2010 SKKU BK 21 Math Modeling Presentations

(Photo, PPT, Lecture Note, Movie Clips)

▣ Date  : 2010
▣ Room : 31351A or 31316 etc
▣ Audience : Math Major Under and Graduates, Faculties
▣ Speakers :

 Speaker (연사) Date Talk Title   (제목) Abstract Movie

 LeRoy Beasley Utah State Univ. 2010 Feb 19 Linear Preserver Problems and their Solutions, Matrices over Fields. There are two forms of preserver problems, one  xes a function, set, or relation and asks what linear transformations leave it invariant. This is the most common form studied. The other form  xes the structure of a linear transformation and asks what functions, sets, and relations are fixed by it. The  rst form of problem is well studied, the second is not as easy and few full characterizations are known. We consider the  first form  first. LeRoy Beasley Utah State Univ. 2010 Feb 23 Linear Preserver Problems and their Solutions, Matrices over Semirings In this article we will survey the research concerning linear transformations on "vector" spaces over semirings (which are not rings).
 Sang-Gu LEE SungkyunkwanUniv. 2010 Feb 19 Combination of Tradition and Leading Edge of Korean Mathematics We will start with recent discovery on old Korean Mathematics and try to find a couple of area that we can contribute to the world of mathematics. "Korea's e-Campus Vision 2007” was a program begun in 2003. Most of lecture rooms at Sungkyunkwan University were equipped with beam projector, viewcam, tablet PC and internet database before 2006. This provided a modern learning environment for our linear algebra classes. Computer demonstrations are easy, and lectures can easily be recorded so that students can review them right after class. Today, we would like to share what we have experienced for teaching of Linear Algebra over the years in this new learning environment. It does include Java, Flash, random problem generator and Mobile Sage.

 LeRoy Beasley Utah State Univ. 2010 March 4 Preserving Regular Tournaments and Term Rank-1 We investigate linear operators which map certain types of tournaments to themselves. To this end we also characterize term rank-1 preservers on the set of matrices whose associated digraphs are simple loopless directed graphs, and  nd that this set of operators is more diverse than might be expected.
 LeRoy Beasley Utah State Univ. 2010 March 4 Preserving Regular Tournaments and Term Rank-1 (part 2) Linear Preserver Problems and their Solutions, Problems, Conjectures, etc. Linear Preserver Problems and their Solutions, Problems, Conjectures, etc. We investigate linear operators which map certain types of tournaments to themselves. To this end we also characterize term rank-1 preservers on the set of matrices whose associated digraphs are simple loopless directed graphs, and  nd that this set of operators is more diverse than might be expected.

 Speaker (연사) Date Talk Title   (제목) Abstract Movie 이재화 박사 (중국과학원) 2010 Feb 9 "A subspace algorithm for nonlinear equality constrained optimization"    Subspace methods for optimization are of a special class for solving optimization problems. Their main feature is, at each iteration, to search for an optimal solution in the subspace. Since subspace techniques for nonlinear optimization can reduce both computation cost and memory size, they are able to improve the efficiency in solving large scale problems and widen the scope of solvable problems. In this talk, we present a subspace algorithm for nonlinear equality constrained optimization (ECO). Based on SQP method, this algorithm is designed and we propose a theoretically suitable subspace. In practice, we consider reduced constraints and two different possible subspaces. We prove that our search direction is a descent direction for the L_{/infty} exact penalty function and, under certain conditions, obtain a global convergence property. Preliminary numerical results are given and some implementations issues are discussed. 박정필 박사 (서울대) 2010 Feb 9 "Hilbert functions of almost reverse lexicographic ideals"  We introduce Moreno-Socias conjecture on generic initial ideals of ideals generated by generic forms, which is closely related with Fr\"{o}berg conjecture. Then we study Hilbert functions of almost reverse  lexicographic ideals. We give an equivalent condition for a given sequence of nonnegative integers to be the Hilbert function of an almost reverse lexicographic ideal. 이희권 박사 (KAIST) 2010 Feb 9 "On nonnegatively curved 4-manifolds with discrete symmetry"  Let  be the closed, simply connected, -manifold with nonnegative sectional curvature, called a nonnegatively curved -manifold, with an effective and isometric -action for a positive integer . Assume that  acts trivially on the homology of . The goal of this short  paper is to prove that if the fixed point set of any nontrivial element of has at most one two-dimensional component, then  is homeomorphic to , , , or , . The main strategy of this paper is to give an upper bound of the Euler characteristic  under the homological assumption of a -action as above by using the Lefschetz fixed point formula. 곽진호 교수님 (Postech) 2010 Sep 27 Matrix Integrals and Map enumeration  - A Gaussian integral on the space of hermitian matrics; (analytic one).   - For a given natural number  and , fix a long cycle  in the      symmetric group  and count the number of involutions  in the      group  such that  has  orbits; (group theoretical one).   - Enumeration of maps: For a given orientable surface  with       handles and for the bouquet  of  circles, count the number of      different cellular embeddings of  into ; (combinatorial one).      It will be discussed how the above three problems can be related  one another. In fact it is known that this topic is related with the Feynman path integrals and string theory in physics. For further random matrix techniques in combinatorics, see the maps book by Lando and  Zvonkin. 김희철 상무님  (MIRAE ASSET) 2010 Oct 1 금융산업에서의 Actuary의 역할과 Vision    (abstract attached in PDF file)