Takumi Murayama
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Takumi Murayama

E-mail:
Office: East Hall 3068

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

I am currently (as of Fall 2018) on the job market for postdoctoral positions. Here is a detailed description of my research and my Curriculum Vitæ.

Teaching

Research (also on arXiv)

  1. "The gamma construction and asymptotic invariants of line bundles over arbitrary fields." arXiv:1809.01217. Submitted.
  2. "Effective generation and twisted weak positivity of direct images," coauthored with Y. Dutta. arXiv:1712.08723. Submitted.
  3. "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.
  4. "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.
  5. "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. University of Michigan Algebraic Geometry Seminar, December 2018.
  2. University of Michigan Commutative Algebra Seminar, November 2018.
  3. Central Michigan University Algebra and Combinatorics Seminar, November 2018.
  4. University of Arkansas Algebra Seminar, November 2018.
  5. AMS Fall Southeastern Sectional Meeting 2018, Special Session on Advances in Birational Geometry, November 2018.
  6. AMS Fall Central Sectional Meeting 2018, Special Session on Multiplicities and Volumes: An Interplay Among Algebra, Combinatorics, and Geometry, October 2018.
  7. University of Illinois–Chicago Commutative Algebra Seminar, October 2018.
  8. Princeton University Algebraic Geometry Seminar, February 2018.
  9. University of Arkansas Algebra Seminar, November 2017.
  10. Tokyo University Algebraic Geometry Seminar, November 2017.
  11. Nihon University Singularities Seminar, November 2017.
  12. University of Utah Algebraic Geometry Seminar, October 2017.
  13. University of Connecticut Algebra Seminar, September 2017.
  14. Midwest Algebraic Geometry Graduate Conference at University of Illinois at Chicago, April 2017.
  15. Mathematics Department Open House, Princeton University, May 2014.
  16. Berkeley-Stanford REU Joint Conference, July 2013, with T. Duff and K. Schaefer. Slides

Lecture Notes

I have been LiveTeX-ing some classes and seminars at Michigan, and am uploading 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. "Test ideals for pairs via generalized tight closure," from a talk given in the Singularities reading group, November 1, 2018. PDF.
  2. "A short proof of the subadditivity theorem for test ideals," formerly an appendix to arXiv:1809.01217, September 2018. PDF.
  3. "F-singularities for non-F-finite rings," formerly an appendix to arXiv:1809.01217, August 2018. PDF.
  4. "F-modules and finiteness of associated primes," from talks given in a reading seminar, January 29 and February 5, 2018. PDF.
  5. "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
  6. "D-modules and mixed Hodge modules," Fall 2016 and Winter 2017. PDF
  7. "Continuous valuations and the adic spectrum," from a talk given in the arithmetic geometry learning seminar, February 16, 2017. PDF
  8. "Knot Theory and Problems on Affine Space," from a talk given in the Student Algebraic Geometry seminar, September 27, 2016. PDF
  9. "Ascent of finiteness of flat dimension," from a talk given in the Student Commutative Algebra seminar, February 9, 2016. PDF
  10. "Applications of local cohomology," from a talk given in the Student Commutative Algebra seminar, February 2, 2016. PDF
  11. "The classification of thick subcategories and Balmer's reconstruction theorem," final project for MATH613, Winter 2015. PDF
  12. "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
  13. "Using Grothendieck groups to define and relate the Hilbert and Chern polynomials axiomatically," final project for MATH631, Fall 2014. PDF
  14. "Fiber Bundles in Analytic, Zariski, and Étale Topologies," senior thesis, Spring 2014. PDF
  15. "An elementary proof of the classification of vector bundles on P1 and line bundles on Pn," Fall 2013. PDF
  16. "Counting exceptional curves on blowups of P2," Fall 2013. PDF
  17. "Free Resolutions and Hilbert Polynomials," from an expository talk given on July 4, 2013 at Berkeley. PDF
  18. "Orlov's Equivalence and Tensor Products," junior paper, Spring 2013. PDF
  19. "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 have been organizing 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.