## Research Interests

- Number theory
- Automorphic forms
- Geometry and cohomology of Shimura varieties and their compactifications
- Relations between the above

## Employment and Education

- Associate Professor, School of Mathematics. University of Minnesota, Twin Cities. academic years 2015–now.
- Assistant Professor, School of Mathematics. University of Minnesota, Twin Cities. academic years 2012–2015.
- Veblen Research Instructor, joint position of Department of Mathematics. Princeton University. and School of Mathematics. Institute for Advanced Study. academic years 2008–2012.
- Doctor of Philosophy, Department of Mathematics. Harvard University. academic years 2003–2008. (Advisor: Prof. Richard Taylor .)
- Master of Science, Department of Mathematics. National Taiwan University. academic years 1999–2001. (Advisor: Prof. Ki-Seng Tan .)
- Bachelor of Science, Department of Mathematics. National Taiwan University. academic years 1995–1999.

My professional activities have been partially supported by the following grants and fellowships:

- Alfred P. Sloan Research Fellowship. academic years 2014–2016.
- NSF Grant DMS-1352216 (CAREER) (PI), academic years 2014–2019.
- NSF Grant DMS-1258962 (PI), academic years 2012–2014.
- NSF Grant DMS-1069154 (PI), academic years 2011–2012.
- NSF Grant DMS-0635607 (through membership at the Institute for Advanced Study) and Qiu Shi Fellowship at the Institute for Advanced Study in Princeton. academic year 2009–2010.
- Clay Liftoff Fellowship, Summer 2008.

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

- Personal notes are not listed. (Some talk slides or notes might be available in the section below on talks.)
- All documents listed, whether linked directly or not, are available upon request (unless otherwise specified). (Joint works might not be linked until I have obtained the approval from the coauthors.)
- Articles described as submitted might have gone through corrections/revisions since the dates of submissions. (The precise dates of submissions/revisions are not recorded here.)
- Please let me know if the links are broken. This should never happen. (I do not take files down when revising them.)
- Please feel free to send me corrections or questions if you notice anything wrong or confusing.

*Compactifications of subschemes of integral models of Shimura varieties*. with Benoît Stroh. submitted.*Neabry cycles of automorphic étale sheaves*. with Benoît Stroh. submitted.*Vanishing theorems for coherent automorphic cohomology*. to appear in Res. Math. Sci. (MATLAB codes for computing vanishing degrees available upon request.)*Compactifications of splitting models of PEL-type Shimura varieties*. to appear in Trans. Amer. Math. Soc.*Integral models of toroidal compactifications with projective cone decompositions*. IMRN, doi:10.1093/imrn/rnw123.*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.*Compactifications of PEL-type Shimura varieties in ramified characteristics*. Forum Math. Sigma 4 (2016), e1, 98 pp. doi:10.1017/fms.2015.31. Errata*Higher Koecher’s principle*. Math. Res. Lett. 23 (2016), no. 1, pp. 163–199, doi:10.4310/MRL.2016.v23.n1.a9.*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.*On the rigid cohomology of certain Shimura varieties*. with Michael Harris. Richard Taylor. and Jack Thorne. Res. Math. Sci. (special collection in honor of Robert F. Coleman).*Compactifications of PEL-type Shimura varieties and Kuga families with ordinary loci*. to be published by World Scientific Publishing Co. Singapore.*Geometric modular forms and the cohomology of torsion automorphic sheaves*. Fifth International Congress of Chinese Mathematicians, AMS/IP Studies in Advanced Mathematics 51 (2012). part 1, pp. 183–208.*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*Dual BGG complexes for automorphic bundles*. with Patrick Polo. to appear in Math. Res. Lett.*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*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.*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*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*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*Arithmetic compactifications of PEL-type Shimura varieties*. London Mathematical Society Monographs, vol. 36, Princeton University Press, Princeton, 2013. Errata*Arithmetic compactifications of PEL-type Shimura varieties*. Ph.D. thesis, Harvard University, May 20, 2008.

- Official double-spaced version submitted to Harvard University (for electronic publication on the ProQuest Dissertations Theses Database).
- Single-spaced version compiled on May 21, 2008. (Almost identical to the above document.)
- Errata.
- 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.

*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.)

- Colloquium, UC Santa Cruz, May 9, 2017.
- From Number Theory to Arithmetic Geometry, National Taiwan University, Dec 25–26, 2016.
- Workshop on Shimura Varieties, Representation Theory and Related Topics. Kyoto, Nov 21–25, 2016.
*Compactifications of subschemes of integral models of Shimura varieties*. Beijing International Center for Mathematical Research, Jan 14, 2016.*Nearby cycles of automorphic étale sheaves*.

