콜로퀴움을 안내해드립니다.

- 일시: 9월 17일 (수) 오후 5-6시

- 장소: 종A317호 

- 연사: 김영락 (부산대학교)

- 강연 분야: 대수기하학

- 제목: Determinant vs. Permanent 

- 초록: 

 The determinant of a matrix is one of the most fundamental concepts in mathematics, and thus it appears and applies almost everywhere. We usually define this notion using Leibniz's formula, which expresses the determinant as a sum of signed products of matrix entries running over all the permutations. On the other hand, if we take a sum of unsigned products of those matrix entries, then the resulting invariant is called the permanent of a matrix, which is not as good as determinants but is useful in combinatorics. One of the central problems in complexity theory is to compare their computational complexities, often called a "Determinant vs. Permanent" problem. Some of these problems have a connection between the famous P vs. NP problem.

In this talk, I will mostly talk on two complexity notions motivated by a determinantal representation of a polynomial and by the rank of a matrix, and compare the determinant and the permanent with respect to these complexities. In particular, by considering them as n-linear maps, we may regard them as "tensors", represented by n-dimensional array of scalars, that generalize the notion of matrices. We briefly review how to define the rank of a tensor, and then discuss how to get information about the tensor rank of the determinant and permanent. In particular, we will see that there is a huge difference between the tensor rank of the determinant and permanent tensors. If time permits, I will also talk about the exact ranks of them for the case n=4, and discuss the roles of algebra and geometry in this problem.

* 대상: 수학과 학부생, 복수전공자 및 대학원생

* 학부 재학 중 특강 4회 이상 참석은 수학과 졸업요건입니다. (복수전공생도 동일요건)

문의사항: 수학과 사무실 e600186@ewha.ac.kr / 02-3277-2290