Fri Oct 18, 2013
60 Evans Hall, 4:10–6 PM
James Freitag (UC Berkeley)
Differential Algebra and the Model Theory of Groups
Sacks called differential fields the “least misleading” examples of omega-stable theories. This talk will reinforce that philosophy, because the theorems we will discuss fall into two general situations: (1) theorems from model theory which inspired results in differential algebra or (2) theorems from differential algebra which were generalized to the model-theoretic setting. Specifically, we will be discussing theorems regarding differential algebraic groups and groups definable in superstable theories (a generalization of omega-stability). We will discuss three types of theorems: (1) Jordan-Hölder theorems, (2) indecomposability theorems, and (3) results on central extensions. To open the talk, we will give a survey of the model theory of differential fields.