Welcome to winter school on
Tensors: geometric approach and its applications !!!
In this school, we study tensors as elements of the tensor product of finite dimensional vector spaces V_1... V_d. After basis have been fixed, a tensor can be represented by a multidimensional matrix, with d modes (or d ways). The case d=2 correspond to usual matrices. The case d>2 has some analogies and many differences with the case of matrices. When the vector spaces are equal, say V_1=...=V_d, symmetric tensors can be defined in a natural way, and they correspond to homogeneous polynomials of degree d, exactly as symmetric matrices correspond to quadratic forms.
Tensors have many applications in Signal Processing, Phylogenetics, Algebraic Statistic, Complexity Theory. Several aspects of these applications will also be discussed during the school.
All the lectures will be given at a level of (graduate) students. In the afternoon there will be exercise sessions and some additional topics will also be proposed. Some exercises and examples will be presented with the software Macaulay2. It is a symbolic package in commutative algebra, with some numerical
functions implemented.
The interested participants can download and install it on their laptop, before the school.
The software Macaulay2 is free and can be installed from http://www.math.uiuc.edu/Macaulay2/
Practice with this software is not necessary for the understanding of the topics of the school, but it can be useful.
Furthermore, on Friday (Feb. 21th) there will be an one dayworkshop on related topics in KIAS, Seoul. We also gladly welcome your participation in this workshop.
Speakers:

Giorgio Ottaviani (Università di Firenze)

Cristiano Bocci (Università di Siena)
Organizers:

Choe, Insong (Konkuk University)

Han, Kangjin (Korea Institute for Advanced Study, KIAS)

Woo, Youngho (Korea Advanced Institute of Science and Technology, KAIST)

For registration and inquires, please send an email to Woo, Youngho (youngw at kaist dot ac dot kr) or Choe, Insong (ischoe at konkuk dot ac dot kr).

For program of the school, please click here.

Preliminary lecture! On Feb. 14th, in KIAS there will be preliminary lectures for this school by Dr. Youngho Woo. We encourage participations of the students attending our school and anybody who’s interested in this lecture (please, see the schedule as below).

On Friday (Feb. 21th) there will be a miniworkshop on related topics in KIAS, Seoul.

*참가를 원하는 대학원생들은 성명(남/여), 소속, 지도교수, 전공분야&년차, (간단한) 지원동기, 숙소지원여부를 써서 보내주십시오 (숙소는 서울이외의 지역에서 참가하는 학생중 필요하신 분에 대해서 제공됩니다).

*Lecture notes : Ottaviani (you can find relevant materials, here and Lect2_SVD.pdf) , Bocci (Lecture notes_Bocci.pdf)

*Exercise sheets and Macaulay2(M2) files : Exercisesday1.pdf, Exercisesday2.pdf, Exercisesday3.pdf, Ottaviani_222.m2, Bocci_exercises.m2