Bart Kastermans

About Me

Principal Engineer and mathematician with a PhD in Mathematics and experience in academic research, software engineering, security engineering and data science. Combines mathematical logic with practical experience in modern computing infrastructure, encryption services, secrets management, and real-time data processing. Translates abstract and complex problems into secure, reliable and maintainable technical solutions. Brings experience in research, software architecture, technical leadership, scientific publication, and university teaching.

Core Skills

Mathematical research | Technical problem solving | Mathematical logic | Security engineering | Applied encryption | Secrets management | Software architecture | Distributed systems | Real-time data streaming | Technical leadership | Scientific writing and teaching

Experience

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

• Supported Digital Engine teams with platform, security, monitoring and reliability challenges.
• Developed user-side monitoring solution that transfers timing metrics through Apache Kafka into central metrics storage.
• Combined user-side data with platform metrics to identify service issues proactively.
• On loan to strategy, architecture, and technology department for research on quantum computing.

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

• Supported Digital Engine teams with platform, security, monitoring, reliability challenges, and the migration to the cloud.
• Migrated the HashiCorp Vault secrets platform from on-premises infrastructure to the cloud.
• Build and integrated a Kubernetes encryption service with reliable daily key rotation for communication over untrusted channels.
• Build improved tooling to work with our secrets manager.
• Improved technical documentation based on developer questions, reducing support demand, and strengthening trust in the documentation.
• Initial design and implementation of the digital engine conductor for increased speed, flexiblity, and accountability for the digital engine teams in managing access to e.g. Vault and Kafka.

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

• Implemented an on-premises secrets management platform based on HashiCorp Vault.
• Managed platform access through GitOps, allowing teams to request access through pull requests.
• Developed monitoring, backup and recovery tooling that limited downtime and protected data during persistent-volume failures.

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

• Helped establish the Streaming Engine Team and worked as its technical lead.
• Designed the architecture for KPN’s real-time data streaming capabilities.
• Developed Apache Flink jobs and proofs of concept for real-time event processing.
• Worked with privacy and security officers to align the streaming platform with internal policies.

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

• Analysed large-scale data streams to improve targeting and monitor system performance.
• Improved data storage infrastructure to support faster and more accurate queries.
• Worked with Cascalog, Amazon S3, Pail and Thrift on data volumes approaching one terabyte per day.
• Created 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.

• Researched and implemented clustering algorithms in Clojure and Cascalog.
• Researched and implemented data modeling and prediction algorithms in Clojure and R.
• Analysed thousands of events per second in a large-scale advertising environment.

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

• Translated customer requirements into functional and technical software designs.
• Developed backend applications in C++ using an internally developed framework.
• Implemented improvements to the internal framework,
• Worked with MySQL, SQLite and JavaScript and contributed to application security.

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

• Conducted research in mathematical logic.
• Taught undergraduate and graduate courses in model theory, computability theory, algebra and mathematical proofs.
• Co-organised the BLAST 2010 conference and a joint logic seminar with neighbouring universities.
• Department administration: member of several committees including the Graduate Committee.

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

• Conducted research in mathematical logic.
• Taught set theory, computability theory, linear algebra, mathematical proofs and calculus.

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

• Conducted doctoral research and taught precalculus and calculus at several levels.

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

• Conducted research in mathematical logic
• Taught undergraduate and graduate courses in set theory.

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

• Conducted doctoral research and taught precalculus and calculus at several 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.