Nathan Grieve

I am a Canadian Mathematician with interests in Geometry, Algebra and Number Theory. I am primarily based in the Ottawa area and am currently on faculty and a member of the Laboratory of Birational Geometry at National Taiwan University. Some information about Taiwan based activities in Algebraic Geometry is available here. My Math Genealogy information is here. My research is supported by NSTC (Taiwan) and NSERC (Canada). Over the years, I have contributed to the Macaulay2 system.

This past Spring 2026, I gave an invited lecture at the international conference Complex Hyperbolicity, Function fields and Non-archimedean Arithmetic which was held at VIASM (Vietnam). I also gave a lecture at the 2026 Higher Dimensional Algebraic Geometry which was held at NCTS (Taipei). During the Winter 2026, I gave lectures at the Winter 2026 meeting of the Taiwanese Mathematical Society. At the Winter 2025 meeting of the Canadian Mathematical Society, I gave a mini-course on the general theme of my recently published book "An Introduction to Mathematical Programming and Network Sciences". Over the next few years, Lie Fu and I will organize some scientific events on the general theme "Cohomological and Arithmetic aspects of orbifold geometry - recent and emerging developments" in support of our recent joint CNRS (France) award. Also, with Emmanuel Haven, I co-organized a workshop Workshop on the Use of Quantum Algorithms/Formalisms in Finance which took place at the Fields Institute , Toronto, in October 2025.

I was on Faculty at the Department of Mathematics and Statistics at Acadia University from Fall 2023 - Spring 2025. I served as faculty representative to the university research ethics board from Winter 2024 - Spring 2025. During the academic years Fall 2021 - Spring 2023, I was on Faculty at the Royal Military College of Canada.

With colleagues from Acadia University, I helped to organize the highly successful Science Atlantic - Mathematics, Statistics, and Computer Science Conference 2024. The conference took place at Acadia University on 4, 5 October 2024. Also, during the Fall 2024, I ran a very well attended AARMS advanced course via Zoom. The title of the course was "A working introduction to Homological Algebra and its applications". In Fall 2024 semester, I also gave a lecture at the 2024 Winter Meeting of the Canadian Mathematical Society.

During the spring 2022, I co-organized a CIRGET workshop entitled "Geometric and Arithmetic Frontiers of Orbifolds: a focused introductory workshop". The workshop webpage is here. There was a follow-up workshop during spring 2023. The webpage for this past spring 2023 workshop, "Geometric and Arithmetic Frontiers of Orbifolds II: Arithmetic and hyperbolicity", is here. During the winter 2022 semester, I co-organized an informal CIRGET working seminar on Moduli spaces, Algebraic Cycles and related topics. The list of CIRGET seminars and working seminars for the current 2025-2026 academic year is available here.

Over the past several academic years, I have I co-organized the Carleton-Ottawa Number Theory seminar. The seminar webpage for the 2025-2026 academic year is here.

In December 2023, I co-organized a session Algebraic, Arithmetic and Kahler Geometry: Recent developments at the 2023 Winter Meeting of the Canadian Mathematical Society.

In October 2022, I lectured at the Quebec-Maine Number Theory Conference. During the summer 2022, I attended the workshops 22w5162 and 22w5024 at the Banff International Research Station.

In December 2022, I co-organized a session Diophantine Arithmetic Geometry and Number Theory at the 2022 Winter Meeting of the Canadian Mathematical Society. In January 2022, I co-organized the annual CAAC conference. The workshop webpage is here.

Email:

nathan.m.grieve@gmail.com

Selected Research Articles

N. Grieve, Effective calculation of local Weil functions via presentations of Cartier divisors, Houston Journal of Mathematics, Vol. 51, No. 2, 231-245 (2025). pdf

N. Grieve, CM-line bundles and slope K-semistability for big and nef line bundles along subschemes, Asian Journal of Mathematics, Vol. 29, No. 6, 703--710 (2025). pdf

N. Grieve, About the Bohr-Sommerfeld polytope and the multiplicative SU(2)-eigenvalue problem for the trinion, Mathematica Cluj, To appear. pdf

N. Grieve, Abstract simplicial complexes in Macaulay2, Journal of software for algebra and geometry, Vol. 15, No. 1, 29--39 (2025). pdf code

N. Grieve and C. Noytaptim, On relative fields of definition for log pairs, Vojta's height inequalities and asymptotic coordinate size dynamics, Taiwanese Journal of Mathematics, Vol. 29, No. 4, 715--735 (2025). pdf

