수학과

2014-1학기 제5회 수학과 colloquium 일정을 아래와 같이 안내해 드리오니 많은 관심과 참여 부탁드립니다.  


    [2014학년도 1학기 제5회 수학과 Colloquium]  

  강연제목 : The Unfolding Story of the Matrix Geometric Mean
  연    사 : 임용도 교수 [성균관대학교 수학과]  
  일    시 : 5월 9일 (금요일) 오후 5:00 - 6:00  
  장    소 : 팔달관 621호   
  강연초록 : 
The geometric mean of two positive numbers can be generalized to positive definite matrices via several natural approaches, all uniquely yielding the same result. However, generalizations to the multivariable case more than two variables have turned out to be more difficult and complicated. Nonetheless, the recent past has witnessed a number of major breakthroughs.
 The purpose of this talk is to present highlights of this unfolding story in an accessible and coherent manner. The story goes on solutions of the long standing open problem ``what is the best way to average of positive definite matrices in such a way that the answer is again positive definite?", the monotonicity and no (rolling) dice conjectures inspired by K.T Sturm's SLLN, and also on the Birkhoff ergodic and barycentric flow theories on the general setting of nonpositively curved metric spaces.
This is a continuation of the Ajou Math Colloquium on ``The geometric mean, matrices, metrics, and more" presented in 2001.