In 2012 I left a position as an Assistant Professor in Mathematics at the University of Colorado giving in to a longstanding interest in information technology. Since then I have been working as a software engineer and data scientist, developing into the tech lead of the team that has been developing the realtime streaming engine at KPN. I am interested in a position with a great team solving challenging practical problems.

Technologies

I have used all standard platforms (Windows, OS X, and Linux) for extended periods of time; for the last years I have mostly been on OS X. I have used different development environments (e.g. Microsoft Visual Studio, Intellij, Eclipse, RStudio, and vim/emacs with different plugins) for extended periods of time; for the last years I have been using mostly the Intellij, RStudio, and Emacs environments.

I have developed using many different languages. Quite a few languages for small projects, for instance MIX (the language Knuth uses in The art of computer programming) in which I implemented Thompson NFA for regular expressions, i86 assembler for some data structures, and ML for some theorem proving. For website development html, css, php, and javascript. C++, Python and java for learning these languages a bit and playing with different technologies. C++ with SQL and web languages while I was at CoachR. Lots of Clojure (using Cascalog for Hadoop jobs) and R at Adgoji, doing analysis of big data (near a TB a day to permanent storage and many thousands of events a second). And currently Scala for flink jobs, java for our custom components, and python and bash scripting for management of the cluster.

Positions

May 2022–current: Principal Engineer, Ditigal Engine Platform, KPN, Amsterdam.

• General goal: help digital engine teams.

Apr 2020–May 2022: Software Engineer, Digital Engine Platform, KPN, Amsterdam.

• General goal: help digital engine teams.
• Lots of migrations from on-prem to the cloud.
• Build an encryption service for applications to communicate over untrusted channels.
• Build improved tooling to work with our secrets manager.

Jan 2019–Apr 2020: Security Engineer, Technium Security Team, KPN, Amsterdam.

• General goal: help teams within Technium improve their security.
• Set up vault and the pipelines around it to improve the secrets management in the Digital Engine.

Oct 2015–Jan 2019: Data Scientist, KPN, Amsterdam.

• General goal: Architecture and implementation of the realtime streaming engine, and help build a team to accompplish this,
• Note: even though my official job title was data scientist, I was operating as the tech lead of the engineering team,
• plan the basic architecture of the streaming engine, and where the engine fits in with the general digital architecture.
• ensure compliance with privacy and security policies, and working together with the privacy and security officers.
• building basic flink jobs for streaming event handling.
• making architecture choices to ensure maintainability of the platform.

Feb 2014–Sep 2015: Sr. Data Scientist, AdGoji, Amsterdam.

• General goal: Analyse the data flowing through our system to improve targeting and system health,
• improved the storage infrastructure for improved query speed and accuracy (querying using cascalog, storing on S3 using pail and thrift),
• create an offline environment for approximate model testing (extract the data in the right form from our data storage, and run different scenarios in R).

Feb 2013 – Feb 2014: Data Scientist, AdGoji, Amsterdam.

• General goal: Analyse the data flowing through our system to improve targeting and system health,
• research and implement (in clojure using cascalog) different clustering algorithms,
• research and implement (in clojure and R) different data modeling and prediction algorithms.

May 2012 – Jan 2013: Software Developer, CoachR Development, Dodewaard.

• Functional design (in close cooperation with the customers describe the functional behavior of the software),
• technical design (setting up the global design of the software to have the structure in place for building it),
• programming the backend in C++ using the internally developed framework, MySQL and SQLite,
• improvements to the framework,
• frontend implementation with javascript.
• I also helped with further professionalization of the organization helping with company culture and application security.

Jun 2009– Jun 2012: Assistant Professor, University of Colorado, Boulder.

• Research in mathematical logic,
• teaching (e.g., undergraduate and graduate logic classes (model theory and computability theory), undergraduate algebra and introduction to proofs),
• co-organise the BLAST 2010 conference (BLAST: Boolean Algebras, Lattices, Algebraic Logic, Quantum Logic, Universal Algebra, Set Theory, Set-theoretic Topology and Point-free Topology),
• co-organise a logic seminar joint with neighboring universities,
• department administration, e.g. member of several committees including the Graduate Committee.

Sept 2006– May 2009: Van Vleck Visiting Assistant Professor, University of Wisconsin, Madison.

