Tatsunari Watanabe

Associate Professor

Tatsunari.Watanabe@erau.edu

Mathematics Department

Prescott College of Arts & Sciences

Areas of Expertise

Algebraic Geometry

Topology

Number Theory

Tatsunari Watanabe

Overview

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.

Ph.D. - Doctor of Philosophy in Mathematics, Duke University

B.A. - Bachelor of Arts in Mathematics, University of California-Berkeley

A.S. - Associate of Science in Mathematics, Foothill College

  1. Golomb Visiting Assistant Professor of Mathematics,  Purdue University, 08/2015 – 05/2018
  1. AMS
  2. MAA
  1. College of Arts and Sciences Teacher of the Year Award, ERAU-Prescott, 2023
  2. College of Arts and Sciences Commencement Class Marshal, ERAU-Prescott, Spring 2022
  3. Dorothea Klumpke Roberts Prize, University of California, Berkeley, 2009
  4. Highest Honors, University of California, Berkeley, 2009
  5. Phi Beta Kappa, University of California, Berkeley, 2009

Teaching

  • MATH 242: Calculus & Analytical Geom II
  • MATH 243: Calculus & Anyl Geometry III
  • MA 335: Intro Linear/Abstract Algebra
  • MA 441: Math Methods Engr & Physics I
  • MATH 441: Math Methods Engr & Physics I
  • MATH 399: ST in Mathematics

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

MWF: 11AM - 1PM, Tu: 1:30PM - 2:40 PM

Research

Published Papers:

  1. T. Watanabe, Remarks on the Sections of Universal Hyperelliptic Curves, Journal of Algebra, Volume 683, 2025, Pages 761-802, ISSN 0021-8693, https://doi.org/10.1016/j.jalgebra.2025.06.040.
  2. T. Watanabe, Nonabelian Cohomology of Universal Curves in Positive Characteristic, Proc. Amer. Math. Soc. 152 (2024), no. 1, 89–103, https://doi.org/10.1090/proc/16542.
  3. M. Luo, T. Watanabe, Remarks on Collino Cycles and Hyperelliptic Johnson Homomorphisms, J. Algebra, Volume 649 (2024), 96-132, ISSN 0021-8693, https://doi.org/10.1016/j.jalgebra.2024.02.038.
  4.  T. Watanabe, Remarks on Rational Points of Universal Curves. Proc. Amer. Math. Soc. 148 (2020),no. 9, 3761–3773, DOI 10.1090/proc/15008. MR4127823.

  5. T. Watanabe, On the Sections of Universal Hyperelliptic Curves, J. Algebra Volume 533 (2019), 44–89, DOI 10.1016/j.jalgebra.2019.05.023. MR3961806.

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

  7. T. Watanabe, On the Completion of the Mapping Class Group of Genus Two, J. Algebra, Volume 501 (2018), 303-327.

Preprints:

  1. M. Luo, T. Watanabe, On the Universal Curve with Unordered Marked Points in Positive Characteristic, arXiv:2601.01336
  2. M. Luo, T. Watanabe, On the Universal Curves with Unordered Marked Points, arXiv:2511.12354
  3. M. Luo, T. Watanabe, On the Birman Exact Sequence for Subgroups of the Mapping Class Group of Genus Three, arXiv:2502.14343

Proceedings Papers:

  1. T. Watanabe, Notes on the abelianization of the Hyperelliptic Torelli Group, RIMS Kôkyûroku No. No.2334, 2026.
  2. T. Watanabe, Torelli Groups and Hyperelliptic Torelli Groups: Results and Open Problems, Proceedings of the 11th Exchange of Mathematical Ideas, 2026
  3. T. Watanabe, On the hyperelliptic Birman exact sequence, Proceedings of the 10th Exchange of Mathematical Ideas, 2024
  4. T. Watanabe, The Birman exact sequence for the hyperelliptic mapping class group, RIMS Kôkyûroku No. 2291-02, 2024.
  5. T. Watanabe, The Geometry of the Hyperelliptic Torelli Group, Proceedings of the 9th Exchange of Mathematical Ideas, 2023
  6. T. Watanabe, The Geometry of the Mapping Class Group, Proceedings of the 8th Exchange of Mathematical Ideas, 2023.