Tatsunari Watanabe

Dr. Tatsunari Watanabe is an associate professor in the Mathematics Department. He regularly teaches a variety of courses, including calculus, linear algebra, differential equations and complex variables.

Dr. Watanabe holds a Ph.D. in Mathematics from Duke University. Before joining Embry-Riddle, he served as a Golomb assistant professor at Purdue University, where he conducted research in algebraic geometry, focusing on topological surfaces of genus two and utilizing various mathematical tools across multiple areas.

Dr. Watanabe’s research interests span algebraic geometry, differential geometry, topology and number theory. His work focuses on systems of polynomial equations, particularly Diophantine problems, which are fundamental in modern cryptography. His research emphasizes understanding the geometric properties of these equations and their relationship with integer solutions, utilizing interdisciplinary techniques from algebraic geometry, topology and group theory.

At Embry-Riddle, Dr. Watanabe continues to study the geometric properties of systems of polynomial equations, particularly those involving complex variables, with applications across various scientific disciplines.

His dedication to teaching excellence earned him the College of Arts & Sciences Teacher of the Year Award in 2023. Beyond his academic role, Dr. Watanabe actively contributes to the mathematical community as a reviewer for Mathematical Reviews by the American Mathematical Society. Since 2019, he has also served as the faculty advisor for the soccer club at the Prescott campus, actively participating in weekly sessions and promoting student engagement through extracurricular activities.

MA242 - Calculus & Analytical Geom II

MA243 - Calculus & Analytical Geom III

MA335 - Intro to Linear and Abstract Algebra

MA345 - Differential Equations and Matrix Methods

MA399 - Mathematical Problem Solving and Proofs

MA399 - Intro to Knot Theory

MA412 - Probability and Statistics

MA441 - Math Methods for Engineering and Physics I

MA443 - Complex Variables

MA499 - Intro to Group Theory

MA499 - Intro to Riemannian Differential Geometry

MA499 - Intro to Smooth Manifolds

MA499 - Intro to Algebraic Topology

Published Papers:

1. On the universal curves with unordered marked points (with Ma Luo), Journal of Algebra 713 (2027), 991–1037. (Published online October 19, 2026.) arXiv:2511.12354.

2. On the Birman exact sequence of the subgroups of the mapping class group of genus three (with Ma Luo), Journal of Algebra 709 (2027), 110–141. (Published online in 2026.) arXiv:2502.14343.

3. Remarks on the Sections of Universal Hyperelliptic Curves, Journal of Algebra 683 (2025), 761–802. DOI: 10.1016/j.jalgebra.2025.06.040.

4. Nonabelian Cohomology of Universal Curves in Positive Characteristic, Proc. Amer. Math. Soc. 152 (2024), no. 1, 89–103. DOI: 10.1090/proc/16542.

5. Remarks on Collino Cycles and Hyperelliptic Johnson Homomorphisms (with Ma Luo), Journal of Algebra 649 (2024), 96–132. DOI: 10.1016/j.jalgebra.2024.02.038.

6. Remarks on Rational Points of Universal Curves, Proc. Amer. Math. Soc. 148 (2020), no. 9, 3761–3773. DOI: 10.1090/proc/15008. MR4127823.

7. On the Sections of Universal Hyperelliptic Curves, Journal of Algebra 533 (2019), 44–89. DOI: 10.1016/j.jalgebra.2019.05.023. MR3961806.

8. Rational Points of Universal Curves in Positive Characteristics, Trans. Amer. Math. Soc. 372 (2019), no. 11, 7639–7676. DOI: 10.1090/tran/7842. MR4029677.

9. On the Completion of the Mapping Class Group of Genus Two, Journal of Algebra 501 (2018), 303–327.
   

Preprints:

1. The section conjecture for generic pointed curves (with Ma Luo), arXiv:2610.24986 (2026).

2. Relative completions and separating boundary divisors in moduli of curves (with Ma Luo), arXiv:2610.04857 (2026).

3. On the universal curve with unordered marked points in positive characteristic (with Ma Luo), arXiv:2601.01336 (2026).

4. On the universal curves with unordered marked points (with Ma Luo), arXiv:2511.12354 (2025).

Work in Progress:

1. Monodromy of Divisors in Moduli Spaces of Curves in Positive Characteristic (with Ma Luo).

2. Sections of Universal Curves and the Torelli Birman Exact Sequence (with Ma Luo).

3. Relative Completion of the Mapping Class Group in Genus Two (with Ma Luo).

4. Algebraic Cycles and the Hyperelliptic Johnson Homomorphism (with Ma Luo).

Proceedings Papers:

1. アメリカの大学における数学教育について―一教員の視点から (Mathematics Education at American Universities: A Faculty Member's Perspective), RIMS Kôkyûroku 2351 (2026), 36–48. (In Japanese.)

2. Notes on the Abelianization of the Hyperelliptic Torelli Group, RIMS Kôkyûroku 2334 (2026).

3. Torelli Groups and Hyperelliptic Torelli Groups: Results and Open Problems, Proceedings of the 11th Exchange of Mathematical Ideas (2026).

4. On the Hyperelliptic Birman Exact Sequence, Proceedings of the 10th Exchange of Mathematical Ideas (2024).

5. The Birman Exact Sequence for the Hyperelliptic Mapping Class Group, RIMS Kôkyûroku 2291 (2024), paper no. 2.

6. The Geometry of the Hyperelliptic Torelli Group, Proceedings of the 9th Exchange of Mathematical Ideas (2023).

7. The Geometry of the Mapping Class Group, Proceedings of the 8th Exchange of Mathematical Ideas (2023).