Assaf Shani

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

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


November 18: Cameron Freer. A characterization of properly ergodic structures. SC 530 (note change), 2-3.
November 11: Elliot Glazer. ∞-ideals and chain-ideals. SC 232, 2-3.
November 4: Justin Cavitt. Determinacy in the Difference Hierarchy on ∏^1_1. SC 232, 2-3.
October 21: Assaf Shani. Hyperfiniteness via Borel asymptotic dimension, following CJMST-D. SC 232, 2-3.
October 14: Joanna Boyland. Big Ramsey Theory. SC 232, 2-3.
October 7: Justin Cavitt. Classification Problems in Pseudo-Riemannian Geometry. SC 232, 2-3.
September 30: Doug Blue. Strong LSA models. SC 232, 2-3.
September 21: Elliot Glazer. Paradoxes and hat puzzles. SC 530, 3-4.

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). Journal of Mathematical Logic, to appear. 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). Advances in Mathematics, to appear. [pdf]
  • Slides from a talk of Filippo Calderoni.
  • Slides from a talk of Luca Motto Ros.
  • Strong ergodicity around countable products of countable equivalence relations. Israel Journal of Mathematics, to appear. [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]

    • Unpublished notes

  • Unpinned actions via metric Scott analysis. (2022)
  • On b and add(B). (2021)
  • 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)

    • Upcoming travel

    January 4-7: JMM-ASL meeting in Boston, invited address, Jan 6, 1-2pm.
    March 25-29: North American ASL meeting, UC Irvine. Special sessions on Descriptive Dynamics and Set Theory.
    May 23-26: Mid-Atlantic Mathematical Logic Seminar (MAMLS), Rutgers.
    August 21-25: Descriptive Set Theory conference, Warsaw.

    Teaching

    Spring 2023:
    Math 118, Dynamical Systems- Canvas site.
    Fall 2022:
    Math 141B, Mathematical Logic II - Canvas site.
    Spring 2022:
    Math 141A, Mathematical Logic I - Canvas site. Notes, Assignments.
    Fall 2021:
    Math 112, Introductory Real Analysis - Canvas site.
    Math 1B, Calculus, Series, and Differential Equations.
    Spring 2021:
    Math 282X, Topics in Invariant Descriptive Set Theory.
    Math 1B, Calculus, Series, and Differential Equations.
    Fall 2020: Math 145B, Set Theory II. Notes, Assignments.


    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.