Takumi Murayama

I am currently an Assistant Professor at Purdue University.

I am interested in algebraic geometry and commutative algebra, especially birational geometry and the study of singularities in all characteristics.

I am currently co-organizing the Purdue Algebraic Geometry Seminar with Donu Arapura, Zhiyuan Jiang, Shubhodip Mondal, Deepam Patel, and Jaroslaw Wlodarczyk.

I am mentoring a postdoc, Zhiyuan Jiang, starting Fall 2025.

Current Teaching (at Purdue University)

• MA 665 Algebraic Geometry II: Spring 2026. Notes.

Past Teaching (at Purdue University)

• MA 557 Commutative Algebra: Fall 2024.
• MA 595AG Algebraic Geometry I: Fall 2024.
• MA 595AGI Algebraic Geometry I: Fall 2025.
• MA 665 Algebraic Geometry II: Spring 2025.
• MA 265 Linear Algebra and its Applications: Spring 2023, Fall 2023.
• MA 351 Elementary Linear Algebra: Fall 2025.
• MA 341 Foundations of Analysis: Fall 2022.

Past Teaching (at Princeton University)

• MAT 100 Foundations of Calculus: Spring 2021.
• MAT 202 Linear Algebra with Applications: Fall 2021.
• MAT 217 Honors Linear Algebra (preceptor): Spring 2022.
• MAT 447 Commutative Algebra: Fall 2020.

Past Teaching (at the University of Michigan)

• Math 115 Calculus I: Fall 2014, Fall 2017.
• Math 116 Calculus II: Winter 2015, Fall 2015, Winter 2016.
• Math 215 Calculus III (teaching assistant): Spring 2016.
• Michigan Math and Science Scholars "Art and Mathematics" and "Mathematics of Cryptography" (course assistant): Summer 2019.

Research (also on arXiv, MathSciNet, zbMATH, ORCID, or Google Scholar)

1. "Equidimensional morphisms onto splinters are pure." arXiv:2512.15563.
2. "Finiteness of associated primes for local cohomology modules of excellent locally unramified regular rings of finite Krull dimension." arXiv:2506.17875.
3. "Effective Fujita-type theorems for surfaces in arbitrary characteristic." arXiv:2408.06530.
4. "Injectivity theorems and cubical descent for schemes, stacks, and analytic spaces." arXiv:2406.10800.
5. "The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero," coauthored with S. Lyu. To appear in Memoirs of the European Mathematical Society. arXiv:2209.08732.
6. "Pure subrings of Du Bois singularities are Du Bois singularities," coauthored with C. Godfrey. arXiv:2208.14429.
7. "Variants of normality and steadfastness deform," coauthored with A. Bauman, H. Ellers, G. Hu, S. Nair, and Y. Wang. Michigan Mathematical Journal 75.1 (2025), pp. 145–172. doi: 10.1307/mmj/20226231. arXiv:2202.00163.
8. "Rational linear subspaces of hypersurfaces over finite fields," coauthored with M. I. de Frutos Fernández, S. Garai, K. Isham, and G. Smith. arXiv:2111.10976.
9. "Uniform bounds on symbolic powers in regular rings." arXiv:2111.06049. To appear in Journal für die reine und angewandte Mathematik.
10. "Relative vanishing theorems for Q-schemes." Algebraic Geometry 12.1 (2025), pp. 84–144. doi: 10.10.14231/AG-2025-003. arXiv:2101.10397.
11. "New constructions of nef classes on self-products of curves," coauthored with M. Fulger. Mathematische Zeitschrift 302.2 (2022), pp. 1239–1265. doi: 10.1007/s00209-022-03092-7. arXiv:2101.09827.
12. "Excellence, F-singularities, and solidity," coauthored with R. Datta, with an appendix by K. E. Smith. arXiv:2007.10383.
13. "A uniform treatment of Grothendieck's localization problem." Compositio Mathematica 158.1 (2022), pp. 57–88. doi: 10.1112/S0010437X21007715. arXiv:2004.06737.
14. "Tate algebras and Frobenius non-splitting of excellent regular rings," coauthored with R. Datta. Journal of the European Mathematical Society (JEMS) 25.11 (2023), pp. 4291–4314. doi: 10.4171/JEMS/1259. arXiv:2003.13714.
15. "Permanence properties of F-injectivity," coauthored with R. Datta. Mathematical Research Letters 31.4 (2024), pp. 985–1027. doi: 10.4310/MRL.241118233550. arXiv:1906.11399.
16. "Seshadri constants for vector bundles," coauthored with M. Fulger. Journal of Pure and Applied Algebra 225.4 (2021), Paper No. 106559, 35 pp. doi: 10.1016/j.jpaa.2020.106559. arXiv:1903.00610.
17. "The gamma construction and asymptotic invariants of line bundles over arbitrary fields." Nagoya Mathematical Journal 242 (2021), pp. 165–207. doi: 10.1017/nmj.2019.27. arXiv:1809.01217.
18. "Effective generation and twisted weak positivity of direct images," coauthored with Y. Dutta. Algebra & Number Theory 13.2 (2019), pp. 425–454. doi: 10.2140/ant.2019.13.425. arXiv:1712.08723.
19. "Frobenius–Seshadri constants and characterizations of projective space." Mathematical Research Letters 25.3 (2018), pp. 905–936. doi: 10.4310/MRL.2018.v25.n3.a9. arXiv:1701.00511.
20. "Dilated Floor Functions That Commute," coauthored with J. C. Lagarias and D. H. Richman. American Mathematical Monthly 123.10 (2016), pp. 1033–1038. doi: 10.4169/amer.math.monthly.123.10.1033. arXiv:1611.05513.
21. "Robust Graph Ideals," coauthored with A. Boocher, B. C. Brown, T. Duff, L. Lyman, A. Nesky, and K. Schaefer. Annals of Combinatorics 19.4 (2015), pp. 641–660. doi: 120.1007/s00026-015-0288-3. arXiv:1309.7630.

