I am a Benjamin Peirce Fellow at Harvard University.
I received my PhD in 2019 from UCLA, under the supervision of Andrew Marks. During the 2019-20 academic year I was a postdoc at CMU.

shani@math.harvard.edu
Office: SC 333I

Papers

Strong ergodicity for the Gamma-jump operator and for actions of Polish wreath products. arXiv:2203.14427 [pdf] [Slides]

Classifying invariants for E_1: A tail of a generic real. arXiv:2112.12881 [pdf] [Slides]

Actions of tame abelian product groups (with S. Allison). arXiv:2105.05144 [pdf] [Slides]

Strong ergodicity phenomena for bernoulli shifts of bounded algebraic dimension (with A. Panagiotopoulos). arXiv:2105.04989 [pdf]

Anti-classification results for groups acting freely on the line (with F. Calderoni, D. Marker, L. Motto Ros). arXiv:2010.08049 [pdf]

Strong ergodicity around countable products of countable equivalence relations. arXiv 1910.08188. [pdf]

On the Gamma-jumps of Clemens and Coskey. [Slides 25 min]

Strong ergodicity between countable products of countable equivalence relations. [Slides 20 min]

Classification using countable sequences of countable sets of reals. [Slides 25 min]

Borel reducibility and symmetric models. Transactions of the American Mathematical Society, 374 (2021). [pdf] [doi]

Separating the equivalence relations of Hjorth-Kechris-Louveau. [Slides 50 min]

Baire-category analysis of the second Friedman-Stanley jump. [Slides 20 min]

Fresh Subsets of ultrapowers. Archive for Mathematical Logic, vol. 55 (2016), pp. 835-845. [pdf] [doi]

Ultrapowers of forcing notions. Master's thesis, Hebrew University, 2013. [pdf]

As a grad student at UCLA I have been the TA for the following courses.

Spring 18: Math 114L, Mathematical Logic; Math 132, Complex Analysis for Applications. Winter 18: Math 114S, Introduction to set theory; Math 3C, Ordinary Differential Equations with Linear Algebra for Life Sciences Students. Fall 17: Math 132, Complex Analysis for Applications; Math 3C, Ordinary Differential Equations with Linear Algebra for Life Sciences Students. Spring 17: Math 121C, Introduction to Topology, Math 31B, Integration and Infinite Series. Winter 17: Math 114C, Computability Theory, Math 32A, Calculus of Several Variables. Fall 16: Math 180, Graph theory, Math 131A, Analysis. Summer 16: Math 61, Introduction to Discrete Structures. Spring 16: Math 61, Introduction to Discrete Structures; Math 132, Complex Analysis for Applications. Winter 16: Math 132, Complex Analysis for Applications; Math 106, History of Mathematics. Fall 15: Math 1, Precalculus; Math 132, Complex Analysis for Applications. Summer 15: Math 131A, Analysis. Spring 15: Math 123, Foundations of Geometry; Math 32A, Calculus of Several Variables. Winter 15: Math 106, History of Mathematics; Math 32B, Calculus of Several Variables. Fall 14: Math 132, Complex Analysis for Applications; Math 31B, Integration and Infinite Series.