Assaf Shani

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.

Papers

  • 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, to appear. [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]

    • Unpublished notes

  • A note on E_1 and orbit equivalence relations. (2018)
  • On the proof that a tree with an ascent path is not special. (2016)
  • Zero sharp implies all (branchless, fat) trees in L are special. (2015)

    • Teaching:

    Spring 2021:
    Math 282X, Topics in Invariant Descriptive Set Theory.
    Math 1B, Calculus, Series, and Differential Equations.
    Fall 2020: Math 145B, Set Theory II.


    At CMU:

    Spring 2020: Set Theory, 21-329.
    Fall 2019: Algebraic Structures, 21-373.

    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.