Opening Ceremony

+ 7h30 – 8h45: Registration

+ 9h00 – 9h20: Opening Ceremony.

+ 9h20 – 10h10: Lecture

+ 10h10 – 10h30: Tea break

+ 10h30 – 11h20: Lecture

I. Lecturers

1. Vu Ha Van is Professor of Mathematics at Yale University. His research interests are Probabilistic combinatorics, Additive combinatorics, and Random matrices.

For more information, see his website link:http://vanvu.commons.yale.edu/

2. Emo Welzl has been Full Professor of Computer Science at the Institute for Theoretical Computer Science of the ETH Zurich since April 1996. His research interests are in the foundations of computer science, mainly algorithms and data structures, in particular computational geometry and applications, combinatorial models for optimization, analysis of geometric structures, randomized methods, and discrete geometry; recently also satisfiability.

For more information, see his website link: http://www.inf.ethz.ch/personal/emo/

3. Manjunath Krishnapur is assistant professor Department of Mathematics, Indian Institute of Science, Bangalore Karnataka, India. His main research interest is random matrix and random walks.

For more information, see his website link: http://math.iisc.ernet.in/~manju/index.htm

4. Phan Thi Ha Duong is associate professor at the Department Mathematics for Computer Sciences, Institute of Mathematics, Vietnam Academy of Technology and Science. Her research interest is in the structures and algorithms on discrete dynamical systems.

For more information, see her website link: http://vie.math.ac.vn/~phduong/

II. Schedules

Each day, there are two lectures, from 9h to 9h50 and from 10h10 to 11h.

1. Random polynomials:

Lecturers: Manjunath Krisnapur and Vu Ha Van

June 17 – 27

Schedule: Monday to Thursday June 17, 18, 19, 20,

Tuesday to Thursday June 25, 26, 27

Abstract: A random polynomial is a polynomial with coefficients being random variables. The investigation of random polynomials goes back to Waring, but
Systematic studies started with famous works of Littlewood-Offord, Erdos-Offord, and Kac, about 70 years ago. Today random polynomials is a central object in various fields, such as analysis, probability, mathematical physics, and combinatorics. We are going to give an introduction to the theory of random polynomials, along with some current developments, with focus on the classical problem of estimating the number of real roots.

2. Algorithms: Design and Analysis

Lecturer: Phan Thi Ha Duong

July 1 – 5

Schedule: Monday to Friday July 1, 2, 3, 4, 5

Abstract: This course gives an introduction to algorithm in order to help Vietnamese students for preparing to attend the course Computational geometry – randomized algorithms. We present notions and methods to analyze the asymptotic performance of algorithms and to apply important algorithmic design paradigms (divide and conquer, greedy, dynamic programming). At the end, we give some first examples of Randomized algorithms to illustrate the Monte Carlo and Las Vegas algorithms (Random Quick Sort and Min-Cut Algorithms).

Materials:

         Lecture 1                          Lecture 2                             Lecture 3                              Lecture 4                                    Lecture 8

3. Computational geometry – randomized algorithms

Lecturer: Emo Welzl

July 8 – 17

Schedule:

Monday to Thursday July 8, 9, 10, 11

Monday to Wednesday July 15, 16, 17

Abstract: The field of Computational Geometry deals with design and analysis of efficient algorithms for geometric problems, typically involving many simple objects (points, lines, line segments, etc.) in low dimensions (2,3,…, although many methods generalize to higher dimensions). Classical structures considered for computation are convex hulls, Delaunay triangulation, Voronoi diagrams, line arrangements, etc. Moreover, geometric optimization problems like linear programming, smallest enclosing balls, etc. are investigated.

In this course we will present some of the known solutions, with emphasis on the methods used. Here randomization played a crucial role, more concretely randomized incremental construction (Clarkson-Shor analysis, backwards analysis) and random sampling (Vapnik-Chervonenkis dimension based epsilon-nets).

Moreover, understanding the behavior of geometric algorithms goes always hand in hand with extremal problems in combinatorial geometry – so some results in this direction will be encountered and derived in the course.

Materials: 

1. http://www.ti.inf.ethz.ch/ew/courses/CG12/lecture/CG%20lecture%20notes.pdf

2. http://www.ti.inf.ethz.ch/ew/lehre/APC12/ra.pdf

3. http://www.inf.ethz.ch/personal/gaertner/cv/lecturenotes/ra.pdf