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Kevin Iga Faculty Profile

Kevin Iga

Professor of Mathematics
Natural Science Division, Seaver College
RAC 129
310.506.4313
/natural-science/content/kevin-iga-cv.pdf

Biography

Kevin Iga has been teaching at Pepperdine University since 1998. Born in Honolulu, Hawai'i, of Japanese American descent, he now lives in Agoura Hills, California. His research is mainly about an area of mathematical physics called supersymmetry, using diagrams called Adinkras. His earlier work was in the differential topology of four dimensional manifolds, and has published in general relativity and cryptography. In general, he is open to working on whatever interesting problems come his way. He has been the Public Information Officer for the Philosophy of Mathematics Special Interest Group of the MAA. He is also involved in Malibu Presbyterian Church, and sings in the Pepperdine University Concert Choir. 

Memberships: Association of Christians in the Mathematical Sciences (ACMS), American Mathematical Society (AMS), American Scientific Affiliation (ASA), Mathematical Association of America (MAA), National Association of Mathematicians (NAM), Philosophy of Mathematics Special Interest Group of the MAA.

Education

  • PhD Mathematics, Stanford University, 1998
  • BS Mathematics, Massachusetts Institute of Technology, 1992
  • BS Physics, Massachusetts Institute of Technology, 1992

 

