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Seminar & Colloquium

제목 | [2019/01/07-11] Seminars and Talks of this week | ||||
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작성자 | 관리자 | 등록일 | 2019-01-04 | 조회수 | 188 |

SKKU, General Bd 3F, AORC Seminar Room
Title: The Characteristic Polynomial of the Alternating Permutation PosetAbstract:
For the symmetric group S_n, a permutation w can be considered as a word of simple transpositions s_i=(i,i+1). We define some order of permutations with respect to the minimal length of the word expression of each permutation. Then S_n with this order is a poset. We consider the set of alternating permutations with the same order, which is also a poset. We call it the alternating permutation poset. It turns out that its characteristic polynomial has a nice form. In this talk we prove this property.
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Title: Combinatorial proof of two constant term identitiesAbstract:
These constant term identities was introduced in 〈A COMBINATORIAL MODEL FOR COMPUTING VOLUMES OF FLOW POLYTOPES〉. We prove these identities using labeled dyck path and parenthesizing. Chains of noncrossing partitions play an important role in our proof
The main purpose of this talk is to provide an effective version of a result due to Einsiedler, Mozes, Shah and Shapira, on the equidistribution of primitive rational points on expanding horospheres in the space of unimodular lattices in at least 3 dimensions. Their proof uses techniques from homogeneous dynamics and relies in particular on measure-classification theorems due to Ratner. Instead, we pursue an alternative strategy based on spectral theory, Fourier analysis and Weil’s bound for Kloosterman sums which yields an effective estimate on the rate of convergence in the space of (d+1)-dimensional Euclidean lattices with d>1. This extends my work with J. Marklof, on the 3-dimensional case (2017). This is a joint work with D. El-Baz and B. Huang. |

이전글 | [2019/01/25] Dr. Jehanne Dousse (University of Lyon 1, France) |
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다음글 | [2019/01/09] Dr. Min Lee (University of Bristol, UK) |