Elliot Kaplan

Avenue Victor Maistriau 15 · 7000 Mons · Elliot.KAPLAN@umons.ac.be

I am an FNRS postdoctoral researcher at the University of Mons. My research lies in model theory and its applications.

Research

I am interested in o-minimality, the model theory of valued fields, and the model theory of differential fields. Much of my work is focused on fields of transseries and related structures.

Preprints


  1. Generic derivations, differential largeness, and NTP2.
    With C. Kesting.
    Submitted.    

  2. Dimension theory for the asymptotic couple of the field of logarithmic transseries.
    With A. Gehret and N. Pynn-Coates.
    Preprint.    

  3. Constant power maps on Hardy fields and transseries.
    Submitted.    

  4. Hyperserial fields.
    With V. Bagayoko and J. van der Hoeven.
    Submitted.    


Publications


  1. Monotone T-convex T-differential fields.
    With N. Pynn-Coates.
    Model Theory (2025).    

  2. Hilbert polynomials for finitary matroids.
    With A. Fornasiero.
    Pacific Journal of Mathematics (2024).    

  3. A dichotomy for T-convex fields with a monomial group.
    With C. Kesting.
    Mathematical Logic Quarterly (2024).    

  4. Liouville closed HT-fields.
    Journal of Algebra (2023).    

  5. T-convex T-differential fields and their immediate extensions.
    Pacific Journal of Mathematics (2022).    

  6. Surreal ordered exponential fields.
    With P. Ehrlich.
    Journal of Symbolic Logic (2021).    

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

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

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

  10. 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).    

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

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

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


Dissertation


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

Teaching

I am not teaching currently.

Past Teaching (McMaster)


Fall 2023:
Math 1B03 (Linear Algebra I).

Fall 2022:
Math 1ZA3 (Engineering Mathematics I).

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).

Curriculum Vitae

A detailed CV is available here.

Employment


University of Mons (September 2025 – present)
FNRS Postdoctoral Fellow

Max Planck Institute for Mathematics (September 2024 – August 2025)
Postdoctoral Fellow

McMaster University (July 2021 – June 2024)
NSF Postdoctoral Fellow
From July 2021 through June 2022, I was located at the Fields Institute.


Education


University of Illinois at Urbana-Champaign
Doctorate in Mathematics, May 2021
Advisor: Lou van den Dries

Ohio University
Bachelor of Science, May 2015