Other Writing

1. "Closure-theoretic proofs of uniform bounds on symbolic powers in regular rings." arXiv:2205.01153. Now incorporated into "Uniform bounds on symbolic powers in regular rings."
2. "Projectivity of the moduli of curves," coauthored with R. Cheng and C. Lian, in collaboration with Y. Kovacheva and M. Marinescu. Stacks Project Expository Collection (SPEC). London Mathematical Society Lecture Note Series, Vol. 480. Cambridge: Cambridge University Press, 2022, pp. 1–43. doi: 10.1017/9781009051897.003.

Thesis

Seshadri Constants and Fujita's Conjecture via Positive Characteristic Methods. arXiv:1905.03839.

Published version: http://hdl.handle.net/2027.42/149842 or https://search.proquest.com/docview/2273364341.

Organization

1. Purdue University Algebraic Geometry Seminar (co-organized with Donu Arapura, Zhiyuan Jiang, Shubhodip Mondal, Deepam Patel, Jaroslaw Wlodarczyk, and (for 2023–2025) Yilong Zhang). Fall 2022–.
2. AMS Fall Eastern Sectional Meeting 2020, Special Session on Algebraic Singularities in Arbitrary Characteristic (co-organized with Rankeya Datta). On Zoom, October 3–4, 2020.
3. eCARs: Early Commutative Algebra Researchers (co-organized with Alessandra Costantini and Kyle Maddox). On Zoom, June 27–28, 2020.

