# 1 Weak convergence methods for nonlinear PDEs

- Giảng viên: Trần Vĩnh Hưng (ĐH Wisconsin, Madison, Mỹ) ( This email address is being protected from spambots. You need JavaScript enabled to view it.). Hỗ trợ: Bùi Lê Trọng Thanh ( This email address is being protected from spambots. You need JavaScript enabled to view it.)
- Thời gian: 4 buổi, mỗi buổi 1,5 giờ (9g--10g30 sáng), thứ 2-4-6 (ngày 15 tháng 7, ngày 18 tháng 7, ngày 20 tháng 7, ngày 22 tháng 7).
- Tóm tắt: I will explain some weak convergence methods, and give applications to the study of calculus of variations and nonlinear PDEs. This is an introductory course with the aim at advanced undergraduate students or graduate students.

# 2 Introduction to expander graphs and expansion in groups

- Giảng viên: Nguyễn Hữu Hội (Ohio State University, Mỹ). Tổ chức: Nguyễn Trọng Toán ( This email address is being protected from spambots. You need JavaScript enabled to view it.), Nguyễn Hoài Minh ( This email address is being protected from spambots. You need JavaScript enabled to view it.). Hỗ trợ: Lê Văn Luyện ( This email address is being protected from spambots. You need JavaScript enabled to view it.)
- Thời gian: 25--29/7, 2016. Monday: 8:30--10am; Tuesday: 10:30--noon; Wednesday: 8:30--10am, 2--4pm; Thursday: 10:30--noon, 2--4pm.
- Tóm tắt: In the first half of the course I will introduce various notions of expander graphs together with some of their nice applications. In the second half we will learn more about expansion in groups; results to be discussed in detail include theorems by Bourgain-Katz-Tao and by Bourgain-Gamburd.

# 3 Quantum kinetic theory (canceled)

- Giảng viên: Trần Minh Bình (University of Wisconsin at Madison, Mỹ). Tổ chức: Nguyễn Trọng Toán, Nguyễn Hoài Minh. Hỗ trợ: Vũ Đỗ Huy Cường ( This email address is being protected from spambots. You need JavaScript enabled to view it.)
- Thời gian: 25--29/7, 2016. Monday: 10:30--noon; Tuesday: 2--4pm.
- Tóm tắt: In this course, I review some basic concepts in quantum field theory and derive connections between quantum field theory and kinetic theory.

# 4 Mean-field approximation for large quantum systems

- Giảng viên: Phan Thành Nam (Institute of Science and Technology Austria). Tổ chức: Nguyễn Trọng Toán, Nguyễn Hoài Minh. Hỗ trợ: Bùi Lê Trọng Thanh
- Thời gian: 25--29/7, 2016. Monday: 2--4pm; Tuesday: 8:30--10am; Wednesday: 10:30--noon; Thursday: 8:30--10am; Friday: 10:30--noon.
- Tóm tắt: Quantum mechanics is a linear theory but its complexity grows dramatically when the number of particles becomes large. In this course, some effective theories for large quantum systems will be derived using mean-field approximation and semiclassical analysis. We will focus on the Gross-Pitaevskii theory for Bose gases and the Thomas-Fermi theory for atoms and molecules.
- Prerequisites: No knowledge in quantum mechanics is assumed, but some background in Hilbert spaces and Sobolev’s inequalities will be helpful.

# 5 MATLAB for solving inverse problems

- Giảng viên: Trần Trọng Hiền (North Carolina State University Raleigh, Mỹ) ( This email address is being protected from spambots. You need JavaScript enabled to view it.). Hỗ trợ: Ông Thanh Hải ( This email address is being protected from spambots. You need JavaScript enabled to view it.)
- Thời gian: 21--22/7/2016, ~ 2 hours/day. Thursday: 9:00--11:00am; Friday: 2:00--4:00pm.
- Tóm tắt: I am thinking of offering to the students/participants a special hands-on learning experience on the topics of inverse problems. This would require students access to computers/laptops with MATLAB and a toolbox called SimBiology. I will give some lectures on computational methods for inverse problems and working through some examples with the students/participants interactively using the available computers/laptops.

# 6 Statistics for high-dimensional data

- Giảng viên: - Lý thuyết: Vincent Rivoirard (ĐH Paris Dauphine, Pháp). Bài tập + thực hành, hỗ trợ: Hoàng Văn Hà (ĐH Lille 1) ( This email address is being protected from spambots. You need JavaScript enabled to view it.)
- Thời gian: - Lý thuyết: từ 25/7 đến 29/7. Mỗi ngày 3 giờ, tổng cộng 15 giờ lý thuyết. - Bài tập + thực hành: dự kiến có từ 4 đến 6 buổi, mỗi buổi 2 giờ. Phần thực hành sẽ làm trên Matlab hoặc R.
- Tóm tắt: Classical statistical methods developed during the last century were suitable when the number of observations is much larger than the number of parameters to infer. Unfortunately, many fields such as astronomy, genetics, medicine or neuroscience produce large and complex data sets, and consequently with models containing a large number of parameters for which classical tools are not adapted. This issue is often referred as the curse of dimensionality. The goal of this course is to provide most of fundamental statistical tools to face with high-dimensional data. The aim is to present the main concepts and ideas on some selected topics of high-dimensional statistics based on modern nonparametric methodologies such as multiple testing, kernel, wavelets and penalized estimators with a special focus on Lasso estimation. Theoretical aspects are motivated by applicable developments of presented methods. This course is based on lectures given in the master program from Paris Sud University (Orsay).
- Đối tượng tham dự: môn học cũng có thể có ích cho người ở các ngành khác có quan tâm.
- Tài liệu tham khảo:

- Bühlmann, Peter and van de Geer, Sara Statistics for high-dimensional data. Methods, theory and applications. Springer Series in Statistics. Springer, Heidelberg, 2011. xviii+556 pp. ISBN: 978-3-642-20191-2

- Giraud, Christophe, Introduction to high-dimensional statistics. Monographs on Statistics and Applied Probability, 139. CRC Press, Boca Raton, FL, 2015. xvi+255 pp. ISBN: 978-1-4822-3794-8

- Härdle, Wolfgang Kerkyacharian, Gerard Picard, Dominique and Tsybakov, Alexander Wavelets, approximation, and statistical applications. Lecture Notes in Statistics, 129. Springer-Verlag, New York,1998. xviii+265 pp. ISBN: 0-387-98453-4

- Rivoirard Vincent and Stoltz Gilles, Statistique mathématique en action. Vuibert. ISBN: : 978-2311007206

- Tibshirani, Robert, Regression shrinkage and selection via the lasso. J. Roy. Statist. Soc. Ser. B 58 (1996),no. 1, 267–288.