Dr. Nickolas啊

Nickolas啊 grew up in Wichita and came to BC in 2016. 他获得了博士学位.D. in mathematics at Texas A&M after receiving B.A. 和M.A. degrees in mathematics at KU in Lawrence. His research includes algebraic geometry, combinatorics, and numerical analysis. 特别是, his interests include Schubert calculus, 加泰罗尼亚的对象, certification of numerical solutions, reality in algebraic geometry, and experimental mathematics. Dr. Hein is an active reviewer for the American Mathematical Society Mathematical Reviews. He began a one-year term as chair for the Kansas section of the Mathematical Association of America in Spring 2022.

Nickolas is grateful to have been called to Atchison and enjoys raising his four children, 和他的妻子, surrounded by the stable presence of the local Benedictine community. Dr. Hein is the faculty advisor to the Mathematics and Computer Science club at BC. He also helps run the St. Benedict Elementary School chess club.

教育

Ph.D.德克萨斯州A&硕士大学，2013年

Dissertation: Reality and Computation in Schubert Calculus

M.A., The University of Kansas, 2006

Thesis: The Riemann-Roch Theorem for Complex Curves

B.A., The University of Kansas, 2003

Honors Thesis: Constructible Numbers and the Insolvability of the Quintic

类

• Intermediate College Algebra, College Algebra
• 有关微积分的知识
• Applied Differential Calculus, Applied Integral Calculus
• 微积分1、2
• Multivariable Calculus
• Discrete Mathematical Structures
• 欧几里德几何
• 线性代数
• Modern Algebra I, II
• 复杂的分析
• 指导研究
• Senior Comprehensive Exam
• Numerical Solution of Polynomial Systems Arising in Engineering and Science
• Introduction to Graph Theory
• Groebner Bases and Convex Polytopes
• Modern Algebra with Geometry (graduate)
• Algebraic Geometry (graduate)

研究兴趣

Reformulating classical problems to optimize solution by modern techniques, computational solution of problems with structure, experiments involving reality in algebraic geometry, variants of the Catalan numbers.

For some computational archives, 点击这里.

出版物

Nickolas啊 and Jia 黄. Variations of the Catalan numbers from some nonassociative binary operations, Discrete Mathematics, Volume 345, Issue 3, 2022, ISSN 0012-365X, 21 pp., http://doi.org/10.1016/j.阀瓣.2021.112711 .

Timothy Duff, Nickolas啊, and 弗兰克Sottile. Certification for Polynomial Systems via Square Subsystems, Journal of Symbolic Computation, July 2020, 21 pp., http://doi.org/10.1016/j.约翰逊航天中心.2020.07.010 .

Nickolas啊, 弗兰克Sottile, Igor Zelenko. A congruence modulo four for real Schubert Calculus with isotropic flags, Canadian Mathematical Bulletin, Published electronically ahead of print, 2017, 9 pp., http://dx.doi.org/10.4153 / cmb - 2016 - 087 - 2 .

Nickolas啊 and 弗兰克Sottile. A lifted square formulation for certifiable Schubert calculus, Journal of Symbolic Computation (2017), pp. 594 - 608, http://dx.doi.org/10.1016/j.约翰逊航天中心.2016.07.021 .

Nickolas啊, Jia 黄. Modular Catalan Numbers, European Journal of Combinatorics, Vol. 61年国际空间站. C, 3月. 2017, pp. 197 - 218, http://dx.doi.org/10.1016/j.ejc.2016.11.004 .

Jonathan 霍恩斯坦,Nickolas啊, and 弗兰克Sottile. A primal-dual formulation for certifiable computations in Schubert calculus, Foundations of Computational Mathematics, 16 (2016), pp. 941 - 963, http://dx.doi.org/10.1007/s10208-015-9270-z .

Nickolas啊, 弗兰克Sottile, and Igor Zelenko. A congruence modulo four for real Schubert calculus Journal für die reine und angewandte Mathematik, vol. 2016年,国际空间站. 714 (2016), pp. 151 - 174, http://dx.doi.org/10.1515/crelle-2013-0122 .

Nickolas啊, 克里斯多夫这一, Abraham Martín del Campo-Sanchez, 弗兰克Sottile, 还有扎克·泰特勒. The monotone secant conjecture in the real Schubert calculus, Experimental Mathematics, 24 (2015), pp. 261 - 269, http://dx.doi.org/10.1080/10586458.2014.980044 .

Nickolas啊, 克里斯多夫这一, and 弗兰克Sottile. Lower bounds in real Schubert calculus, São Paulo Journal of Mathematics, 7, 1 (2013), pp. 33-58. DOI: 10.11606 / issn.2316-9028.v7i1p33-58

Luis Garcia-Puente, Nickolas啊, 克里斯多夫这一, Abraham Martín del Campo-Sanchez, 詹姆斯Ruffo, 弗兰克Sottile, 还有扎克·泰特勒. The secant conjecture in the real Schubert calculus, Experimental Mathematics, 21, 3 (2012), pp. 252-265.

REFEREED EXTENDED ABSTRACTS

N. 海因和J. 黄. Variations of the Catalan Numbers From Some Nonassociative Binary Operations, 扩展的抽象, presented at Séminaire Lotharingien de Combinatoire – FPSAC 2018, published in Issue 80B,  Proceedings of the 30th International Conference on “Formal Power Series and Algebraic Combinatorics”, 2018年7月, 扩展的抽象, 12 pp.

J.D. 霍恩斯坦,N. Hein和F. Sottile, Certifiable Numerical Computations in Schubert Calculus, 扩展的抽象, presented at MEGA 2013, Frankfurt, Germany.

J.D. 霍恩斯坦,N. 嗯,C.J. 这一,. Martín del Campo-Sanchez, F. sotttile和Z. Teitler. The monotone secant conjecture in the real Schubert calculus, 扩展的抽象, presented at MEGA 2011, Stockholm, Sweden.

REFEREED EXTENDED ABSTRACTS

海因和J. 黄. Variations of the Catalan Numbers From Some Nonassociative Binary Operations, 扩展的抽象, presented at Séminaire Lotharingien de Combinatoire – FPSAC 2018, published in Issue 80B,  Proceedings of the 30th International Conference on “Formal Power Series and Algebraic Combinatorics”, 2018年7月, 扩展的抽象, 12 pp.

J.D. 霍恩斯坦,N. Hein和F. Sottile, Certifiable Numerical Computations in Schubert Calculus, 扩展的抽象, presented at MEGA 2013, Frankfurt, Germany.

J.D. 霍恩斯坦,N. 嗯,C.J. 这一,. Martín del Campo-Sanchez, F. sotttile和Z. Teitler. The monotone secant conjecture in the real Schubert calculus, 扩展的抽象, presented at MEGA 2011, Stockholm, Sweden.