# 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.

**email**: assafshani at ucla.edu

** Papers**

Borel reducibility and symmetric models. arXiv 1810.06722.
Fresh Subsets of ultrapowers. Archive for Mathematical Logic, vol. 55 (2016), pp. 835–845. [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** Unpublished notes**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, Video] 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*.