. Higher Rank Automorphic Forms and L-functions, University of Warwick, May 2, 2013.
    6. Northwestern Number Theory Seminar, Apr 22, 2013.
    7. Princeton University / IAS Number Theory Seminar, Feb 21, 2013.
    8. Algebra Seminar, Michigan State University, Oct 31, 2012.
    9. NCTS/TPE Seminar on Arithmetic Geometry (at National Taiwan University), Aug 9, 2012.
    10. Seminar on Arithmetic Geometry, Hokkaido University, 2 lectures, Jul 30, 2012; continuation of the following workshop lecture.
    11. Workshop on the Arithmetic Geometry of Shimura Varieties, Representation Theory, and Related Topics, Sapporo, Jul 19, 2012.
    12. Workshop on Arithmetic Geometry and Representation Theory, HKUST IAS, Hong Kong, Dec 28, 2011.
  16. Kodaira-type vanishing on good reduction fibers of Shimura varieties:
    1. Workshop on the Arithmetic Geometry of Shimura Varieties and Rapoport-Zink Spaces, Kyoto University, Jul 8, 2011.
    2. NCTS Number Theory Seminar, Hsinchu, Taiwan, Jun 28, 2011.
    3. Caltech Number Theory Seminar, May 31, 2011.
  17. Geometric modular forms in higher dimensions:
    1. Colloquium, UC Santa Cruz, May 9, 2017.
    2. Colloquium, Cornell University, Feb 8, 2011.
    3. Special Colloquium, UC Irvine, Jan 18, 2011.
    4. Colloquium, McMaster University, Jan 10, 2011.
    5. Colloquium, University of Minnesota, Twin Cities, Dec 7, 2010.
    6. Colloquium, Boston College, Nov 30, 2010.
  18. Vanishing theorems for torsion automorphic sheaves (on general PEL-type Shimura varieties):
    1. Seminar on Arithmetic Geometry, Hokkaido University, 2 lectures, July 17, 2012.
    2. Workshop on Cohomology of Shimura Varieties: Arithmetic Aspects and The Construction of Galois Representations, Fields Institute, Mar 23, 2012.
    3. Quebec-Vermont Number Theory Seminar, Feb 2, 2012.
    4. 2011 NCTS International Conference on Galois Representations, Automorphic Forms and Shimura Varieties, Hsinchu, Taiwan, Jun 20, 2011.
    5. Caltech Number Theory Seminar, May 26, 2011.
    6. Automorphic Forms and Representation Theory Seminar, Purdue University, Mar 31, 2011.
    7. Workshop on Automorphic Forms and Shimura Varieties, Columbia University, Mar 19, 2011.
    8. Boston University Number Theory Seminar, Jan 28, 2011.
    9. Lie Groups and Representation Theory Seminar, University of Maryland, Jan 26, 2011.
    10. International Congress of Chinese Mathematicians, Tsinghua University, Beijing, Dec 19, 2010.
    11. Galois Representations and Automorphic Forms Seminar, Institute for Advanced Study, Dec 9, 2010.
    12. Bay Area Algebraic Number Theory and Arithmetic Geometry Day I (special day of Stanford/AIM Number Theory Seminar), Nov 6, 2010.
    13. BC-MIT Number Theory Seminar, Sep 21, 2010.
    14. Number Theory Seminar, Academia Sinica, Jul 20, 2010; continuation of the following workshop lecture.
    15. Workshop on Arithmetic Geometry and Related Topics, Taipei, Jul 14, 2010.
    16. University of Chicago Number Theory Seminar, Apr 9, 2010.
    17. Members Seminar, Institute for Advanced Study, Apr 5, 2010.
  19. Liftability of mod p cusp forms of regular weights, GCOE Number Theory Joint Seminar, Kyoto University, Dec 4, 2009.
  20. Vanishing theorems for torsion automorphic sheaves (on compact PEL-type Shimura varieties):
    1. Northwestern Number Theory Seminar, Feb 22, 2010.
    2. Number Theory / Representation Theory Seminar, University of Toronto, Jan 27, 2010.
    3. Workshop on Arithmetic Geometry in Kanazawa, Nov 24, 2009.
  21. Analytic coordinates for degenerations of PEL structures, NCTS/TPE (at National Taiwan University), Aug 3, 6, and 10, 2009.
  22. Elevators for degenerations of PEL structures, Workshop on Automorphic Representations, Geometry, and Arithmetic, Taipei, Jul 22, 2009.
  23. Cohomology of automorphic bundles / Coherent cohomology of automorphic bundles:
    1. International Congress of Chinese Mathematicians, Beijing, Aug 8, 2016.
    2. Number Theory Seminar, Beijing International Center for Mathematical Research, 4 lectures, Dec 15, 16, 21, and 23, 2015.
    3. Short Talks by Postdoctoral Members, Institute for Advanced Study, Sep 29, 2009.
    4. Mini-course at NCTS/TPE (at National Taiwan University), Dec 16, 24, and 30, 2008.
  24. Toroidal compactifications of certain Kuga families / Extensions (of various structures) over toroidal boundaries of Shimura varieties:
    1. Stanford/AIM Number Theory Seminar, May 8, 2009.
    2. Princeton University / IAS Number Theory Seminar, Apr 23, 2009.
    3. Algebra and Number Theory Seminar, University of Maryland, Feb 16, 2009.
    4. Algebra Seminar, University of Pennsylvania, Feb 2, 2009.
    5. Workshop on Shimura Varieties, Automorphic Representations and Related Topics, Kyoto, Nov 27, 2008.
    6. Group, Lie and Number Theory Seminar, University of Michigan, Nov 10, 2008.
    7. Joint Columbia-CUNY-NYU Number Theory Seminar, Oct 2, 2008.
  25. Arithmetic compactifications of (general) PEL-type Shimura varieties:
    1. Shimura Varieties and Trace Formula Seminar, Institute for Advanced Study, Oct 31 and Nov 3, 2008.
    2. Algebra Seminar, Michigan State University, Apr 15, 2008.
    3. Number Theory and Representation Theory Seminar, University of Michigan, Apr 14, 2008.
    4. Number Theory Seminar, Harvard University, Mar 19, 2008.
    5. Seminar on Automorphic Forms and Galois Representations, Princeton University, Feb 6, 2008.
    6. Department Colloquium, Indiana University, Feb 1, 2008.
    7. KIAS (Korea Institute for Advanced Study), 4 lectures, Jan 14–15, 2008.
    8. Number Theory Seminar, Academia Sinica, 4 lectures, Jan 2–3, 2008.
    9. Seminar on Arithmetic Geometry, Hokkaido University, 4 lectures, Aug 28–29, 2007.
    10. Mini-Workshop on Automorphic Representations and Shimura Varieties, Kyoto, May 31, 2007. (Full-day informal seminar, May 29, 2007.)
    11. Algebraic Geometry Seminar, NCTS/TPE (at National Taiwan University), Jan 2, 2007.
  26. Arithmetic compactifications of Shimura varieties associated to certain unitary groups:
    1. Caltech Number Theory Seminar, Sep 7, 2006.
    2. Lecture series, National Taiwan University, May 23 and 30, and Jun 6, 2006.

Seminars

Weekly schedule

Regular Seminars:

Reading Seminars:

A list of academic visitors since the fall of 2012.


Teaching


Conferences / Special Programs (Selection)


Miscellany

(Please don't ask for the source files.)