Research Talks

1. University of Missouri Algebra Seminar, March 2026.
2. Purdue University Algebraic Geometry Seminar, August 2025.
3. AMS 2025 Spring Central Sectional Meeting at the University of Kansas, Special Session on Interplay between birational geometry, complex geometry and Hodge theory, March 2025.
4. Cornell University Algebra Seminar, October 2024.
5. Kyoto University Algebraic Geometry Seminar, March 2024.
6. University of Notre Dame Algebraic Geometry/Commutative Algebra Seminar, March 2024.
7. University of Arizona Algebraic Geometry Seminar, February 2024.
8. Purdue University Commutative Algebra Seminar, October 2023.
9. University of Michigan Algebraic Geometry Seminar, October 2023.
10. Purdue University Algebraic Geometry Seminar, October 2023.
11. Recent Trends in Algebraic Geometry, Mathematisches Forschungsinstitut Oberwolfach, June 2023. Report doi: 10.14760/OWR-2023-27.
12. MPS Conference on Higher Dimensional Geometry, Simons Center, May 2023.
13. Morgantown Algebra Days 2023, West Virginia University, April 2023.
14. IIT Bombay Virtual Commutative Algebra Seminar, March 2023.
15. University of Utah Algebraic Geometry Seminar, February 2023.
16. Tsinghua University Algebraic Geometry Seminar, December 2022.
17. Tokyo University Algebraic Geometry Seminar, December 2022.
18. Purdue University Commutative Algebra Seminar, November 2022.
19. University of Illinois–Chicago Algebraic Geometry Seminar, October 2022.
20. Purdue University Algebraic Geometry Seminar, September 2022.
21. Seminar at Waseda University, May 2022.
22. AMS Spring Central Sectional Meeting 2022 formerly at Purdue University, Special Session on Recent Developments in Commutative Algebra, March 2022.
23. Commutative and Homological Algebra Market Presentations, January 2022.
24. Zoom Algebraic Geometry Seminar, January 2022. Report doi: 10.1201/9781003286363.
25. University of Illinois–Chicago Algebraic Geometry Seminar, October 2021.
26. Tokyo University/Kyoto University, Joint Algebraic Geometry Seminar, May 2021.
27. City University of New York Commutative Algebra & Algebraic Geometry Seminar, March 2021.
28. Princeton University Algebraic Geometry Seminar, March 2021.
29. Stony Brook University Algebraic Geometry Seminar, February 2021.
30. Stanford University Algebraic Geometry Seminar, January 2021.
31. Fellowship of the Ring, October 2020.
32. AMS Fall Eastern Sectional Meeting 2020 formerly at Pennsylvania State University, Special Session on Geometry and Arithmetic of Algebraic Varieties, October 2020.
33. Experimental Talks in AG, June 2020.
34. Joint NU/UIC/UofC algebraic geometry and commutative algebra seminar, June 2020.
35. University of California, Berkeley Commutative Algebra and Algebraic Geometry Seminar, January 2020.
36. Pennsylvania State University Algebra and Number Theory Seminar, December 2019.
37. Purdue University Commutative Algebra Seminar, December 2019.
38. École Polytechnique Fédérale de Lausanne Groups, Arithmetic and Algebraic Geometry Seminar, November 2019.
39. Mini-Workshop: Seshadri Constants, Mathematisches Forschungsinstitut Oberwolfach, November 2019. Report doi: 10.14760/OWR-2019-53.
40. University of Connecticut Algebra Seminar, October 2019.
41. Yale University Algebraic and Tropical Geometry Seminar, October 2019.
42. Princeton University Algebraic Geometry Seminar, October 2019.
43. Princeton University New Faculty Talks, October 2019.
44. KUMUNUjr 2019, University of Nebraska–Lincoln, March 2019.
45. Johns Hopkins University Algebraic Geometry Seminar, March 2019.
46. Northwestern University Algebraic Geometry Seminar, January 2019.
47. University of Michigan Algebraic Geometry Seminar, December 2018.
48. University of Michigan Commutative Algebra Seminar, November 2018.
49. Central Michigan University Algebra and Combinatorics Seminar, November 2018.
50. University of Arkansas Algebra Seminar, November 2018.
51. AMS Fall Southeastern Sectional Meeting 2018 at the University of Arkansas, Special Session on Advances in Birational Geometry, November 2018.
52. AMS Fall Central Sectional Meeting 2018 at the University of Michigan, Special Session on Multiplicities and Volumes: An Interplay Among Algebra, Combinatorics, and Geometry, October 2018.
53. University of Illinois–Chicago Commutative Algebra Seminar, October 2018.
54. Princeton University Algebraic Geometry Seminar, February 2018.
55. University of Arkansas Algebra Seminar, November 2017.
56. Tokyo University Algebraic Geometry Seminar, November 2017.
57. Nihon University Singularities Seminar, November 2017.
58. University of Utah Algebraic Geometry Seminar, October 2017.
59. University of Connecticut Algebra Seminar, September 2017.
60. Midwest Algebraic Geometry Graduate Conference, University of Illinois–Chicago, April 2017.
61. Mathematics Department Open House, Princeton University, May 2014.
62. Berkeley–Stanford REU Joint Conference, Stanford University, July 2013, with T. Duff and K. Schaefer.

Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.