- Conference on the Cohomology of Arithmetic Groups on the occasion of Joachim Schwermer’s 66th birthday. MPI, Bonn, Jun 10, 2016.
- Morningside Center of Mathematics. Academy of Mathematics and Systems Science. Chinese Academy of Sciences, Dec 18, 2015.

*Cohomology of automorphic bundles*.

- International Congress of Chinese Mathematicians. Beijing, Aug 8, 2016.
- Beijing International Center for Mathematical Research. 4 lectures, Dec 15, 16, 21, and 23, 2015.

*Compactifications of splitting models of PEL-type Shimura varieties*.

- 2016 Workshop on Number Theory. Morningside Center of Mathematics, Beijing, Aug 2, 2016.
- Journées arithmétiques à Lyon. June 12, 2015.

*Vanishing theorems for coherent automorphic cohomology*.

- Group, Lie and Number Theory Seminar. University of Michigan, Oct 5, 2015.
- Frontiers in Serre’s Modularity Conjecture: Torsion and Low Weights. Luxembourg, Jun 18, 2015.
- Arithmetic Geometry and Automorphic Representations. ESI, Vienna, May 20, 2015.
- Lie Theory Seminar. University of Minnesota, Twin Cities, Mar 27 and Apr 3, 2015.

*Higher Koecher’s principle*.

- Automorphic Forms, Shimura Varieties, Galois Representations and L-Functions (a workshop in honor of Michael Harris). MSRI, Dec 2, 2014. Video
- Stanford/AIM Number Theory Seminar. Nov 7, 2014.
- Lie Theory Seminar. University of Minnesota, Twin Cities, Oct 17 and 24, 2014.
- Pan Asia Number theory (ICM satellite conference), POSTECH, Pohang, South Korea, Aug 8, 2014.

*Compactifications of PEL-type Shimura varieties in ramified characteristics*.

- Morningside Center of Mathematics. Academy of Mathematics and Systems Science. Chinese Academy of Sciences, Dec 18, 2015.
*p*-adic Methods in the Theory of Classical Automorphic Forms. CRM, Montréal, Mar 12, 2015.- University of Chicago Number Theory Seminar. Feb 24, 2015.
- Caltech Number Theory Seminar. Jan 15, 2015.
- NCTS/TPE Seminar on Arithmetic Geometry and Representation Theory (at Academia Sinica and National Taiwan University), July 28, 2014.

*An example-based introduction to Shimura varieties and their compactifications*.

- Motives and Complex Multiplication. Ascona, Switzerland, minicourse, Aug 15–17, 2016.
- Introductory Workshop: New Geometric Methods in Number Theory and Automorphic Forms. MSRI, 3 lectures, Aug 18–20, 2014. Videos: 1 2 3
- NCTS/TPE Seminar on Arithmetic Geometry and Representation Theory (at Academia Sinica and National Taiwan University), July 28, 2014.

*Galois representations for regular algebraic (cuspidal) automorphic forms/representations over CM fields*.

- Number Theory–Representation Theory Seminar. University of Wisconsin, Madison, Mar 7, 2013.
- Number Theory Seminar. University of North Carolina, Chapel Hill, Mar 5, 2013.
- Arithmetic and Geometry. Hausdorff Trimester Program, Bonn, Jan 31 and Feb 1, 2013.
- Stanford/AIM Number Theory Seminar. Jan 18, 2013.
- University of Chicago Number Theory Seminar. Oct 9, 2012.
- Lie Theory Seminar. University of Minnesota, Twin Cities, Oct 5 and 12, 2012.
- NCTS/TPE Seminar on Arithmetic Geometry (at National Taiwan University), Aug 9, 2012.
- Workshop on the Arithmetic Geometry of Shimura Varieties, Representation Theory, and Related Topics. Sapporo, Jul 21, 2012.

*Compactifications of PEL-type Shimura varieties and Kuga families with ordinary loci*.

