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Motives with exceptional Galois groups and the inverse Galois problem

- Zhiwei Yun
- Mathematics
- 12 December 2011

We construct motivic ℓ-adic representations of $\textup {Gal}(\overline {\mathbb{Q}}/\mathbb{Q})$ into exceptional groups of type E7,E8 and G2 whose image is Zariski dense. This answers a question of… Expand

On Koszul duality for Kac-Moody groups

- R. Bezrukavnikov, Zhiwei Yun
- Mathematics
- 6 January 2011

For any Kac-Moody group $G$ with Borel $B$, we give a monoidal equivalence between the derived category of $B$-equivariant mixed complexes on the flag variety $G/B$ and (a certain completion of) the… Expand

The fundamental lemma of Jacquet and Rallis

- Zhiwei Yun, J. Gordon
- Mathematics
- 1 February 2011

We prove both the group version and the Lie algebra version of the Fundamental Lemma appearing in a relative trace formula of Jacquet-Rallis in the function field case when the characteristic is… Expand

Geometric representations of graded and rational Cherednik algebras

- A. Oblomkov, Zhiwei Yun
- Mathematics
- 21 July 2014

Kloosterman sheaves for reductive groups

- J. Heinloth, N. Chau, Zhiwei Yun
- Mathematics
- 16 May 2010

Deligne constructed a remarkable local system on P 1 f 0;1g attached to a family of Kloosterman sums. Katz calculated its monodromy and asked whether there are Kloosterman sheaves for general… Expand

Shtukas and the Taylor expansion of L-functions (II)

- Zhiwei Yun, Wei Zhang
- MathematicsAnnals of Mathematics
- 8 December 2015

For arithmetic applications, we extend and refine our results in \cite{YZ} to allow ramifications in a minimal way. Starting with a possibly ramified quadratic extension $F'/F$ of function fields… Expand

The fundamental lemma of Jacquet-Rallis in positive characteristics

- Zhiwei Yun
- Mathematics
- 7 January 2009

We prove both the group version and the Lie algebra version of the Fundamental Lemma appearing in a relative trace formula of Jacquet-Rallis in the function field case when the characteristic is… Expand

Lectures on Springer theories and orbital integrals

- Zhiwei Yun
- Mathematics
- 3 February 2016

These are the expanded lecture notes from the author's mini-course during the graduate summer school of the Park City Math Institute in 2015. The main topics covered are: geometry of Springer fibers,… Expand

Macdonald formula for curves with planar singularities

- D. Maulik, Zhiwei Yun
- Mathematics
- 12 July 2011

We generalize Macdonald's formula for the cohomology of Hilbert schemes of points on a curve from smooth curves to curves with planar singularities: we relate the cohomology of the Hilbert schemes to… Expand

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