General
| organizer | Nicolas Macris |
| office | INR 134 |
| phone | 38114 |
| [email protected] |
| schedule | monday 11h – 12h30 |
| location | room INR 113 |
Topic
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.
Additional reading material
Numerical path following, by Eugene Allgower, Kurt Georg (1994)
Non linear functional analysis, by Gerald Teschl (2005)
Evolving schedule
| 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 |