Takumi Murayama
Email: 

Office: 
East Hall 3068 
I am currently a Ph.D. candidate, in my fourth 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.
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
 "Frobenius–Seshadri constants and characterizations of projective
space." arXiv:1701.00511.
Accepted to Mathematical Research Letters.
 "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.
Research Talks
 "Characterizations of projective space and Seshadri constants in
arbitrary characteristic,"
University of
Arkansas Algebra Seminar, November 2017.
 "Characterizations of projective space and Seshadri constants in
arbitrary characteristic," Tokyo
University Algebraic Geometry Seminar, November 2017.
 "Seshadri constants and separation of jets on singular varieties,"
Nihon University
Singularities Seminar, November 2017.
 "Characterizations of projective space and Seshadri constants in
arbitrary characteristic," University of Utah
Algebraic Geometry Seminar, October 2017.
 "Characterizations of projective space and Seshadri constants in
positive characteristic," University
of Connecticut Algebra Seminar, September 2017.
 "Characterizations of projective space and Seshadri constants in
arbitrary characteristic," Midwest
Algebraic Geometry Graduate Conference at University of Illinois at
Chicago, April 2017.
 "Using Linear Algebra to Classify Vector Bundles," Princeton
University, May 2014.
 "Bounds for Geometric Invariants on Monomial Curves," with T. Duff and
K. Schaefer at BerkeleyStanford REU Joint Conference, July 2013.
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
 "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
 "Dmodules and mixed Hodge modules." PDF (accessible for umich.edu
email addresses; email me if you want a copy)
 "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
 "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.