## Tsao-Hsien Chen

Associate Professor

Email: chenth@umn.edu

School of Mathematics University of Minnesota, Twin Cities

206 Church St. S.E., Minneapolis, 451 Vincent Hall

### Research Interests

I am interested in geometric representation theory.

### Summer Schools and Conferences

Summer School and Workshop on Relative Langlands Duality, June 3-8, 2024 (Notes from summer schools and workshops)

### Geometric methods in Langlands program seminar

Spring 2024: Perverse sheaves

Fall 2022: Character sheaves on loop groups

Spring 2022: Weil representation and Metaplectic groups

Fall 2021: Hecke-Jacquet-Langlands' theory

### Preprints

A description of the integral depth-r Bernstein center (with Sarbartha Bhattacharya)

Real groups, symmetric varieties and Langlands duality (with David Nadler)

Slices in loop spaces of symmetric varieties and the formality conjecture (with Lingfei Yi).

Quaternionic Satake equivalence (with Mark Macerato, David Nadler, John O’Brien)

Affine Matsuki correspondence for sheaves (with David Nadler).

On the Hitchin fibration for algebraic surfaces (with Ngo Bao Chau).

Twisted global section functor for D-modules on affine Grassmannian (with Giorgia Fortuna).

Publications

Hitchin map and opers in characteristic p (with Roman Bezrukavnikov, Roman Travkin, and Xinwen Zhu), an Appendix to Quantization of Hitchin integrable system via positive characteristic by Roman Bezrukavnikov and Roman Travkin, Pure and Applied Mathematics Quarterly (issue dedicated to David Kazhdan), to appear.

Real and symmetric quasi-maps (with David Nadler), XI Southesatern Lie theory confereence proceddings, to appear.

Real and symmetric matrices (with David Nadler), Duke Math. J., to appear.

Invariant theory for the commuting scheme of symplectic Lie algebras (with Ngo Bao Chau), Proceedings of the TIFR conference on Arithmetic Geometry, to appear.

A vanishing conjecture: the GL_n-case, Selecta Math. 28, 13 (2022).

On a conjecture of Braverman-Kazhdan, J. Amer. Math. Soc. 35 (2022), 1171-1214.

On the Hitchin morphism for higher dimensional varieties (with Ngo Bao Chau), Duke Math. J. Volume 169 (2020), 1971-2004.

On the Casselman-Jacquet functor (with Dennis Gaitsgory and Alexander Yom Din), Representations of Reductive Groups, Proc. Sympos. Pure Math. 101 (2019), 73-112 (volume in honor of J.Bernstein).

Survey on geometric Langlands and non-abelian Hodge theory in characteristic p (Expository), Proceedings of ICCM in Beijing 2016.

Springer correspondence for the split symmetric pair in type A (with Kari Vilonen and Ting Xue), Compositio Math, Volume 154, Issue 11, 2403-2425.

On the cohomology of Fano varieties and Springer correspondence (with Kari Vilonen and Ting Xue), with an Appendix by Dennis Stanton, Advances in Math 318 (2017), 515-533.

Hessenberg varieties, intersection of quadrics, and Springer correspondence (with Kari Vilonen and Ting Xue), Trans. Amer. Math. Soc. 373 (2020), 2427-2461.

Springer correspondence, hyperelliptic curves, and cohomology of Fano varieties (with Kari Vilonen and Ting Xue), Mathematical Research Letters, Vol. 27, No. 5 (2020), pp. 1281-1323.

A formula for the geometric Jacquet functor and its character sheaf analogue (with Alexander Yom Din), Geometric and Functional Analysis, Volume 27 (2017), no. 4, 772-797.

Preservation of depth in local geometric Langlands correspondence (with Masoud Kamgarpour), Trans. Amer. Math. Soc. 369 (2017), no. 2, 1345-1364.

Non-abelain Hodge theory for algebraic curves in characteristic p (with Xinwen Zhu), Geometric and Functional Analysis, Volume 25 (2015), pp 1706-1733.

Geometric Langlands in prime characteristic (with Xinwen Zhu), Compositio Math, Volume 153, Issue 2 February 2017, pp. 395-452.

Vinberg's θ-Groups and rigid connections , IMRN, Volume 2017, Issue 23, pp. 7321-7343.