• Research in mathematical logic,
• teaching (e.g., undergraduate and graduate logic classes (set theory and computability theory), undergraduate linear algebra, introduction to proofs, and calculus (a large lecture with 270 students and a group of graduate students to do recitation sections)).

Jan 2006 – May 2006: Graduate Student Instructor, University of Michigan, Ann Arbor.

• Research in mathematical logic (finishing and defending my thesis),
• teaching (precalculus, and calculus at different levels).

2005: Visiting Scholar, Sun Yat-Sen University, Guangzhou, China.

• Research in mathematical logic,
• teaching (one undergraduate and one graduate set theory class).

Aug 2000 – Dec 2004: Graduate Student Instructor, University of Michigan, Ann Arbor.

• Research in mathematical logic,
• teaching (precalculus, and calculus at different levels).

Education

2000–2006: University of Michigan, Mathematics, PhD.

1999: Mathematical Research Institute, Master Class in Mathematical Logic (with honors).

1995–2000: Vrije Universiteit Amsterdam, Mathematics, MSc (with honors).

Publications

• My Thesis: Cofinitary Groups and Other Almost Disjoint Families (written under supervision of Andreas Blass and Yi Zhang) pdf file abstract

  Abstract: We study two different types of (maximal) almost disjoint families: very mad families and (maximal) cofinitary groups. For the very mad families we prove the basic existence results. We prove that MA implies there exist many pairwise orthogonal families, and that CH implies that for any very mad family there is one orthogonal to it. Finally we prove that the axiom of constructibility implies that there exists a coanalytic very mad family.
  Cofinitary groups have a natural action on the natural numbers. We prove that a maximal cofinitary group cannot have infinitely many orbits under this action, but can have any combination of any finite number of finite orbits and any finite (but nonzero) number of infinite orbits.
  We also prove that there exists a maximal cofinitary group into which each countable group embeds. This gives an example of a maximal cofinitary group that is not a free group. We start the investigation into which groups have cofinitary actions. The main result there is that it is consistent that the direct sum of ℵ₁ many copies of Z₂ has a cofinitary action.
  Concerning the complexity of maximal cofinitary groups we prove that they cannot be K_σ, but that the axiom of constructibility implies that there exists a coanalytic maximal cofinitary group. We prove that the least cardinality a_g of a maximal cofinitary group can consistently be less than the cofinality of the symmetric group.
  Finally we prove that a_g can consistently be bigger than all cardinals in Cichon's diagram.

• Cardinal Invariants Related to Permutation Groups, with Yi Zhang (Ann. Pure Appl. Logic 143 (2006), pp. 139-146) pdf file abstract

  Abstract: We consider the possible cardinalities of the following three cardinal invariants which are related to the permutation group on the set of natural numbers:
  a_g := the least cardinal number of maximal cofinitary permutation groups;
  a_p := the least cardinal number of maximal almost disjoint permutation families;
  c(Sym(N)) := the cofinality of the permutation group on the set of natural numbers.
  We show that it is consistent with ZFC that a_p = a_g < c(Sym(N)) = 2; in fact we show that in the Miller model a_p = a_g = ℵ₁ < ℵ₂= c(Sym(N)).

• Very Mad Families (published in Contemporary Mathematics 425, Advances in Logic, The North Texas Logic Conference, October 8-10, 2004, University of North Texas, Denton, Texas, edited by Su Gao, Steve Jackson, and Yi Zhang, pp. 105-112) pdf file abstract

  Abstract: The notion of very mad family is a strengthening of the notion of mad family of functions. Here we show existence of very mad families in different contexts.

• Analytic and Coanalytic Families of Almost Disjoint Functions, with Juris Steprans and Yi Zhang (JSL, Vol. 73 (2008), no. 4, pp. 1158-1172) pdf file abstract

  Abstract: If F Ì N^N is an analytic family of pairwise eventually different functions then the following strong maximality condition fails: For any countable H Ì N^N, no member of which is covered by finitely many functions from F, there is f Î F such that for all h Î H there are infinitely many integers k such that f(k) = h(k). However if V = L then there exists a coanalytic family of pairwise eventually different functions satisfying this strong maximality condition.

