NSF Assistant Adjunct Professor
Email: allen [at] math.ucla.edu
Office: MS 7935
My research interests include the
algebra and model theory of: valued fields, valued differential fields, asymptotic differential algebra, Hardy fields, transseries, asymptotic couples and ordered abelian groups
Distality for the asymptotic couple of the field of logarithmic
transseries (with Elliot Kaplan), Notre Dame J. Form. Log., to appear.
Hamel spaces and distal expansions (with Travis Nell), J. Symb. Log., to appear.
A tale of two Liouville closures, Pacific J. Math. 290 (2017), no. 1, 41-76.
NIP for the asymptotic couple of the field of logarithmic transseries, J. Symb. Log. 82 (2017), 35-61.
The asymptotic couple of the field of logarithmic transseries, J. Algebra 470 (2017), 1-36.
Distality in valued fields and related structures (with Matthias Aschenbrenner, Artem Chernikov, and Martin Ziegler), submitted.
Ph.D. Thesis, Towards a model theory of logarithmic transseries, Aug. 2017. (Thesis defense video )
Slides from some talks
Distal and non-distal ordered abelian groups, Model Theory Seminar, University of Notre Dame, Notre Dame, IN, December 2017.
A tale of two Liouville closures..., Kolchin Research and Training Workshop III, Graduate Center, CUNY, New York City, NY, May 2017.
Towards a model theory of logarithmic transseries, Thesis defense, University of Illinois at Urbana-Champaign, Urbana, IL, April 2017.
Math182 Algorithms Summer Session A 2020 (Here are lecture notes)
Math33b Differential Equations 2020 (Here are Lecture notes, last updated: <\span>)
Math61 Introduction to Discrete Structures Winter 2020 (Here are lecture notes)
Math131a Real Analysis Fall 2019 (Here are lecture notes)
Math131a Real Analysis Summer Session A 2019
Math170b Probability Theory Spring 2019 (Here are lecture notes and memes.)
Math170a Probability Theory Winter 2019
Math115a Linear Algebra Fall 2018
Math167 Mathematical Game Theory Summer Session A 2018
Math131a Real Analysis Summer Session A 2018
UCLA graduate model theory seminar