Takumi Murayama
Email: 

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 was (as of Fall 2018) on the job market for postdoctoral
positions. Here is a detailed description of
my research and my Curriculum Vitæ.
Teaching
 Math 115:
Fall 2014, Fall 2017.
 Math 116:
Winter 2015, Fall 2015, Winter 2016.
 Math 215:
Spring 2016.
 Math 631, 632 (grading): Fall 2015, Winter 2016, Winter 2017.
Research (also on arXiv)
 "Permanence properties of Finjectivity," coauthored with Rankeya
Datta.
arXiv:1906.11399.
 "Seshadri constants for vector bundles," coauthored with Mihai Fulger. Submitted. arXiv:1903.00610.
 "The gamma construction and asymptotic invariants of line bundles over
arbitrary fields." Submitted. arXiv:1809.01217.
 "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.
 "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.
 "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.
 "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/s0002601502883.
arXiv:1309.7630.
Thesis
Seshadri Constants and Fujita's Conjecture via Positive Characteristic
Methods.
arXiv:1905.03839.
Research Talks
 KUMUNUjr
2019, March 2019.
 Johns
Hopkins University Algebraic Geometry Seminar, March 2019.
 Northwestern
University Algebraic Geometry Seminar, January 2019.
 University
of Michigan Algebraic Geometry Seminar, December 2018.
 University
of Michigan Commutative Algebra Seminar, November 2018.
 Central
Michigan University Algebra and Combinatorics Seminar, November
2018.
 University of
Arkansas Algebra Seminar, November 2018.
 AMS Fall Southeastern Sectional Meeting 2018, Special
Session on Advances in Birational Geometry, November 2018.
 AMS Fall Central Sectional Meeting 2018, Special
Session on Multiplicities and Volumes: An Interplay Among Algebra,
Combinatorics, and Geometry, October 2018.
 University
of Illinois–Chicago Commutative Algebra Seminar, October
2018.
 Princeton
University Algebraic Geometry Seminar, February 2018.
 University of
Arkansas Algebra Seminar, November 2017.
 Tokyo
University Algebraic Geometry Seminar, November 2017.
 Nihon University
Singularities Seminar, November 2017.
 University of Utah
Algebraic Geometry Seminar, October 2017.
 University
of Connecticut Algebra Seminar, September 2017.
 Midwest
Algebraic Geometry Graduate Conference at University of Illinois at
Chicago, April 2017.
 Mathematics Department Open House, Princeton University, May
2014.
 Berkeley–Stanford REU Joint Conference, July 2013, with
T. Duff and
K. Schaefer.
Slides
Lecture Notes
I have been LiveTeXing some classes and seminars at Michigan, and am
uploading them for other people to use.
 Learning seminar on Drinfel'd modules, Fall 2017, organized by Bhargav
Bhatt and Andrew
Snowden. See the
seminar page.
 MATH732, Topics in Algebraic Geometry II: Rationality of Algebraic
Varieties, Winter 2017, taught by Mircea Mustaţă (see his
notes as well). PDF
 Learning seminar on Faltings's proof of the Mordell conjecture, Fall
2016, organized by Bhargav
Bhatt and Andrew
Snowden.
PDF
 MATH731, Topics in Algebraic Geometry: Berkovich Spaces, taught by Mattias Jonsson (see
course website).
PDF
 Learning seminar on Deligne's Weil II theorem, Summer 2016,
organized by Bhargav
Bhatt (see plan).
PDF
 MATH731, Topics in Algebraic Geometry: Perverse
Sheaves, taught by Bhargav
Bhatt (see course website). PDF
Other Notes
 "A characteristic zero proof of the lifting theorem via Seshadri
constants," May 11, 2019. PDF.
 "Test ideals for pairs via generalized tight closure," from a talk
given in the Singularities
reading group, November 1, 2018. PDF.
 "A short proof of the subadditivity theorem for test ideals," formerly
an appendix to arXiv:1809.01217,
September 2018.
PDF.
 "Fsingularities for nonFfinite rings," formerly
an appendix to arXiv:1809.01217,
August 2018.
PDF.
 "Fmodules and finiteness of associated primes," from talks
given in a reading seminar, January 29 and February 5, 2018. PDF.
 "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
 "Projectivity of moduli of curves," written with
Raymond Cheng,
Yordanka Kovacheva,
Carl Lian, and
Monica Marinescu,
with guidance from
Davesh Maulik,
from the
Stacks Project Workshop,
August 2017.
PDF
 "Dmodules and mixed Hodge modules," Fall 2016 and Winter
2017. PDF
 "Continuous valuations and the adic spectrum," from a talk given in
the arithmetic geometry learning seminar, February 16, 2017. PDF
 "Knot Theory and Problems on Affine Space," from a talk given in the
Student Algebraic Geometry seminar, September 27, 2016. PDF
 "The minimal model program," from a summer minicourse taught May
30–June 2, 2016. PDF
 "Ascent of finiteness of flat dimension," from a talk given in the Student
Commutative Algebra seminar, February 9, 2016. PDF
 "Applications of local cohomology," from a talk given in the Student
Commutative Algebra seminar, February 2, 2016. PDF
 "The classification of thick subcategories and Balmer's reconstruction
theorem," final project for MATH613, Winter 2015.
PDF
 "Finite generation of Kgroups of rings of integers in number
fields," from a talk given in the Ktheory
seminar on March 26 and April 3, 2015.
PDF
 "Using Grothendieck groups to define and relate the Hilbert and Chern
polynomials axiomatically," final project for MATH631, Fall 2014.
PDF
 "Fiber Bundles in Analytic, Zariski, and Étale Topologies," senior thesis, Spring 2014. PDF
 "An elementary proof of the classification of vector bundles on
P^{1} and line bundles on
P^{n}," Fall 2013. PDF
 "Counting exceptional curves on blowups of
P^{2}," Fall 2013.
PDF
 "Free Resolutions and Hilbert Polynomials," from an expository talk given on July 4, 2013 at Berkeley. PDF
 "Orlov's Equivalence and Tensor Products," junior paper, Spring 2013. PDF
 "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 MiniCourses 2016 and 2017
I have been organizing series of summer minicourses taught by graduate
students in the mathematics department at Michigan. Schedules with notes for
past series are still available: see 2016
and 2017.