• The Complexity of Maximal Cofinitary Groups (Proceedings AMS, Vol. 137 (2009), no. 1, pp. 307-316) pdf file abstract

  Abstract: A cofinitary group is a subgroup of the infinite symmetric group in which each element of the subgroup has at most finitely many fixed points. A maximal cofinitary group is a cofinitary group that is maximal with respect to inclusion. We investigate the possible complexities of maximal cofinitary groups, in particular we show that (1) under the axiom of constructibility there exists a coanalytic maximal cofinitary group, and (2) there does not exist an eventually bounded maximal cofinitary group. We also suggest some further directions for investigation.

• Comparing Notions of Randomness, with Steffen Lempp. (Theoretical Computer Science, Vol. 411 (2010), no. 3, pp. 602-616) pdf file abstract

  Abstract: It is an open problem in the area of effective (algorithmic) randomness whether Kolmogorov-Loveland randomness coincides with Martin-Löf randomness. Joe Miller and André Nies suggested some variations of Kolmogorov-Loveland randomness to approach this problem and to provide a partial solution. We show that their proposed notion of injective randomness is still weaker than Martin-Löf randomness. Since in its proof some of the ideas we use are clearer, we also show the weaker theorem that permutation randomness is weaker than Martin-Löf randomness.

• Stability and Posets, with Carl G. Jockusch, Jr., Steffen Lempp, Manuel Lerman, and Reed Solomon (JSL, 74 (2009), no. 2, pp 693-711) pdf file abstract

  Abstract: Hirschfeldt and Shore have introduced a notion of stability for infinite posets. We define an arguably more natural notion called weak stability, and we study the existence of infinite computable or low chains or antichains, and of infinite Π⁰₁-chains and antichains, in infinite computable stable and weakly stable posets. For example, we extend a result of Hirschfeldt and Shore to show that every infinite computable weakly stable poset contains either an infinite low chain or an infinite computable antichain. Our hardest result is that there is an infinite computable weakly stable poset with no infinite Π⁰₁-chains or antichains. On the other hand, it is easily seen that every infinite computable stable poset contains an infinite computable chain or an infinite Π⁰₁-antichain. In Reverse Mathematics, we show that SCAC, the principle that every infinite stable poset contains an infinite chain or antichain, is equivalent over RCA₀ to WSCAC, the corresponding principle for weakly stable posets.

• On Computable Self-Embeddings of Computable Linear Orderings, with Rodney G. Downey, and Steffen Lempp (JSL, Volume 74, Issue 4 (2009), pp. 1352-1366) pdf file abstract

  Abstract: We make progress toward solving a long-standing open problem in the area of computable linear orderings by showing that every computable η-like linear ordering without an infinite strongly η-like interval has a computable copy without nontrivial computable self-embedding. The precise characterization of those computable linear orderings which have computable copies without nontrivial computable self-embedding remains open.

• Isomorphism Types of Maximal Cofinitary Groups (BSL, September 2009, Volume 15, pp. 300-319) pdf file abstract

  Abstract: A cofinitary group is a subgroup of Sym(N) where all nonidentity elements have finitely many fixed points. A maximal cofinitary group is a cofinitary group, maximal with respect to inclusion. We show that a maximal cofinitary group cannot have infinitely many orbits. We also show, using Martin's Axiom, that no further restrictions on the number of orbits can be obtained. We show that Martin's Axiom implies there exist locally finite maximal cofinitary groups. Finally we show that there exists a uniformly computable sequence of permutations generating a cofinitary group whose isomorphism type is not computable.

• An Example of a Cofinitary Group in Isabelle/HOL (In: G. Klein, T. Nipkow, and L. Paulson (ed), The Archive of Formal Proofs, http://afp.sourceforge.net/entries/CofGroups.shtml, August 2009, Formal proof development) pdf file abstract

  Abstract: We formalize the usual proof that the group generated by the function k ↦ k+1 on the integers gives rise to a cofinitary group.

• On Cofinitary Groups, with Yi Zhang (Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 2012, Volume 154, Book 2, Pages 159–166) pdf file abstract

  Abstract: A cofinitary group is a subgroup of the symmetric group on the natural numbers in which all non-identity members have finitely many fixed points. In this note we describe some questions about these groups that interest us; questions on related cardinal invariants and isomorphism types.