Takumi Murayama
      drinking Mariage Frères

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Takumi Murayama

Office: Fine Hall 310

I am currently a Postdoctoral Research Fellow at Princeton University, funded by the National Science Foundation. My mentor is János Kollár.

I am interested in algebraic geometry and commutative algebra, especially in positive characteristic.

I was previously a Ph.D. student at the University of Michigan, where my advisor was Mircea Mustaţă.


  1. 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.
  2. eCARs: Early Commutative Algebra Researchers (co-organized with Alessandra Costantini and Kyle Maddox). On Zoom, June 27–28, 2020.

Teaching (at Princeton University)

Teaching (at the University of Michigan)

Research (also on arXiv or MathSciNet)

  1. "Excellence, F-singularities, and solidity," coauthored with R. Datta, with an appendix by Karen E. Smith. arXiv:2007.10383.
  2. "A uniform treatment of Grothendieck's localization problem." Submitted. arXiv:2004.06737.
  3. "Tate algebras and Frobenius non-splitting of excellent regular rings," coauthored with R. Datta. Submitted. arXiv:2003.13714.
  4. "Permanence properties of F-injectivity," coauthored with R. Datta. Submitted. arXiv:1906.11399.
  5. "Seshadri constants for vector bundles," coauthored with M. Fulger. To appear in Journal of Pure and Applied Algebra. doi: 10.1016/j.jpaa.2020.106559. arXiv:1903.00610.
  6. "The gamma construction and asymptotic invariants of line bundles over arbitrary fields." To appear in Nagoya Mathematical Journal. doi: 10.1017/nmj.2019.27. arXiv:1809.01217.
  7. "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.
  8. "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.
  9. "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.
  10. "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.


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.

Research Talks

  1. Fellowship of the Ring, October 2020.
  2. AMS Fall Eastern Sectional Meeting 2020 formerly at Pennsylvania State University, Special Session on Geometry and Arithmetic of Algebraic Varieties, October 2020.
  3. Experimental Talks in AG, June 2020. Worksheet.
  4. Joint NU/UIC/UofC algebraic geometry and commutative algebra seminar, June 2020. Notes.
  5. Morgantown Algebra Days 2020, West Virginia University, April 2020 (canceled due to COVID-19).
  6. University of California, Berkeley Commutative Algebra and Algebraic Geometry Seminar, January 2020.
  7. Pennsylvania State University Algebra and Number Theory Seminar, December 2019.
  8. Purdue University Commutative Algebra Seminar, December 2019.
  9. École Polytechnique Fédérale de Lausanne Groups, Arithmetic and Algebraic Geometry Seminar, November 2019.
  10. Mini-Workshop: Seshadri Constants, Mathematisches Forschungsinstitut Oberwolfach, November 2019.
  11. University of Connecticut Algebra Seminar, October 2019.
  12. Yale University Algebraic and Tropical Geometry Seminar, October 2019.
  13. Princeton University Algebraic Geometry Seminar, October 2019.
  14. Princeton University New Faculty Talks, October 2019.
  15. KUMUNUjr 2019, University of Nebraska–Lincoln, March 2019.
  16. Johns Hopkins University Algebraic Geometry Seminar, March 2019.
  17. Northwestern University Algebraic Geometry Seminar, January 2019.
  18. University of Michigan Algebraic Geometry Seminar, December 2018.
  19. University of Michigan Commutative Algebra Seminar, November 2018.
  20. Central Michigan University Algebra and Combinatorics Seminar, November 2018.
  21. University of Arkansas Algebra Seminar, November 2018.
  22. AMS Fall Southeastern Sectional Meeting 2018 at the University of Arkansas, Special Session on Advances in Birational Geometry, November 2018.
  23. 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.
  24. University of Illinois–Chicago Commutative Algebra Seminar, October 2018.
  25. Princeton University Algebraic Geometry Seminar, February 2018.
  26. University of Arkansas Algebra Seminar, November 2017.
  27. Tokyo University Algebraic Geometry Seminar, November 2017.
  28. Nihon University Singularities Seminar, November 2017.
  29. University of Utah Algebraic Geometry Seminar, October 2017.
  30. University of Connecticut Algebra Seminar, September 2017.
  31. Midwest Algebraic Geometry Graduate Conference, University of Illinois–Chicago, April 2017.
  32. Mathematics Department Open House, Princeton University, May 2014.
  33. 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. "F-purity and Frobenius splitting do not coincide in rigid analytic geometry," from a talk given June 3, 2020. PDF
  2. "The property of being Japanese (aka N-2) is not local," written with R. Datta, February 22, 2020. PDF.
  3. "A characteristic zero proof of the lifting theorem via Seshadri constants," May 11, 2019. PDF.
  4. "Test ideals for pairs via generalized tight closure," from a talk given in the Singularities reading group, November 1, 2018. PDF.
  5. "A short proof of the subadditivity theorem for test ideals," formerly an appendix to arXiv:1809.01217, September 2018. PDF.
  6. "F-singularities for non-F-finite rings," formerly an appendix to arXiv:1809.01217, August 2018. PDF.
  7. "F-modules and finiteness of associated primes," from talks given in a reading seminar, January 29 and February 5, 2018. PDF.
  8. "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
  9. "Projectivity of moduli of curves," written with R. Cheng, Y. Kovacheva, C. Lian, and M. Marinescu, with guidance from D. Maulik, from the Stacks Project Workshop, August 2017. PDF
  10. "D-modules and mixed Hodge modules," Fall 2016 and Winter 2017. PDF
  11. "Continuous valuations and the adic spectrum," from a talk given in the arithmetic geometry learning seminar, February 16, 2017. PDF
  12. "Knot Theory and Problems on Affine Space," from a talk given in the Student Algebraic Geometry seminar, September 27, 2016. PDF
  13. "The minimal model program," from a summer mini-course taught May 30–June 2, 2016. PDF
  14. "Ascent of finiteness of flat dimension," from a talk given in the Student Commutative Algebra seminar, February 9, 2016. PDF
  15. "Applications of local cohomology," from a talk given in the Student Commutative Algebra seminar, February 2, 2016. PDF
  16. "The classification of thick subcategories and Balmer's reconstruction theorem," final project for MATH613, Winter 2015. PDF
  17. "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
  18. "Using Grothendieck groups to define and relate the Hilbert and Chern polynomials axiomatically," final project for MATH631, Fall 2014. PDF
  19. "Fiber Bundles in Analytic, Zariski, and Étale Topologies," senior thesis, Spring 2014. PDF
  20. "An elementary proof of the classification of vector bundles on P1 and line bundles on Pn," Fall 2013. PDF
  21. "Counting exceptional curves on blowups of P2," Fall 2013. PDF
  22. "Free Resolutions and Hilbert Polynomials," from an expository talk given on July 4, 2013 at Berkeley. PDF
  23. "Orlov's Equivalence and Tensor Products," junior paper, Spring 2013. PDF
  24. "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.