Elliot Kaplan

Fields Institute Room 408 · Toronto, ON · M5T 3J1 · kaplae2@mcmaster.ca

I am an NSF postdoctoral fellow at McMaster University. This year, I am at the Fields Institute for the thematic programs on trends in model theory and tame geometry. I completed my PhD at the University of Illinois at Urbana-Champaign, where my advisor was Lou van den Dries.


Research

I am interested in o-minimality, valued fields, and differential fields.

Preprints


T-convex T-differential fields and their immediate extensions.
Submitted (2021).    

Hyperserial fields.
With V. Bagayoko and J. van der Hoeven.
Submitted (2021).    

Publications


Surreal ordered exponential fields.
With P. Ehrlich.
Journal of Symbolic Logic (to appear).    

Generic derivations on o-minimal structures.
With A. Fornasiero.
Journal of Mathematical Logic (2021).    

Pairs of theories satisfying a Mordell-Lang condition.
With A. Block Gorman and P. Hieronymi.
Fundamenta Mathematicae (2020).    

Distality for the asymptotic couple of the field of logarithmic transseries.
With A. Gehret.
Notre Dame Journal of Formal Logic (2020).    

Continuous regular functions.
With A. Block Gorman, P. Hieronymi, R. Meng, E. Walsberg, Z. Wang, Z. Xiong, and H. Yang.
Logical Methods in Computer Science (2020).    

Logarithmic hyperseries.
With L. van den Dries and J. van der Hoeven.
Transactions of the American Mathematical Society (2019).    

Number systems with simplicity hierarchies II.
With P. Ehrlich.
Journal of Symbolic Logic (2018).    

Resolution depth of positive braids.
With D. Krcatovich and P. O'Brien.
Journal of Knot Theory and Its Ramifications (2015).    

Dissertation


Derivations on o-minimal fields.
University of Illinois at Urbana-Champaign (2021).  


Teaching

I am not teaching this year.

Past Teaching (UIUC)


Fall 2020:
Head TA for Math 415 (Applied Linear Algebra).

Summer 2020:
TA for Math 231 (Calculus II).

Fall 2019:
TA for Math 241 (Calculus III).

Fall 2018:
TA for Math 241 (Calculus III).

Spring 2018:
Head TA for Math 415 (Applied Linear Algebra).

Fall 2017:
Head TA for Math 125 (Elementary Linear Algebra).
Grader for Math 570 (Mathematical Logic) and Math 535 (General Topology).

Spring 2017:
TA for Math 241 (Calculus III).

Fall 2016:
TA for Math 241 (Calculus III).
Grader for Math 570 (Mathematical Logic).

Fall 2015:
TA for Math 231 (Calculus II).