Takumi Murayama
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Takumi Murayama

Office: East Hall 3068

I am currently a Ph.D. candidate, in my third year in the mathematics department at the University of Michigan. I am interested in algebraic geometry and commutative algebra. My advisor is Mircea Mustaţă. I was previously an undergraduate mathematics major at Princeton University, where my advisor was János Kollár.

Summer Mini-Courses 2017

I am organizing a series of summer mini-courses taught by graduate students in the mathematics department at Michigan. See the schedule.



  1. "Frobenius–Seshadri constants and characterizations of projective space." arXiv:1701.00511. Submitted.
  2. "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.
  3. "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.

Research Talks

  1. "Characterizations of projective space and Seshadri constants in arbitrary characteristic," Midwest Algebraic Geometry Graduate Conference at University of Illinois at Chicago, April 2017.
  2. "Using Linear Algebra to Classify Vector Bundles," Princeton University, May 2014.
  3. "Bounds for Geometric Invariants on Monomial Curves," with T. Duff and K. Schaefer at Berkeley-Stanford REU Joint Conference 2013, July 2013. Slides

Lecture Notes

I have been LiveTeX-ing some classes and seminars at Michigan, and am uploading them for other people to use. Matt Stevenson is LiveTeX-ing notes for Bhargav Bhatt's course on Perfectoid spaces.

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

Other Notes

  1. "D-modules and mixed Hodge modules." PDF (accessible for umich.edu e-mail addresses; e-mail me if you want a copy)
  2. "Continuous valuations and the adic spectrum," from a talk given in the arithmetic geometry learning seminar, February 16, 2017. PDF
  3. "Knot Theory and Problems on Affine Space," from a talk given in the Student Algebraic Geometry seminar, September 27, 2016. PDF
  4. "Ascent of finiteness of flat dimension," from a talk given in the Student Commutative Algebra seminar, February 9, 2016. PDF
  5. "Applications of local cohomology," from a talk given in the Student Commutative Algebra seminar, February 2, 2016. PDF
  6. "The classification of thick subcategories and Balmer's reconstruction theorem," final project for MATH613, Winter 2015. PDF
  7. "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
  8. "Using Grothendieck groups to define and relate the Hilbert and Chern polynomials axiomatically," final project for MATH631, Fall 2014. PDF
  9. "Fiber Bundles in Analytic, Zariski, and Étale Topologies," senior thesis, Spring 2014. PDF
  10. "An elementary proof of the classification of vector bundles on P1 and line bundles on Pn," Fall 2013. PDF
  11. "Counting exceptional curves on blowups of P2," Fall 2013. PDF
  12. "Free Resolutions and Hilbert Polynomials," from an expository talk given on July 4, 2013 at Berkeley. PDF
  13. "Orlov's Equivalence and Tensor Products," junior paper, Spring 2013. PDF
  14. "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

The schedule with notes is still available.