Research areas
My main research area is computability theory. In this field, we look at the theoretical power of computers if there were no limits on the memory and running time of programs. In my subfield, Reverse Mathematics, we apply computability to study mathematics itself. We can separate mathematical theorems into different levels of strength depending on how much noncomputability the theorems require. I have also published papers in other areas, including combinatorics and general topology.
I regularly supervise student projects in mathematics and computer science. I have co-authored three peer-reviewed papers with undergraduates to date.
I am also interested in educational research in Inquiry Based Learning, and in Digital Humanities.
Research papers
- “Banach's theorem in higher order reverse mathematics”, Jeffry. L. Hirst and Carl Mummert. Computability 12, 2023, pp. 203–225.
- “Using Ramsey’s Theorem Once”, Jeffry L. Hirst and Carl Mummert.
Archive for Mathematical Logic 58 (2019), pp. 857–866.
DOI: 10.1007/s00153-019-00664-z.
Preprint: author’s accepted copy - “On erasure combinatorial batch codes”, JiYoon Jung,
Carl Mummert,
Elizabeth Niese,
and Michael Schroeder.
Advances in Mathematics of Communications v. 12 n. 1, 2018, pp. 49–65.
Preprint: http://arxiv.org/abs/1511.04580. - “Reverse mathematics of matroids”, Jeffry L. Hirst and Carl Mummert. In
Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60th Birthday, Day, Fellows, Greenberg, Khoussainov, Melnikov, and Rosamond (Eds.), Theoretical Computer Science, 2017, pp. 143–159.
Preprint: http://arxiv.org/abs/1604.04912 - “On the existence of a connected component of a graph”, Kirill Gura, Jeffry L. Hirst, and Carl Mummert. Computability v. 4, 2015, pp. 103–117.
DOI 10.3233/COM-150039.
Preprint: arXiv:1406.4786 - “The modal logic of Reverse Mathematics”, Carl Mummert, Alaeddine Saadaoui, and Sean Sovine. Archive for Mathematical Logic v. 54, 2015, pp. 424–437.
DOI 10.1007/s00153-015-0417-z.
Preprint: arXiv:abs/1401.0648 - “On the number of mates of Latin squares of size 7 and 8”, Megan Bryant, James Figler, Roger Garcia, Carl Mummert, and Yudhisthir Singh. Proceedings of the 44th Southeastern International Conference on Combinatorics, Graph Theory, and Computing, Congressus Numerantium v. 217, 2013, pp. 53–64.
Preprint: PDF - “Reverse mathematics and properties of finite character”, Damir D. Dzhafarov and Carl Mummert. Annals of Pure and Applied Logic, v. 163, 2012, pp. 1243–1251. DOI 10.1016/j.apal.2012.01.007.
Preprint: arXiv:1109.3378 - “On the strength of the finite intersection principle”, Damir D. Dzhafarov and Carl Mummert. Israel Journal of Mathematics, v. 191, 2012, pp. 1–17. DOI 10.1007/s11856-012-0150-9.
Preprint: arXiv:1109.3374 - “Reverse mathematics and uniformity in proofs without excluded middle”, Jeffry L. Hirst and Carl Mummert, Notre Dame Journal of Formal Logic v. 52, 2011, pp. 149–162. DOI 10.1215/00294527-1306163.
Preprint: arXiv:1010.5165 - “Stationary and convergent strategies in Choquet games”, François G. Dorais and Carl Mummert, Fundamenta Mathematicae v. 209, 2010, pp. 59–79. DOI 10.4064/fm209-1-5.
Preprint: arXiv:0907.4126 - “Topological aspects of poset spaces”, Carl Mummert and Frank Stephan, Michigan Mathematical Journal v. 59, 2010, pp. 3–24. DOI 10.1307/mmj/1272376025.
Preprint: arXiv:0912.3191 - “Subsystems of second-order arithmetic between WKL0 and RCA0“, Archive for Mathematical Logic v. 47 n. 3, 2008, pp. 205–210. DOI 10.1007/s00153-008-0074-6.
Preprint: ps pdf - “Reverse mathematics of MF spaces”, Journal of Mathematical Logic v. 6 n. 2, 2007, pp. 203–232. DOI 10.1142/S0219061306000578.
Preprint: ps pdf - “Filters on computable posets”, Steffen Lempp and Carl Mummert, Notre Dame Journal of Formal Logic v. 47 n. 4, 2006, pp. 479–485. DOI 10.1305/ndjfl/1168352662.
Preprint: ps pdf - “Reverse Mathematics and Π12 comprehension”, Carl Mummert and Stephen G. Simpson, Bulletin of Symbolic Logic v. 11 n. 4, 2005, pp. 526–533. DOI 10.2178/bsl/1130335208.
Preprint: ps pdf -
“An incompleteness theorem for βn models”, Carl Mummert and Stephen G. Simpson, Journal of Symbolic Logic v. 29 n. 2, 2004, pp. 612–616. DOI 10.2178/jsl/1082418545.
Preprint: ps pdf
Books
- Reverse Mathematics, Damir D. Dzhafarov and Carl Mummert, Theory and Applications of Computability, CIE/Springer, 2022. 507 pages. ISBN: 978-3-0311-1366-6.
- Finite Fields and Applications, Gary Mullen and Carl Mummert, AMS Student Mathematical Library v. 41, 2007. 175 pages. ISBN: 978-0-8218-4418-2.
Dissertation
- On the Reverse Mathematics of General Topology. PhD thesis, Penn State, 2005. Download: pdf.
Author identifiers
My ORCID id is orcid.org/0000-0002-8290-9458.
My arXiv id is au:Mummert_C.