- Arithmetic Algebraic Geometry. Paderborn, Oct 11, 2013.
- NCTS Seminar on Arithmetic Geometry and Representation Theory (at Academia Sinica and National Taiwan University), 8 lectures, Jul 23, 25, 29, and 31, 2013.
- International Congress of Chinese Mathematicians. Taipei, Jul 16, 2013.
*p*-adic Modular Forms, L-functions, and Galois representations. UCLA, May 11, 2013.- Higher Rank Automorphic Forms and L-functions. University of Warwick, May 2, 2013.
- Northwestern Number Theory Seminar. Apr 22, 2013.
- Princeton University / IAS Number Theory Seminar. Feb 21, 2013.
- Algebra Seminar. Michigan State University, Oct 31, 2012.
- NCTS/TPE Seminar on Arithmetic Geometry (at National Taiwan University), Aug 9, 2012.
- Seminar on Arithmetic Geometry (organized by Prof. Iku Nakamura ), Hokkaido University, 2 lectures, Jul 30, 2012; continuation of the following workshop lecture.
- Workshop on the Arithmetic Geometry of Shimura Varieties, Representation Theory, and Related Topics. Sapporo, Jul 19, 2012.
- Workshop on Arithmetic Geometry and Representation Theory. HKUST IAS, Hong Kong, Dec 28, 2011.

*Kodaira-type vanishing on good reduction fibers of Shimura varieties*.

- Workshop on the Arithmetic Geometry of Shimura Varieties and Rapoport-Zink Spaces. Kyoto University, Jul 8, 2011.
- NCTS Number Theory Seminar. Hsinchu, Taiwan, Jun 28, 2011.
- Caltech Number Theory Seminar. May 31, 2011.

*Geometric modular forms in higher dimensions*.

- Colloquium, Cornell University, Feb 8, 2011.
- Special Colloquium. UC Irvine, Jan 18, 2011.
- Colloquium. McMaster University, Jan 10, 2011.
- Colloquium, University of Minnesota, Twin Cities, Dec 7, 2010.
- Colloquium, Boston College, Nov 30, 2010.

*Vanishing theorems for torsion automorphic sheaves*(*on general PEL-type Shimura varieties*) .

- Seminar on Arithmetic Geometry (organized by Prof. Iku Nakamura ), Hokkaido University, 2 lectures, July 17, 2012.
- Workshop on Cohomology of Shimura Varieties: Arithmetic Aspects and The Construction of Galois Representations. Fields Institute, Mar 23, 2012.
- Quebec-Vermont Number Theory Seminar. Feb 2, 2012.
- 2011 NCTS International Conference on Galois Representations, Automorphic Forms and Shimura Varieties. Hsinchu, Taiwan, Jun 20, 2011.
- Caltech Number Theory Seminar. May 26, 2011.
- Automorphic Forms and Representation Theory Seminars. Purdue University, Mar 31, 2011.
- Workshop on Automorphic Forms and Shimura Varieties. Columbia University, Mar 19, 2011.
- Boston University Number Theory Seminar. Jan 28, 2011.
- Lie Groups and Representation Theory Seminar. University of Maryland, Jan 26, 2011.
- International Congress of Chinese Mathematicians. Tsinghua University, Beijing, Dec 19, 2010.
- Galois Representations and Automorphic Forms Seminar. Institute for Advanced Study, Dec 9, 2010.
- Bay Area Algebraic Number Theory and Arithmetic Geometry Day I (special day of Stanford/AIM Number Theory Seminar ), Nov 6, 2010.
- BC-MIT Number Theory Seminar. Sep 21, 2010.
- Number Theory Seminar. Academia Sinica, Jul 20, 2010; continuation of the following workshop lecture.
- Workshop on Arithmetic Geometry and Related Topics. Taipei, Jul 14, 2010.
- University of Chicago Number Theory Seminar. Apr 9, 2010.
- Members Seminar. Institute for Advanced Study, Apr 5, 2010.

*Liftability of mod p cusp forms of regular weights*. GCOE Number Theory Joint Seminar. Kyoto University, Dec 4, 2009.*Vanishing theorems for torsion automorphic sheaves*(*on compact PEL-type Shimura varieties*) .

- Northwestern Number Theory Seminar. Feb 22, 2010.
- Number Theory / Representation Theory Seminar. University of Toronto, Jan 27, 2010.
- Workshop on Arithmetic Geometry in Kanazawa. Nov 24, 2009.

*Coherent cohomology of automorphic bundles*. Short Talks by Postdoctoral Members, Institute for Advanced Study, Sep 29, 2009.*Analytic coordinates for degenerations of PEL structures*. NCTS/TPE (at National Taiwan University), Aug 3, 6, and 10, 2009.*Elevators for degenerations of PEL structures*. Workshop on Automorphic Representations, Geometry, and Arithmetic. Taipei, Jul 22, 2009.*Cohomology of automorphic bundles*. mini-course at NCTS/TPE (at National Taiwan University), Dec 16, 24, and 30, 2008.*Toroidal compactifications of certain Kuga families*/*Extensions (of various structures) over toroidal boundaries of Shimura varieties*.

