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 |