Faculty & Staff

Dr. Nickolas Hein

Dr. Nickolas Hein

Assistant Professor
Founders Hall, 2142
(308) 865-8635
heinnj@unk.edu

Dr. Hein earned a Ph.D. in mathematics from Texas A&M University and a M.A. from the University of Kansas.

Syllabi
Math 102-01 (Spring 2014)
Math 123-04 (Spring 2014)
Math 440-01 (Spring 2014)

Classes Taught at the University of Nebraska, Kearney
Modern Algebra with Geometry
Linear Algebra
5 hour Calculus 1
3 hour Calculus 1
College Algebra

Classes Taught at Texas A&M University
3 hour Calculus 1
5 hour Calculus 1 (TA and lab instructor)
5 hour Calculus 2 (TA and lab instructor)
Functions (TA)

Classes Taught at the University of Kansas
5 hour Calculus 1
5 hour Calculus 2
3 hour Calculus 1
3 hour Calculus 2
College Algebra
Intro to College Algebra

I study algebraic geometry and specialize in Schubert calculus. Combinatorial commutative algebra provides results about the structure of intersection problems from Schubert calculus, and this structure makes Schubert problems well-suited for study in computational algebraic geometry. I develop general techniques for for solving Schubert problems more effectively with modern software tools, and I use these tools to study related instances of geometric problems and uncover phenomena which may occur in general intersection problems.

Preprints

[arXiv soon] Certifiable numerical computation in Schubert calculus. Preprint. (with Hauenstein, Sottile).
arXiv A congruence modulo four in real Schubert calculus with isotropic flags. Preprint. (with Sottile, Zelenko).
arXiv A congruence modulo four in real Schubert calculus, Crelles Journal, 2014 (with Sottile and Zelenko).
arXiv Lower bounds in real Schubert calculus, Resenhas, 2014 (with Hillar and Sottile).
arXiv The secant conjecture in the real Schubert calculus, Experimental Mathematics, 2012 (with García-Puente, Hillar, Martín del Campo, Ruffo, Sottile, Teitler).

Data sets

www Beyond the Shapiro Conjecture and Eremenko-Gabrielov lower bounds. Data Set, 2013 (with Sottile).
www Beyond the Shapiro Conjecture and Eremenko-Gabrielov lower bounds. Preliminary Data Set, 2010 (with Hauenstein, Martín del Campo, Sottile).

Extended abstracts

arXiv Certifiable numerical computations in Schubert calculus, Extended Abstract presented at MEGA 2013 (with Hauenstein and Sottile).
arXiv The monotone secant conjecture in the real Schubert calculus. Extended Abstract in MEGA 2011 proceedings (with Hauenstein, Hillar, Martín del Campo, Sottile, Teitler).

Dissertation

arXiv Reality and computation in Schubert calculus

Here are examples of primal-dual square formulations for solving (traditionally overdetermined) Schubert problems.  They were solved using regeneration in bertini and certified using rational arithmetic in alphaCertified.