- Stanford/AIM Number Theory Seminar. May 8, 2009.
- Princeton University / IAS Number Theory Seminar. Apr 23, 2009.
- Algebra and Number Theory Seminar. University of Maryland, Feb 16, 2009.
- Algebra Seminar. University of Pennsylvania, Feb 2, 2009.
- Workshop on Shimura Varieties, Automorphic Representations and Related Topics. Kyoto, Nov 27, 2008.
- Group, Lie and Number Theory Seminar. University of Michigan, Nov 10, 2008.
- Joint Columbia-CUNY-NYU Number Theory Seminar. Oct 2, 2008.

*Arithmetic compactifications of (general) PEL-type Shimura varieties*.

- Shimura Varieties and Trace Formula Seminar. Institute for Advanced Study, Oct 31 and Nov 3, 2008.
- Algebra Seminar, Michigan State University, Apr 15, 2008.
- Number Theory and Representation Theory Seminar. University of Michigan, Apr 14, 2008.
- Number Theory Seminar, Harvard University, Mar 19, 2008.
- Seminar on Automorphic Forms and Galois Representations, Princeton University, Feb 6, 2008.
- Department Colloquium. Indiana University, Feb 1, 2008.
- KIAS (Korea Institute for Advanced Study). 4 lectures, Jan 14–15, 2008.
- Number Theory Seminar, Academia Sinica, 4 lectures, Jan 2–3, 2008.
- Seminar on Arithmetic Geometry (organized by Prof. Iku Nakamura ), Hokkaido University, 4 lectures, Aug 28–29, 2007.
- Mini-Workshop on Automorphic Representations and Shimura Varieties. Kyoto, May 31, 2007. (Full-day informal seminar, May 29, 2007.)
- Algebraic Geometry Seminar, NCTS/TPE (at National Taiwan University), Jan 2, 2007.

*Arithmetic compactifications of Shimura varieties associated to certain unitary groups*.

- Caltech Number Theory Seminar. Sep 7, 2006.
- Lecture series, National Taiwan University, May 23 and 30, and Jun 6, 2006.

## Seminars

Reading Seminars:

- Fall 2012 on D-modules
- Spring 2015 (associated with the topic course Math 8270)
- Summer 2015 (associated with an REU)
- Spring 2016 (associated with the topic course Math 8280)

## Teaching

- University of Minnesota, Twin Cities:

- Math 8272: Lie Groups and Lie Algebras, Spring 2017.
- Math 8271: Lie Groups and Lie Algebras, Fall 2016.
- Math 8280: Topics in Number Theory: Automorphic and Galois Representations, Spring 2016 (section 001) (with a reading seminar ).
- Math 8270: Topics in Algebraic Geometry: Abelian Schemes and Their Moduli, Spring 2015 (with a reading seminar ).
- Math 8254: Algebraic Geometry, Spring 2014.
- Math 8253: Algebraic Geometry, Fall 2013.
- Math 4242: Applied Linear Algebra, Fall 2012 (sections 010 and 060 ).
- REU/UROP/URS/Honors Thesis/Senior Project. Feel free to contact me if you are interested.
- MathCEP /UMTYMP.

(If you are not officially enrolled in the courses, but still want to have access to the Moodle pages, please feel free to contact me.) - Princeton University:

- MAT 204: Advanced Linear Algebra with Applications, Spring 2012 (coursehead).
- MAT 203: Advanced Multivariable Calculus, Fall 2011 (2 sections).
- MAT 203: Advanced Multivariable Calculus, Spring 2011 (1 section and 1 review, coursehead).
- MAT 203: Advanced Multivariable Calculus, Fall 2010 (2 sections).
- MAT 202: Linear Algebra With Applications, Spring 2009 (2 sections).
- MAT 203: Advanced Multivariable Calculus, Fall 2008 (2 sections).

- Harvard University:

- Math 21a: Multivariable Calculus, Spring 2008 (2 sections).
- Math 21a: Multivariable Calculus, Fall 2006.
- Math 21a: Multivariable Calculus, Fall 2005.
- Math 99r: Tutorial on
*Binary Quadratic Forms*(with Chung Pang Mok), Fall 2005. - Math 21a: Multivariable Calculus, Fall 2004.

- National Taiwan University: Differential Geometry (as a teaching assistant), Fall 2000.

## Conferences / Special Programs (Selection)

## Miscellany

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

- Foreign Language Glossaries. French. German. These are prepared primarily for reading mathematical texts, which also seemed to be helpful for the foreign language exams when I was at Harvard.