# Mathematics Colloquia and Seminars

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### Non-Emptiness of Affine Deligne-Lusztig Varieties

**Algebra & Discrete Mathematics**

Speaker: | Elizabeth Townsend Beazley, University of Chicago |

Location: | 2112 MSB |

Start time: | Fri, Jan 23 2009, 2:10PM |

Deligne-Lusztig varieties, which can be thought of as Frobenius-twisted Schubert varieties, were invented for studying the representation theory of finite Chevalley groups. We introduce several affine variants and recall the history of progress made in studying these affine versions. In particular, we demonstrate two methods for proving that certain affine Deligne-Lusztig varieties are non-empty as sets. Both methods are combinatorial in nature, the first of which uses the combinatorics of a certain set of Newton polygons, and the second of which involves the combinatorics of lengths of elements in finite Coxeter groups.

Elizabeth Beazley will also give an introductory talk on the topics of this research talk. The introductory talk is on Thursday in the student-organized discrete math seminar, at 3pm.