Assaf Shani

I am a graduate student at UCLA, expecting to graduate in Spring 2019. My advisor is Andrew Marks.
My thesis work focuses on Borel equivalence relations, specifically by the use of forcing techniques.

Papers

  • Borel reducibility and symmetric models. arXiv 1810.06722.
  • Fresh Subsets of ultrapowers. Archive for Mathematical Logic, vol. 55 (2016), pp. 835845. [doi]
  • Ultrapowers of forcing notions. Master's thesis, Hebrew University, 2013.
  • Unpublished notes

  • A note on 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)

  • Talks

  • Borel equivalence relations and symmetric models. [Abstract, Slides] Set theory today, Vienna, Austria (September 2018).
  • Topologies for the Friedman-Stanley jumps. [Abstract, Slides] European ASL meeting, Udine, Italy (July 2018).
  • Borel equivalence relations and weak choice principles. [Abstract, Slides] North American ASL meeting, Macomb, IL, USA (May 2018).

  • Teaching:

    Fall 18 - Spring 19: I am on a Dissertation Year Fellowship.

    Past teaching

    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.