Insko, Erik (PhD)
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EducationPhD from University of Iowa in 2012
SpecialtiesAlgebraic Geometry, Algebraic combinatorics, and Discrete Mathematics
Research and Teaching InterestsDr. Insko has mentored many student research projects in algebraic combinatorics and discrete mathematics, and his primary teaching interests are in Abstract Algebra, Linear Algebra, Computation, and Combinatorics. His preferred coding language is python. He encourages all of his research students to use coding as part of their research, and his former research students are quite successful in their academic and professional pursuits, which have included pursuing doctoral degrees, working national defense labs, or working in data analytics at many local corporations and the US census bureau.
Courses OfferedModern Algebra I and II, Advanced Linear Algebra, Abstract Algebra I and II, Applied Combinatorics, Linear Algebra, Discrete Mathematics, Calculus II, Elementary Calculus, College Algebra, Finite Mathematics
- Patch ideals and Peterson varieties (with Alexander Yong), Transformation Groups, December 2012, Volume 17, Issue 4, pp. 1011-1036.
- On (t,r) broadcast domination numbers of grids (with David Blessing, Katie Johnson, and Christie Mauretour), Journal of Discrete and Applied Mathematics, Volume 187, May 2015, Pages 19–40. doi:10.1016/j.dam.2015.02.005.
- Supercoiled tangles and stick numbers of 2-bridge links (with Rolland Trapp), Journal of Knot Theory and its Ramifications, April 2015, Volume 24, Issue 05, 1550029. doi:10. 1142/S0218216515500297
- Schubert calculus and the homology of the Peterson variety, Electronic Journal of Combinatorics, Volume 22, Issue 2, #P2.26 (2015).
- Intersection theory of the Peterson variety and certain singularities of Schubert varieties (with Julianna Tymoczko) Geometriae Dedicata, Springer Netherlands, pp. 1-22. June 2015.
- The adjoint representation of a Lie algebra and Kostant’s weight multiplicity formula (with Pamela Harris and Lauren Kelly Williams), Journal of Combinatorics, Volume 7 (2016) Number 1 pp. 75-116.
- Peak sets of classical Coxeter groups (with Alexander Diaz-Lopez, Pamela E. Harris, and Darleen Perez-Lavin) Involve, 10(2): 263 –290, 2017.
- A proof of the peak polynomial positivity conjecture (with Alex Diaz-Lopez, Pamela Harris, and Mohamed Omar), Journal of Combinatorial Theory, Series A 149C (2017) pp. 21-29. (Extended abstract accepted by FPSAC 2017)
- An ordered partition expansion of the determinant (with Katie Johnson and Shaun Sullivan), Integers 17 (A36), 2017.
- Computing weight q-multiplicities for the representations of the simple Lie algebras (with Pamela Harris and Anthony Simpson), Applicable Algebra in Engineering, Communications, and Computing (2018).
- The q-analog of Kostant’s partition function and the highest root of the simple Lie algebras, Australasian Journal of Combinatorics (with Pamela Harris and Mohamed Omar) 71, p.68- 91, 2018.
- The singular locus of semisimple Hessenberg varieties (with Martha Precup), Journal of Algebra, 521 p. 65-96, 2019.
- Descent Polynomials , Discrete Math. (with Alexander Diaz-Lopez, Pamela Harris, Mohamed Omar, and Bruce Sagan) 342 , no. 6, 1674-1686, 2019
- I was invited to give a talk on "Singularities of Hessenberg varieties" at the Hessenberg varieties in Combinatorics, Geometry, and Representation Theory Workship at the Banff Internation Research Station Nov 21-26, 2018.
- I was invited to speak on “Classifying singularities of Semisimple Hessenberg varieties” at the Midwest AMS Sectional Meeting in Denton, TX on Sep 9-10, 2017 and on “Peak polynomials” at the Eastern AMS Sectional Meeting in Buffalo, NY on Sept 16-17, 2017, but sadly Hurricane Irma prevented me from travelling those weekends.
- I was invited to speak at the 31st Annual SIDIM conference at the University of Puerto Rico - Humacao on March 5-6 2016.
- I was invited to speak on “Problems in abstract algebra and domination theory” at the SACNAS National Meeting on Oct 28-Nov 1, 2015.
- I was invited to speak on “Schubert calculus and the intersection theory of the Peterson variety” at the PREP Workshop - Implementing and Creating POGIL Activities on July 15--18 and the "Recent developments in Hessenberg varieties" workshop at the Fields Institute, July 22--24, 2015.
Grants & Awards
- I was awarded FGCU's Junior Faculty Scholarship Excellence Award and Excellence in Mentoring Award in April 2016.
- Principal Investigator: NSF “Underrepresented Students in Topology and Algebra Research Symposium (USTARS) 2018-2020" - DMS-1808177 - awarded April 2018 $45,000.00 Co-PI’s: Syvillia Averett, Candice Price, Shannon Talbott
- Principal Investigator: NSF “Underrepresented Students in Topology and Algebra Research Symposium (USTARS) 2017" - DMS-1711937 - awarded December 2016 $34,391.00 Pi: Candice Price and Co-PI’s: Syvillia Averett, Candice Price, Gabriel Sosa, Shannon Talbott
- Co-Principal Investigator: NSF “Underrepresented Students in Topology and Algebra Research Symposium (USTARS) 2016" - DMS-1602558 - awarded February 2015 $30,186.00 Pi: Candice Price and Co-PI’s: Syvillia Averett, Shannon Talbott, Garrett Jones
- Principal Investigator: NSF “Underrepresented Students in Topology and Algebra Research Symposium (USTARS) 2015" - DMS-1458396 - - awarded February 2015 $30,000.00 Co PI’s: Candice Price, Syvillia Averett, Shannon Talbott, Garrett Jones