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Until recently, I was a Clinical Assistant Professor at the Department of Mathematics of Boise State University. I happily served as the Department of Mathematics Faculty Liasion for the Concurrent Enrollment Program. I also ran the Problem Of The Month Series - check it out!
Before coming to Boise State I was a Postdoctoral Research Associate (and a Lecturer) at the Department of Mathematics of Princeton University, hosted by Prof. Charles Fefferman.
My PhD was completed at the Mathematics Department of the Weizmann Institute of Science under the supervision of Prof. Dmitry Gourevitch. In my master's degree (thesis can be found here) I worked under the supervision of Prof. Maria Gorelik, in the same department.
Prior to that I received a bachelor's degree in Mathematics and Physics from Tel-Aviv University.
Research interests
These days I am mainly interested in (Whitney's) extension problems, a field that lies in the realm of functional analysis. I am also interested in real (algebraic / semi-algebraic / sub-analytic / differential / definable) geometry (and some quasiconformal geometry), and in particular in Schwartz spaces that may (or may not) be defined in these categories. Previously I studied generalizations of root systems, and their relation to Kac-Moody super-algebras.
Publications
Generalized reflection root systems (joint with M. Gorelik), Journal of Algebra 491 (2017) pp. 490-516 (journal, arXiv).
Schwartz functions on real algebraic varieties (joint with B. Elazar), Canadian Journal of Mathematics 70 (2018) no. 5, pp. 1008-1037 (journal, arXiv).
Tempered distributions and Schwartz functions on definable manifolds, Journal of Functional Analysis 278 (2020) 108471 (journal, arXiv). See also a corrigendum published at Journal of Functional Analysis 283 (2022) 109482 (journal).
On Schwartz equivalence of quasidiscs and other planar domains (joint with E. Prywes), Mathematische Zeitschrift 301 (2022) pp. 3641-3669 (journal, arXiv).
Board games, random boards and long boards, Discrete Mathematics 364 (2023) 113111 (journal, arXiv).
A property of ideals of jets of functions vanishing on a set (joint with C. Fefferman), Revista Matemática Iberoamericana 40 (2024), no.2, pp. 719-752 (journal, arXiv).
Classification of implication-closed ideals in certain rings of jets (joint with C. Fefferman), accepted to Journal d'Analyse Mathématique 2024 (arXiv).
Teaching
Boise State
MATH 170 (Calculus I) - Spring 2024.
MATH 170 (Calculus I, Honors Section) - Fall 2023.
Princeton
Mat 202 (Linear Algebra with Applications) - Fall 2021.
Mat 202 (Linear Algebra with Applications) - Spring 2021.
Mat 215 (Single Variable Analysis with an Introduction to Proofs) - Fall 2020
Mat 202 (Linear Algebra with Applications) - Spring 2020.
Mat 202 (Linear Algebra with Applications) - Fall 2019.
Weizmann Institute (TA)
Introduction to Representation Theory - Fall 2017.
Mathematics Around Us, previously known as Engineering Mathematics (Rothschild-Weizmann program) - Fall 2017.
Introduction to Algebraic Geometry - Fall 2016.
Algebra - from equations to structures (Rothschild-Weizmann program) - Spring 2016.
Engineering Mathematics (Rothschild-Weizmann program) - Fall 2015.
Contact
I can be reahced at ashaviv at math dot princeton dot edu
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