Seminar On Applied Analysis

Selected topics on analysis which may be useful in applied math.

Time table and course meterial

Detailed Plan:pdf

Week1

Convex Analysis, Optimization and Variational Problems

Speaker:Yiping Lu

Objectives:

Text Book:

Ivar Ekeland Roger Teman, Convex analysis and variational  problems.

Reference

Lecture note:link,Assignment:link,reference:link


Week2

Partial Differential Equation

Speaker:Yiping Lu

Objectives:

class note will be available soon

Text Book:

L.Evans Partial Differential Equation(chapter 4,9)
Weinan E. Principle Of multiscale methods.

Reference:

Week3

Numerical Methods

As a reward for following such hard seminar and giving presentations. (This week we will cover the course ‘An introduction to applied math’ and give discuss about several advanced topics in NLA and Numerical PDEs)

Objectives:

Week4

Optimal Control

Also known as PDE constrained optimization

Objectives:

Week5-8

Optimal Transport

Discussion Weak

Objectives:

Text Book:

Villani,2008, Optimal transport, old and new
Santambrogio, 2015, Optimal Transport for Applied Mathematicians.
Ambrosio and Gigli, 2011, A User’s Guide to Optimal Transport.

Reference:

Week9-10

Stochastic Analysis

Speaker:Yiping Lu

Outline:

Text Book:

L.Evans Introduction to Stochastic Differential Equation
Bernt Oksendal. Stochastic Differential Equation.
Xiaoliang Wan Introduction to uncertain certainty quantification.

Presentation Next Week

Other Topics

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