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 Deepam Patel and Yilong Zhang.

Teaching (at Purdue University)

• MA 26500 Linear Algebra and its Applications: Spring 2023, Fall 2023.
• MA 34100 Foundations of Analysis: Fall 2022.

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.

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. "The relative minimal model program for excellent algebraic spaces and analytic spaces in equal characteristic zero," coauthored with S. Lyu. arXiv:2209.08732.
2. "Pure subrings of Du Bois singularities are Du Bois singularities," coauthored with C. Godfrey. arXiv:2208.14429.
3. "Variants of normality and steadfastness deform," coauthored with A. Bauman, H. Ellers, G. Hu, S. Nair, and Y. Wang. To appear in Michigan Mathematical Journal. doi: 10.1307/mmj/20226231. arXiv:2202.00163.
4. "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.
5. "Uniform bounds on symbolic powers in regular rings." arXiv:2111.06049.
6. "Relative vanishing theorems for Q-schemes." arXiv:2101.10397.
7. "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.
8. "Excellence, F-singularities, and solidity," coauthored with R. Datta, with an appendix by K. E. Smith. arXiv:2007.10383.
9. "A uniform treatment of Grothendieck's localization problem." Compositio Mathematica 158.1 (2022), pp. 57–88. doi: 10.1112/S0010437X21007715. arXiv:2004.06737.
10. "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.
11. "Permanence properties of F-injectivity," coauthored with R. Datta. To appear in Mathematical Research Letters. arXiv:1906.11399.
12. "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.
13. "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.
14. "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.
15. "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.
16. "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.
17. "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.
Corrected version: PDF or PDF of only corrections.

Organization

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

Lecture Notes

I LiveTeXed some classes and seminars at Michigan, and uploaded them for other people to use.

1. Learning seminar on Drinfel'd modules, Fall 2017, organized by Bhargav Bhatt and Andrew Snowden. See the seminar page.
2. MATH732, Topics in Algebraic Geometry II: Rationality of Algebraic Varieties, Winter 2017, taught by Mircea Mustaţă (see his notes as well). PDF
3. Learning seminar on Faltings's proof of the Mordell conjecture, Fall 2016, organized by Bhargav Bhatt and Andrew Snowden. PDF
4. MATH731, Topics in Algebraic Geometry: Berkovich Spaces, taught by Mattias Jonsson (see course website). PDF
5. Learning seminar on Deligne's Weil II theorem, Summer 2016, organized by Bhargav Bhatt (see plan). PDF
6. MATH731, Topics in Algebraic Geometry: Perverse Sheaves, taught by Bhargav Bhatt (see course website). PDF

Other Notes

1. "The property of being Japanese (aka N-2) is not local," written with R. Datta, February 22, 2020. PDF.
2. "A characteristic zero proof of the lifting theorem via Seshadri constants," May 11, 2019. PDF.
3. "Test ideals for pairs via generalized tight closure," from a talk given in the Singularities reading group, November 1, 2018. PDF.
4. "A short proof of the subadditivity theorem for test ideals," formerly an appendix to arXiv:1809.01217, September 2018. Now incorporated into my Ph.D. thesis as Theorem 5.5.8. PDF.
5. "F-singularities for non-F-finite rings," formerly an appendix to arXiv:1809.01217, August 2018. Now incorporated into my Ph.D. thesis as Appendix A. PDF.
6. "F-modules and finiteness of associated primes," from talks given in a reading seminar, January 29 and February 5, 2018. PDF.
7. "Poincaré homology spheres and exotic spheres from links of hypersurface singularities," from a talk given in the Student Algebraic Geometry seminar, September 22, 2017. PDF
8. "D-modules and mixed Hodge modules," Fall 2016 and Winter 2017. PDF
9. "Continuous valuations and the adic spectrum," from a talk given in the arithmetic geometry learning seminar, February 16, 2017. PDF
10. "Knot Theory and Problems on Affine Space," from a talk given in the Student Algebraic Geometry seminar, September 27, 2016. PDF
11. "The minimal model program," from a summer mini-course taught May 30–June 2, 2016. PDF
12. "Ascent of finiteness of flat dimension," from a talk given in the Student Commutative Algebra seminar, February 9, 2016. PDF
13. "Applications of local cohomology," from a talk given in the Student Commutative Algebra seminar, February 2, 2016. PDF
14. "The classification of thick subcategories and Balmer's reconstruction theorem," final project for MATH613, Winter 2015. PDF
15. "Finite generation of K-groups of rings of integers in number fields," from a talk given in the K-theory seminar on March 26 and April 3, 2015. PDF
16. "Using Grothendieck groups to define and relate the Hilbert and Chern polynomials axiomatically," final project for MATH631, Fall 2014. PDF
17. "Fiber Bundles in Analytic, Zariski, and Étale Topologies," senior thesis, Spring 2014. PDF
18. "An elementary proof of the classification of vector bundles on P¹ and line bundles on Pⁿ," Fall 2013. PDF
19. "Counting exceptional curves on blowups of P²," Fall 2013. PDF
20. "Free Resolutions and Hilbert Polynomials," from an expository talk given on July 4, 2013 at Berkeley. PDF
21. "Orlov's Equivalence and Tensor Products," junior paper, Spring 2013. PDF
22. "Maximal Tori and the Weyl Integration Formula," expository paper for Junior Seminar on "Lie Groups, Lie Algebras, and their Representations" at Princeton, Fall 2012. PDF

Summer Mini-Courses 2016 and 2017

I organized series of summer mini-courses taught by graduate students in the mathematics department at Michigan. Schedules with notes for past series are still available: see 2016 and 2017.

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.