세미나/포럼
[세미나/포럼] [2015.03.27 금] 2015학년도 수학과 위상조합세미나
- 세미나/포럼
- 교내
- 윤혜주
- 2015-03-24
2015학년도 1학기 두 번째 수학과 위상조합세미나 일정을 안내해 드립니다.
강연제목 : High-Dimensional Trees and Metroids
연 사 : 이강주 [서울대학교]
일 시 : 3월 27일 (금요일) 오후 4:30 - 6:30
장 소 : 아주대학교 팔달관 621호
초 록 :
Part 1. High-dimensinoal trees: We introduce high-dimensional trees as a high-dimensional analogue of spanning trees. G. Kalai (1983) initiated a study of these objects, giving a formula for the high-dimensional tree numbers of standard simplexes as a high-dimensional analogue of Cayley’s fomrula (for the number of spanning trees in complete graphs). We also present our formula for high-dimensional weighted tree numbers.
Part 2. Introduction to matroid theory: We see the definition of a matroid and some terminologies, examples, and invariants from matroid theory.
Part 3. Weighted tree numbers of matroid complexes: We give a new formula for the weighted high-dimensional tree numbers of matroid complexes. This formula is derived from our result that the spectra of the weighted combinatorial Laplacians of matroid complexes are polynomials in the weights. In the formula, Crapo’s β-invariant appears as the key factor relating weighted combinatorial Laplacians and weighted tree numbers for matroid complexes. As an applicaion of our formula, we answer the question posed by R. Adin (1992) for weighted tree numbers of complete colorful complexes. This is a joint work with Woong Kook (SNU).
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