A mathematical approach to chemotaxis: the Keller-Segel model

This is a 6 hours mini-course, to take place during the period 10-17 november, 2017.

Interest students should send me an e-mail by november 7 to fully organize the timetable

Tentative timetable
First lecture:  Friday, 10/11, 11.30-13.30 aula B
Second lecture:   Tuesday, 14/11,  11.30-13.30  seminar room at 2nd floor  CV2 (To be confirmed)
Third lecture: Wednesday, 15/11,  14.30-16.30 aula G
a further possible slot is on Thursday, 16/11, 11.30-13.30 seminar room at 2nd floor CV2
 

Title: A mathematical approach to chemotaxis: the Keller-Segel model

Lecturer: Prof. Juan Calvo Yagüe (Univ. Granada, Spain)

Abstract:

Chemotactic processes encompass various instances of cellular motion induced by chemical substances. Mathematicians are interested in chemotaxis due to a number of reasons, among which we highlight the fact that chemotactic interactions can lead to self-organization phenomena and the emergence of collective behavior. These topics can be addressed under a partial-differential-equation framework provided by the Keller-Segel model and its many variants. 

The aim of this course is twofold: 

(i) connect the standard Keller-Segel model with biased random walks. This is a flexible mechanism that allows to introduce a number of interesting variants in the dynamics. 

(ii) display the rudiments of the mathematical theory for the parabolic-elliptic version of the Keller-Segel model, including elementary solution properties, the celebrated mass threshod in dimension two and global existence of solutions in the no-aggregation regime. 

The functional analytic tools that are used here have a wide range of applicability in the analysis of various types of partial differential equations.