organizer | Nicolas Macris |
office | INR 134 |
phone | 38114 |
nicolas.macris@epfl.ch |
schedule | monday 11h - 12h30 |
location | room INR 113 |
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:
A Topological Introduction to Non Linear Analysis, by Robert Brown (Birkhauser 1993)
Another set of useful techniques use various perturbation methods. In a second stage we may read pieces of the short book:
Perturbation Techniques for Mathematics, Engineering, Physics, by Richard Bellman (Dover 2004)
Relevant material will be distributed to interested participants. We will meet on a weekly basis for presentations of 1h or 1h30.
Numerical path following, by Eugene Allgower, Kurt Georg (1994)
Non linear functional analysis, by Gerald Teschl (2005)
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 |