# LE-Series

## Alf Dolich

### The City University of New York

In this expository talk I will discuss the construction of the field of LE-series after van den Dries, Macintyre, and Marker. The field of LE-series is an ordered differential field extending the field of real Laurent series which also has a well-behaved exponential function. The field of LE-series is closed under a host of operations, in particular it is closed under formal integration as well as compositional inverse (once composition has been properly interpreted). As such this field may be viewed, at least conjecturally, as providing a universal domain for ordered differential algebra as witnessed in Hardy fields.

Professor Dolich (Ph.D. 2002 University of Maryland, M.A. Columbia University, B.A. University of Pennsylvania) held a VIGRE Van Vleck Assistant Professorship at the University of Wisconsin, Madison, before coming to the New York area, where he now holds an Assistant Professor position at Kingsborough CC of CUNY. Professor Dolich conducts research in model theory, simple theories, and o-minimal theories with secondary interests in algebraic geometry and set theory.