profile for Alex Kruckman at Mathematics Stack Exchange, Q&A for people studying math at any level and professionals in related fields

This page will go away soon. Please visit my new faculty page at IU Bloomington.

Hello, my name is Alex Kruckman.

I've just finished my PhD in mathematics at Berkeley. My advisor was Tom Scanlon. Starting in Fall '16, I will be a Zorn Postdoctoral Fellow at Indiana University Bloomington.

My interests are mathematical logic in general, model theory in particular, and the model theory of random structures and infinitary limits of finite structures in particular particular.

My email address is (my last name)@math.berkeley.edu, and my office is 1057 Evans.

Papers:

  • Infinitary limits of finite structures - My PhD thesis.
  • Disjoint n-amalgamation and pseudofinite countably categorical theories - submitted to Notre Dame Journal of Formal Logic.
  • Properly ergodic structures - with Nate Ackerman, Cameron Freer, and Rehana Patel. In preparation.
  • Actions arising from intersection and union - with Lawrence Valby, Journal of Logic, Language and Information.
  • A Myhill-Nerode theorem for automata with advice - with Sasha Rubin, John Sheridan, and Ben Zax. This paper is the result of a project at the Cornell Math REU, Summer 2009.
  • Chains of distributions, hierarchical Bayesian models and Benford's Law - with Dennis Jang, Jung Uk Kang, Jun Kudo, and Steven J. Miller. This paper is the result of an undergraduate research project at Brown University in Fall 2007.

    Notes and Expository Writing:

  • Notes on ultrafilters - prepared for the Berkeley Math Toolbox Seminar.
  • Notes on the stability spectrum - an exposition of Shelah's stability spectrum for countable theories that I prepared while studying for my qual.
  • The Ax-Kochen Theorem: an application of model theory to algebra - my undergraduate senior thesis.
  • An elementary proof of the Markov Chain Tree Theorem - with Amy Greenwald and John Wicks. This paper is one result of an REU project at Brown in Summer 2008. Our idea was that the paper, which is accessible to undergrads in math or computer science, could be an educational tool to give students practice reading mathematics. If anyone knows of an outlet for that sort of thing, please let me know!

    Slides:

  • Pseudofinite countably categorical structures - from my talk at the AMS Central Fall Sectional Meeting in October '15.
  • Amalgamation and the finite model property - from my talk at the Spring ’15 ASL meeting at UIUC.
  • Sampling measures and limits of finite structures - from my talk at the Spring ’14 ASL meeting at UC Boulder.

    Teaching:

  • Fall 2010: Math 1A, Calculus (TA).
  • Spring 2011: Math 1B, Calculus (TA).
  • Summer 2011: Math 54, Linear Algebra & Differential Equations (Instructor).
  • Fall 2011: Math 53, Multivariable Calculus (TA).
  • Spring 2012: Math 32, Precalculus (TA).
  • Fall 2012: Math 32, Precalculus (Instructor).
  • Spring 2013: Math 32, Precalculus (Instructor).
  • Summer 2013: Math 113, Abstract Algebra (Instructor).
  • Fall 2013: Math 32, Precalculus (Instructor).
  • Fall 2014: Math 110, Linear Algebra (TA).
  • Summer 2015: Math 54, Linear Algebra & Differential Equations (Instructor).
  • Spring 2016: Math 110, Linear Algebra (TA).

  • I passed my qualifying exam on June 12, 2012. Here is my syllabus.

    If, like Aaron, you need to calculate with Adem relations for the mod 2 Steenrod algebra, you can do so here.