Takumi Murayama
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Takumi Murayama

Office: East Hall 2852

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

I am the organizer for graduate student-run summer mini-courses in the mathematics department at Michigan for 2017. We are currently in the process of proposing possible courses; e-mail me if you want to be involved.

I was also the organizer for the summer of 2016. The schedule is still accessible, and contains links to notes for some of the mini-courses.


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 LiveTeXing 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. 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


  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. "Bounds for Geometric Invariants on Monomial Curves," with T. Duff and K. Schaefer at Berkeley-Stanford REU Joint Conference 2013, July 2013.


  1. "Continuous valuations and the adic spectrum," from a talk given in the arithmetic geometry learning seminar, February 16, 2017. PDF
  2. "Ascent of finiteness of flat dimension," from a talk given in the Student Commutative Algebra seminar, February 9, 2016. PDF
  3. "Applications of local cohomology," from a talk given in the Student Commutative Algebra seminar, February 2, 2016. PDF
  4. "The classification of thick subcategories and Balmer's reconstruction theorem," final project for MATH613, Winter 2015. PDF
  5. "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
  6. "Using Grothendieck groups to define and relate the Hilbert and Chern polynomials axiomatically," final project for MATH631, Fall 2014. PDF
  7. "Fiber Bundles in Analytic, Zariski, and Étale Topologies," senior thesis, Spring 2014. PDF
  8. "An elementary proof of the classification of vector bundles on P1 and line bundles on Pn," Fall 2013. PDF
  9. "Counting exceptional curves on blowups of P2," Fall 2013. PDF
  10. "Free Resolutions and Hilbert Polynomials," from an expository talk given on July 4, 2013 at Berkeley. PDF
  11. "Orlov's Equivalence and Tensor Products," junior paper, Spring 2013. PDF
  12. "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