====== Non Linear Analysis ======

==== General ====

^ ^ ^ 
|organizer   |Nicolas Macris| 
|office      |INR 134|
|phone       |38114|
|email       |nicolas.macris@epfl.ch|
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|schedule  |monday 11h - 12h30|
|location  |room INR 113| 
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==== Topic ====
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We often seek information on solutions of non-linear differential or integral 
equations. Non linear analysis combines methods from analysis and topology including fixed point theorems (Brouwer, Schauder), degree theory (Brouwer, Leray-Schauder degree), the Krasnoselskii-Rabinowitz bifurcation
theorem. We plan to study a little book which contains an introduction to these topics plus applications:\\
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**A Topological Introduction to Non Linear Analysis, by Robert Brown (Birkhauser 1993)**
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Another set of useful techniques use various perturbation methods. In a second stage we may read pieces of the short book:\\
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**Perturbation Techniques for Mathematics, Engineering, Physics, by Richard Bellman (Dover 2004)**
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Relevant material will be distributed to interested participants. We will meet on a weekly basis for presentations of 1h or 1h30.
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==== Additional reading material ====
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Numerical path following, by Eugene Allgower, Kurt Georg (1994)\\
Non linear functional analysis, by Gerald Teschl (2005)\\
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==== Evolving schedule ====
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^ speaker ^ date ^ topic ^
|        |       |        |
| Nicolas Macris | Oct 24 | Nishimori identities |
| Satish Korada | Oct 31 | Exact replica symmetric solution of an SK like model|
| Sanket Dusad | Nov 7 | Compactness in metric spaces |
| Sanket Dusad | Nov 13 | Ascoli-Arzela theorem |
| Ruediger Urbanke | Nov 21 | Fixed point theorems: Brouwer and Schauder |
| Ruediger Urbanke | Nov 28 | Schauder fixed point theorem and applications|    
| Henry Pfister | Dec 5 |Fixed points equations with a parameter and GEXIT curves|
| Vishwambar Rathi | Dec 12 | Homotopy and Brouwer's theorem for the disc|
| Vishwambar Rathi | Dec19 | Homotopy and Brouwer's theorem for the disc|
| break | Jan 9 | - - -  |    
| Harm Cronie | Jan 16 | Brouwer mapping degree|
| Harm Cronie | Jan23 | Brouwer mapping degree|
| Shrinivas Kudekar | Jan 30 | Leray Schauder degree |
| Shrinivas Kudekar | Feb 15 (wed 14h15 !) |Leray Schauder continued|
| Shrinivas Kudekar | Feb 20 | Compact linear operators|
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