Here are some of my mathematical interests.

• Papers

• Vaught's Two Cardinal Theorem in Continuous Logic (In preparation)

• Continuous Logic

  I am interested in developing the correct characterization of strong miniality in the continuous setting, and using this to answer questions in continuous model theory, such as finding characterizations of uncountable categoricity.

  • General Properties of Definable and Algebraic Closure
    I became interested in continuous logic during Fall 2012, when I took Isaac Goldbring's course, Model Theory For Metric Structures. This was my final project for the course, Exercises 10.7, 10.8, 10.11, and 10.12 from MTFMS.

• o-minimality

  • Model Theory of Real Closed Fields
    During the spring of my last year as an undergraduate at Carnegie Mellon, I wrote this as my senior thesis under the supervision of James Cummings.

  • o-minimality Exercises
    During Summer 2012, I attend the MSRI Graduate Model Theory Workshop about o-minimality and algebraic dynamics. These are some exercises about o-minimality that I typed up during the course.

  • Model Theory of Real Closed Fields for LHLS
    These were the notes for a talk I gave at the Louise Hay Logic Seminar with Maxwell Levine.

  • The Pila-Wilkie Theorem
    These are the notes for a talk I gave in the Louise Hay Logic Seminar about the main theorem in Pila and Wilkie's 2006 paper The Rational Points of a Definable Set. I based the outline on a lecture given by Margaret Thomas at the MSRI Graduate Model Theory Workshop. Here are the slides from my talk on this paper at the XIV Graduate Student Conference in Logic.

• Other

  • Proof Theory Project
    In 2011, while I was still at UCLA, I did a project from the appendix of Jeremy Avigad's paper Weak Theories of Nonstandard Arithmetic and Analysis with Henry Towsner.

  • Notes on Fields
    These were my class notes from Paul Balmer's Math 210BC (graduate algebra sequence) in 2009 at UCLA.

• Louise Hay Logic Seminar, UIC

  • Minimal Predicates in Continuous Logic, November 3, 2016
  • Dp-Minimality in Continuous Logic, March 31, 2016
  • A Primer on Model Theory, September 10, 2015
  • Randomizations, February 26, 2015
  • Paris-Harrington Theorem, Part 5, October 30, 2014
  • Dp-Minimality, October 10, 2013
  • Definable Linear Orders in o-minimal Structures, March 21, 2013
  • Strong Minimality in Continuous Logic, Pt. 2, January 31, 2013
  • Strong Minimality in Continuous Logic, Pt. 1, January 24, 2013
  • The Pila Wilkie Theorem, October 4, 2012
  • Model Theory of Real Closed Fields, September 9, 2012, with Maxwell Levine
  • Pseudo-Finite Model Theory, February 23, 2012
  • Weak Theories of Non-Standard Analysis, September 29, 2012

• Model Theory Seminar, UIC

  • Extensions of Operators by Ultrapowers, March 1, 2016
  • On dp-Minimal Fields, Parts 1-4, September 21, 2015 - October 12, 2015
  • Hyperimaginary Forking, Parts 1-6, September 30, 2013 - November 18, 2013
  • NIP Theories, Parts 1-3, October 30, 2012 - November 13, 2012

• Graduate Student Colloquium, UIC

  • An Introduction to Model Theory and Categoricity, January 9, 2017

• Graduate Student Conference in Logic

  • Dp-Rank in Randomizations, April 25, 2015
  • Rational Points of a Definable Set, April 21, 2013

• Model Theory Month in Munster

• Strong Minimality in Continuous Logic, May 20, 2016

• MSRI Semester in Model Theory, Arithmetic Geometry and Number Theory

  • 5 Minute Talk, Feburary 14, 2014

• UCLA Current Literature Seminar in Logic

  • Atomless Probability Algebras, May 17, 2011
  • The McNaughton Theorem, April 27, 2010
  • Muller Automata, April 20, 2010
  • Nondeterministic Polynomial-Time Computations and Models of Arithmetic, June 2, 2009

• Louise Hay Logic Seminar
• UIC Model Theory Seminar
• UIC Logic Seminar
• UIC Graduate Student Colloqium

• Midwest Model Theory Day, Chicago, IL - attended, 11/1/2016
• International Conference on Model Theory, South Bend, IN - attended, 6/20/16 - 6/24/16
• Thematic Program on Model Theory, Graduate Summer School, South Bend, IN - attended, 6/13/16 - 6/17/16
• Model Theory Month in Munster, Conference, Munster, Germany - presented, 5/17/16 - 5/20/16
• Model Theory Month in Munster, Munster, Germany - attended, 4/18/2016 - 5/17/2016
• Midwest Model Theory Day, Chicago, IL - attended, 4/5/2016
• AMS Sectional Meeting, Chicago, IL - attended, 10/2/15 - 10/4/15
• Graduate Student Conference in Logic, Chicago, IL - presented, 4/25/15 - 4/26/15
• ASL 2015 North American Annual Meeting, Urbana-Champaign, IL - attended, 3/25/15 - 3/28/15
• Midwest Model Theory Day, Chicago, IL - attended, 10/28/14
• Model Theory in Geometry and Arithmetic, Berkeley, CA - attended, 5/12/14 - 5/16/14
• Connections for Women: Model Theory and Its Interactions with Number Theory and Arithmetic Geometry, Berkeley, CA - attended, 2/10/14 - 2/11/14
• Introductory Workshop: Model Theory, Arithmetic Geometry and Number Theory, Berkeley, CA - attended, 2/3/14 - 2/7/14
• Model Theory, Arithmetic Geometry and Number Theory, Berkeley, CA - visiting scholar, 1/20/14 - 5/23/13
• Midwest Model Theory Day, Chicago, IL - attended, 10/22/13
• Model Theory 2013, Ravello, Italy - attended, 6/10/13 - 6/15/13
• ASL 2013 North American Annual Meeting, Waterloo, Canada - attended, 5/8/13 - 5/11/13
• Chicago Logic Day, Chicago, IL - attended, 4/24/13
• Graduate Student Conference in Logic, Urbana-Champaign, IL - presented, 4/20/13 - 4/21/13
• Midwest Model Theory Day, Chicago, IL - attended, 4/18/13
• Joint Mathematics Meetings, San Diego, CA - attended, 1/9/13 - 1/12/13
• Midwest Model Theory Day, Chicago, IL - attended, 10/23/12
• MSRI Summer Graduate Workshop: Model Theory, Berkeley, CA - attended, 7/23/12 - 8/3/12
• ASL 2012 North American Annual Meeting, Madison, WI - attended, 3/31/12 - 4/3/12
• Logic and Mathematics 2011, Urbana-Champaign, IL - attended, 9/3/11 - 9/4/11
• Infinite Possibilities Conference for Minority Women in Mathematics, Los Angeles, CA - attended, 3/18/10 - 3/21/10