N. Grieve and C. Noytaptim, On non-Zariski density of $(D,S)$-integral points in forward orbits and the Subspace Theorem, Journal of Number Theory, Vol. 265, 36--47 (2024). pdf

N. Grieve, On qualitative aspects of the quantitative subspace theorem, Rocky Mountain Journal of Mathematics, Vol. 55, No. 1, 121--146 (2025). pdf

N. Grieve, Expectations, Concave Transforms, Chow weights and Roth's theorem for varieties, Manuscripta Mathematica, Vol. 172, No. 1-2, 291--330 (2023). pdf

N. Grieve, Harder-Narasimhan polygons and Laws of Large Numbers, Canadian Mathematical Bulletin, Vol. 66, No. 1, 340--357 (2023). pdf

N. Grieve, On Duistermaat-Heckman measure for filtered linear series, Comptes Rendus Mathématiques de l'Académie des Sciences. La Société Royale du Canada. Mathematical Reports of the Academy of Science. The Royal Society of Canada, Vol. 44, No. 1, 16--32 (2022). pdf

N. Grieve, Numerical contraction for orbifold surfaces, Bulletin of the Institute of Mathematics. Academia Sinica. New Series, Vol. 16, No. 3, 241--261 (2021). pdf

N. Grieve, Wedderburn components, the index theorem and continuous Castelnuovo-Mumford regularity for semihomogeneous vector bundles, Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, Vol. 20, 95--119 (2021). pdf

N. Grieve and C. Ingalls, On the Kodaira dimension of maximal orders, Advances in Mathematics, Vol. 392, Paper No. 108013, 70 pp. (2021). pdf

N. Grieve, On cubic torsors, biextensions and Severi-Brauer varieties over Abelian varieties, São Paulo Journal of Mathematical Sciences, Vol. 15, No. 2, 1045--1074 (2021). pdf

N. Grieve, On arithmetic inequalities for points of bounded degree, Research in Number Theory, Vol. 7, No. 1, Paper No. 1, 14 pp. (2021). pdf

N. Grieve and J. T. -Y. Wang, Greatest common divisors and consequences for linear recurrence sequences, Transactions of the American Mathematical Society, Vol. 373, No. 11, 8095--8126 (2020). pdf

N. Grieve, Divisorial instability and Vojta's Main Conjecture for Q-Fano varieties, Asian Journal of Mathematics, Vol. 24, No. 6, 995--1005 (2020). pdf

N. Grieve, Generalized gcd for toric Fano varieties, Acta Arithmetica, Vol. 195, 415--428, (2020). pdf

N. Grieve, On arithmetic general theorems for polarized varieties, Houston Journal of Mathematics, Vol. 44, No. 4, 1181--1203 (2018). pdf

N. Grieve, Diophantine approximation constants for varieties over function fields, The Michigan Mathematical Journal, Vol. 67, No. 2, 371--404 (2018). pdf

N. Grieve, Reduced norms and the Riemann-Roch theorem for Abelian varieties, New York Journal of Mathematics, Vol. 23, 1087--1110 (2017). pdf

N. Grieve, A brief introduction to Geometric Invariant Theory, in Superschool on Derived Categories and D-branes, (pp. 57--77), (M. Ballard et al. (eds.)), Springer Proceedings in Mathematics and Statistics, Springer Nature (2018). pdf

N. Grieve, Comments related to infinite wedge representations, Comptes Rendus Mathématiques de l'Académie des Sciences. La Société Royale du Canada. Mathematical Reports of the Academy of Science. The Royal Society of Canada, Vol. 39, No. 1, 13--35 (2017). pdf

N. Grieve, Refinements to Mumford's theta and adelic theta groups, Annales mathématiques du Québec, Vol. 38, No. 2, 145--167 (2014). pdf

N. Grieve, Index conditions and cup-product maps on Abelian varieties, International Journal of Mathematics, Vol. 25, No. 4, 31 pp. (2014). pdf

E. Carlini, N. Grieve, and L. Oeding, Four lectures on secant varieties, in Connections Between Algebra, Combinatorics, and Geometry (pp. 101--147), (S. Cooper, S. Sather-Wagstaff, ed.), Springer Proceedings in Mathematics and Statistics, Springer New York (2014). pdf

N. Grieve, Segre embeddings and the canonical image of a curve, Geometriae Dedicata, Vol. 164, No. 1, 1--7 (2013). pdf

Books

Selected Research Articles