I've been studying properties of the Leray transform (a fairly natural analogue of the Cauchy transform in one variable) in the setting of convex Reinhardt domain in C^2, which have rotational symmetry with respect to each variable. I'm mostly interested in the singular spectrum of the Leray transform and how it classifies the underlying convex Reinhardt domain. Can one hear the shape of such a domain? The answer probably depends on the exact meaning of "hearing". "Shape" is only defined up to dilations, variable swaps and taking the projective dual, all of which preserve the spectrum. One of my current results is that in two dimensions, you can distinguish (up to dilations and duality) two "almost" C^2 smooth, convex Reinhardt domains (satisfying one more condition) by looking at each spectrum as a labeled set. The unlabeled case seems more complicated, and might not have a straightforward statement. I was also able to compute the Leray norm for l_p balls and their dilations (given by a|z_1|^2+b|z_2|^p<1 for p>1 and a,b>0) for a special measure, and more generally for domains in this setting, the essential norm for a family of measures.

I've also been studying the setting of rigid Hartogs domains in C^2, which have one rotational symmetry in addition to translation invariance (in the real part of one of the variables), so the spectrum generally lacks eigenvalues (it is generally continuous due to the translation invariance). Still, many similarities between the two settings arise. In both settings, asymptotic analysis plays a special role in establishing sufficient conditions (some are necessary) on the domain for the Leray operator to be L^2 bounded with respect to various measures. Moreover, the inverse spectral problem can be solved in essentially the same way, with the same kind of restriction as before.

My main future direction is to understand these settings in higher dimensions. In fact, the higher the dimension, the more such settings there are. At the same time, there are still things to do in C^2.

Going back a few years, I have a Bachelor's and Master's in Mathematics from Tel Aviv University. My advisor was Daniel Alpay and the title of my thesis is Quaternionic Wiener Algebras, Factorization and the Corona Theorem. The thesis extends theorems from complex analysis to the quaternionic setting. I published one paper, which is the part on Wiener algebras and factorization. The second paper, on the quaternionic Corona theorem, is still an ongoing work since I want to expand the results from my thesis.

• Quaternionic Wiener algebras, factorization and applications

Advances in Applied Clifford Algebras Advances in Applied Clifford Algebras, September 2017, Volume 27, Issue 3, pp 2805–2840,

(available online via Springer).

• Algebraic geometry of Abel differential equation Joint with Shira Giat, Clara Shikhelman and Yosef Yomdin

Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas, March 2014, Volume 108, Issue 1, pp 193-210

Three more papers are currently in preparation in connection to my dissertation, titled A Spectral Exploration of the Leray Transform in Two Different Settings in C^2.

• The inverse spectral problem for the Leray transform in two settings in C^2 Virtual East-West Several Complex Variables Seminar, September 2021.

• An inverse spectral problem for the Leray transform in two settings AMS Special Session on Several Complex Variables, October 2020.

• Exploring the Leray spectrum of convex Reinhardt domains Operators in Complex Analysis Seminar (University of Michigan), December 2019.

At Tel Aviv University (2012-2015) I was a teaching assistant for Complex Analysis, Harmonic Analysis, Calculus and Linear Algebra for engineering students, as well as for Functional Analysis, Calculus 4 and Real Analysis for math students.

At the University of Michigan, I taught Math 105 in Fall 2016, Math 115 in Winter 2017, and Math 116 in Fall 2017 through Winter 2020 (and then again in Spring 2021). In Fall 2020, I was a Matlab instructor for Math 215.

I was a DRP instructor in Winter 2020 and Summer 2020. The former project was about functional equations (with emphasis on finding all continuous solutions to classic equations), while the latter was about geometric integration theory (in particular Steiner symmetrization and the Brunn-Minkowski inequality).