Dr. Mike Krebs

Publications

My Ph.D. dissertation

Toledo invariants of Higgs bundles on elliptic surfaces associated to base orbifolds of Seifert fibered homology 3-spheres. (Appears in Michigan Math. J. Volume 56, Issue 1 (2008), 3-27.)

On the Spectra of Johnson Graphs. Joint work with A. Shaheen. (Appears in Electronic Journal of Linear Algebra, Volume 17, pp. 154-167, March 2008)

Think Around The Box, a crossword puzzle of sorts. The Mathematical Intelligencer, Volume 31, Number 2, 59-60.

I'm the faculty adviser for Fixed Points of Number Derivatives Modulo n by CSULA student F. Bains. Rose-Hulman Undergraduate Math Journal, Vol. 10 (2009), Issue 1.

How to differentiate an integer modulo n. Joint work with C. Emmons and A. Shaheen. College Mathematics Journal, November 2009.

On Cantor's first uncountability proof, Pick's theorem, and the irrationality of the golden ratio. Joint work with T. Wright. Amer. Math. Monthly 117 (2010), no. 7, 633-637

mini-Sudokus and Groups. Joint work with C. Arcos (CSULA student) and G. Brookfield. Math. Mag. 83 (2010), no. 2, 111-122

Expander Families and Cayley Graphs: A Beginner's Guide, co-authored by A. Shaheen, Oxford University Press, New York, Oct. 2011

K-quasiderivations. (K-quasiderivations are maps that satisfy both the Product Rule and Chain Rule.) Central European Journal of Mathematics, Vol. 10 (2012), no. 2, 824-834

A combinatorial trace method: Counting closed paths to assay graph eigenvalues. Joint work with K. Dsouza (CSULA student). Rocky Mountain Journal of Mathematics, Vol. 43 (2013), no. 2, 469-478

Simple examples of the combinatorial trace method in action. Joint work with N. Martinez (CSULA student). College Mathematics Journal, Vol. 44 (2013), no. 1, 32-36

Expander families, group structure, and semidirect products. Joint work with M. Aivazian (CSULA student). Bulletin of the Irish Mathematical Society, Number 71 (2013), 21-30

Expander graphs. In J. Gross and J. Yellen (Eds.), Handbook of Graph Theory, Second Edition. CRC Press, 2013.

ZERO SUMS ON UNIT SQUARE VERTEX SETS, AND PLANE COLORINGS. Joint work with R. Katz and A. Shaheen. The American Mathematical Monthly. Vol. 121, No. 7 (August-September 2014), pp. 610-618.

Al Fares, A. (CSULA student), E. Golvin (CSULA student), M. Krebs. A class of 2-groups of derived length three. Serdica Mathematical Journal, Volume 41, Numbers 2-3, 2015, pp. 329-332

Kevin Cramer (CSULA student), Mike Krebs, Nicole Shabazi (CSULA student), Anthony Shaheen and Edward Voskanian (CSULA student). The Isoperimetric constant and Kazhdan constant of a Paley graph, Involve, 9(2): 293-306, March 2016.

On cardinalities and compact closures.  Applied General Topology, 18(1): 107, April 2017, 107-115

Can a Subset's Topology Detect Continuous Extensions?  The College Mathematics Journal, 49(2): 138-139, March 2018.

Finite epsilon unit-distance graphs.  Journal of Algebra, Combinatorics, Discrete Structures, and Applications, Sept. 2021; 8(3): 161-166

 

Presentations

How to Put Rainbow Sprinkles on a Donut: Chromatic Numbers of Abelian Cayley Graphs

 


I graduated from Johns Hopkins University in May 2005. My thesis advisor was Dr. Richard Wentworth.

This website was last updated in May 2022.


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