J. L. Doob Research Assistant Professor
Department of Mathematics
University of Illinois at Urbana-Champaign
Email: erikw at illinois dot edu
Office: 127 Altgeld
Research Interests: Model Theory, Tame Geometry
I did my PhD at UCLA under the supervision of Matthias Aschenbrenner,
and then did a postdoc at the Hebrew University of Jerusalem under the supervision of Ehud Hrushovski.
My CV, a statement about some aspects of my research, and some questions that I believe to be worthy of attention but will probably not work on.
Here is a poster produced by a Fall 2018 undergraduate research group on automata theory and enumeration systems.
The Interpolative Fusion Program:
Interpolative Fusions, with Alex Kruckman and Minh Chieu Tran
First order expansions of the real line:
Interpreting the Monadic Second Order Theory of One Successor in Expansions of the Real Line, with Philipp Hieronymi, Israel Journal of Mathematics, accepted.
How to Avoid a Compact Set, with Antongiulio Fornasiero and Philipp Hieronymi, Advances in Mathematics, Volume 317 / Sept. 2017 / pp. 758-785.
Wild Theories with O-minimal Open Core, with Philipp Hieronymi and Travis Nell, Annals of Pure and Applied Logic, Volume 169 / Issue 2 / Feb. 2018 / pp. 146-163.
On Continuous Functions Definable in Expansions of the Ordered Real Additive Group, with Philipp Hieronymi
Expansions of the Real Field by discrete subgroups of Gl_n(C), with Philipp Hieronymi and Samantha Xu.
Fractals and the Monadic Second Order Theory of One Successor, with Philipp Hieronymi
Continuous Regular Functions, with Alexi Block Gorman, Philipp Hieronymi, Elliot Kaplan, Ruoyu Meng, Zihi Wang, Ziqin Xiong, and Hongru Yang.
(This work was done in the research project Automata and Differentiable Functions at the Illinois Geometry Lab in Spring 2018).
Coarse Dimension and Definable Sets in Expansions of the Ordered Real Vector Space
Dp-minimal Valued Fields, with Franziska Jahnke and Pierre Simon,The Journal of Symbolic Logic / Volume 82 / Issue 01 / March 2017 / pp. 151-165.
Tame Topology over Dp-minimal Structures, with Pierre Simon, Notre Dame Journal of Formal Logic, accepted.
A Family of Dp-minimal Expansions of the Additive Group of Integers, with Minh Chieu Tran
Dp-minimal expansions of discrete ordered abelian groups
The Marker-Steinhorn Theorem via definable linear orders, Notre Dame Journal of Formal Logic, accepted.
Hausdorff dimension of metric spaces definable in o-minimal expansions of the real field, with Jana Maříková, Fundamenta Mathematicae, accepted.
(I removed some typos and corrected some small mistakes, so this is not the exact version of my thesis that was submitted to UCLA)
Isometric Embeddings of Snowflakes into Finite-Dimensional Banach Spaces, with Enrico Le Donne and Tapio Rajala, Proceedings of the AMS, Volume 16 / Number 2 / 2018 / pp. 685-693.