  • E. Goins, K. Iga, J. Kostiuk, K. Stiffler, The signed monodromy group of an Adinkra, Ann. Inst. Henri Poincaré, Comb. Phys. Interact. 10 (2023), no. 1, pp. 1–30, arXiv: 1909.02609, DOI 10.4171/AIHPD/132
  • K. Iga, C. Klivans, J. Kostiuk, Chi Ho Yuen, Eigenvalues and Critical Groups of Adinkras, Advances in Applied Mathematics 143, (2023) 102450. https://arxiv.org/abs/2202.02821
  • K. Iga, Adinkras: Graphs of Clifford Algebra Representations, Supersymmetry, and Codes, Adv. Appl. Clifford Algebras 31, 76 (2021). arXiv:2110.01665 https://doi.org/10.1007/s00006-021-01181-0
  • S.J. Gates, K.M. Iga, L. Kang, V. Korotkikh, K. Stiffler, Generating All 36,864 Four-Color Adinkras via Signed Permutations and Organizing into l- and ~l-Equivalence Classes, Symmetry 2019, 11(1), 120; arXiv:1712.07826 https://doi.org/10.3390/sym11010120.
  • C.F. Doran, K. Iga, J. Kostiuk, S. Mendez--Diez, Geometrization of $N$-extended 1-dimensional supersymmetry algebras, II, Advances in Theoretical and Mathematical Physics, Vol. 22, No. 3 (2018), pp. 565-613. arXiv:1610.09983
  • C.F. Doran, K.M. Iga, G.D. Landweber, An Application of Cubical Cohomology to Adinkras, AIHPD, European Mathematical Society, Vol. 4, No. 3, (2017), pp. 387--415, arXiv:1207.6806.
  • C.F. Doran, M.G. Faux, S.J. Gates, Jr., T. Hubsch, K.M. Iga, G.D. Landweber, Off-shell supersymmetry and filtered Clifford supermodules, Algebras and Representation Theory, April 2018, Volume 21, Issue 2, pp 375–397, arXiv:math-ph/0603012, DOI 10.1007/s10468-017-9718-8.
  • Structural Theory and Classification of 2D Adinkras, (with Y. X. Zhang), Advances in High Energy Physics, vol. 2016, Article ID 3980613, 12 pages, 2016. doi:10.1155/2016/3980613. arxiv
  • Geometrization of N-Extended 1-Dimensional Supersymmetry Algebras, (with C.F. Doran, G. Landweber, S. Mendez--Diez) Advances in Theoretical and Mathematical Physics, Vol. 19, No. 5 (2015), pp. 1043-1113. arxiv
  • Hardness of Learning Problems over Burnside Groups of Exponent 3 (with N. Fazio, A. Nicolosi, L. Perret, W. Skeith),, Designs, Codes and Cryptography: Volume 75, Issue 1 (2015), Page 59-70, DOI 10.1007/s10623-013-9892-6. Cryptology-ePrint>
  • On General Off-Shell Representations of World Line (1D) Supersymmetry, (with C. Doran, T. Hubsch, G. Landweber), Symmetry 2014, 6(1), 67-88 (2014) arxiv.
  • Hardness of Learning Problems over Burnside Groups of Exponent 3, (with N. Fazio, A. Nicolosi, L. Perret, W. Skeith), Designs, Codes, and Cryptography, Springer, DOI 10.1007/s10623-013-9892-6, (2013) eprint.
  • Pure and entangled N=4 linear supermultiples and their one dimensional sigma models, (with M. Gonzalez, S. Khodaee, and F. Toppan), J. Math. Phys. 53, 103513 (2012) arxiv.
  • Codes and Supersymmetry in One Dimension, (with DFGHILM), Adv. Theor. Math. Phys. 15 (2011), 1909-1970. arxiv
  • Dimensional Enhancement via Supersymmetry (with M. Faux and G. Landweber), Advances in Mathematical Physics (2011), Article ID 259089, 45 pages, doi:10.1155/2011/259089. arxiv
  • A Superfield for Every Dash-Chromotopology (with DFGHIL), Int. J. Mod. Phys., A24 (2009), 5681--5695. arxiv
  • Relating Doubly-Even Error-Correcting Codes, Graphs, and Irreducible Representations of N-Extended Supersymmetry (with DFGHIL), Discrete and Computational Mathematics, eds. F. Liu et al. (Nova Science Pub., Inc. Hauppage, 2008): arxiv
  • Adinkras and the Dynamics of Superspace Prepotentials (with DFGHIL), Adv. S. Th. Phys. 2 (3) (2008) 113-164. arxiv
  • On the matter of N=2 Matter (with DFGHIL), Phys. Lett. B659 (2008) 441-446. arxiv
  • Pebble sets in Polygons (with R. Maddox), J. Discrete Comput. Geom. (2007) 38: 680-700 pdf
  • A Counter-Example to a Putative Classification of 1-Dimensional, N-extended Supermultiplets (with DFGHIL), Adv. S. Th. Phys. 2 (3) (2008) 99-111. arxiv
  • On Graph-theoretic Identifications of Adinkras, Supersymmetry Representations and Superfields (with C. Doran, M. Faux, S. Gates, T. Hubsch, G. Landweber), Int. J. Mod. Phys. A22 (2007) 869-930. arxiv
  • Truckdrivers, A Straw, and Sharing a Glass of Water (with K. Killpatrick) tex pdf
  • What do Topologists want from Seiberg--Witten theory?, International Journal of Modern Physics A, Vol. 17, No. 30 (2002), 4463-4514.
  • Dynamical systems proof of Fermat's little theorem, Math Magazine
  • Superharmonic Functions and the Penrose Inequality (with H. Bray), Comm. Anal. Geom. (10) (2002) 5: 999-1016
  • Generalized Fibonacci Sequences modulo n
  • Moduli Spaces of Seiberg-Witten Flows, Doctoral Dissertation, Stanford University, 1998.
  • A priori bounds on positive superharmonic functions (Joint work with Prof. Hubert Bray, MIT)
  • American Mathematics Society
  • Mathematics Association of America
  • Frank R. Seaver Chair in Natural Science

Topics

  • Mathematical Physics
  • Supersymmetry
  • Topology
  • Cryptology

Courses

  • Algebraic Structures I and II
  • Automata Theory
  • Business Calculus
  • Business Probability, Linear Systems, and Multivariable Optimization
  • Calculus I, II, and III
  • Real Analysis I and II