Takumi Murayama
I am currently an Assistant Professor at Purdue University.
I am interested in algebraic geometry and commutative
algebra, especially
birational geometry and the study of singularities in all characteristics.
I am currently coorganizing the Purdue Algebraic Geometry Seminar
with Deepam Patel and
Yilong Zhang.
Teaching (at Purdue University)
 MA 26500 Linear Algebra and its Applications:
Spring 2023, Fall 2023.
 MA 34100 Foundations of Analysis: Fall 2022.
Teaching (at Princeton University)
 MAT 100 Foundations of Calculus: Spring 2021.
 MAT 202 Linear Algebra with Applications: Fall 2021.
 MAT 217 Honors Linear Algebra (preceptor): Spring 2022.
 MAT 447 Commutative Algebra: Fall 2020.
Teaching (at the University of Michigan)
 "The relative minimal model program for excellent algebraic spaces and
analytic spaces in equal characteristic zero," coauthored
with S. Lyu.
arXiv:2209.08732.
 "Pure subrings of Du Bois singularities are Du Bois singularities,"
coauthored with C. Godfrey.
arXiv:2208.14429.
 "Variants of normality and steadfastness deform," coauthored with
A. Bauman,
H. Ellers, G. Hu,
S. Nair, and Y. Wang.
arXiv:2202.00163.
 "Rational linear subspaces of hypersurfaces over finite fields,"
coauthored with
M. I. de Frutos Fernández,
S. Garai,
K. Isham, and
G. Smith.
arXiv:2111.10976.
 "Uniform bounds on symbolic powers in regular rings." arXiv:2111.06049.
 "Relative vanishing theorems for Qschemes." arXiv:2101.10397.
 "New constructions of nef classes on selfproducts of curves," coauthored with M. Fulger.
Mathematische Zeitschrift 302.2 (2022), pp. 1239–1265.
doi: 10.1007/s00209022030927.
arXiv:2101.09827.
 "Excellence, Fsingularities, and solidity," coauthored with
R. Datta, with an appendix
by K. E. Smith.
arXiv:2007.10383.
 "A uniform treatment of Grothendieck's localization problem."
Compositio Mathematica 158.1 (2022), pp. 57–88.
doi: 10.1112/S0010437X21007715.
arXiv:2004.06737.
 "Tate algebras and Frobenius nonsplitting of excellent regular
rings," coauthored with R.
Datta. To appear in Journal of the European Mathematical
Society (JEMS).
doi: 10.4171/JEMS/1259.
arXiv:2003.13714.
 "Permanence properties of Finjectivity," coauthored with R. Datta.
To appear in
Mathematical Research Letters.
arXiv:1906.11399.
 "Seshadri constants for vector bundles," coauthored with M. Fulger.
Journal of Pure and Applied Algebra 225.4 (2021), Paper No. 106559, 35 pp.
doi: 10.1016/j.jpaa.2020.106559.
arXiv:1903.00610.
 "The gamma construction and asymptotic invariants of line bundles over
arbitrary fields."
Nagoya Mathematical Journal 242 (2021), pp.
165–207.
doi: 10.1017/nmj.2019.27.
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.
Other Writing
 "Closuretheoretic proofs of uniform bounds on symbolic powers in regular rings." arXiv:2205.01153.
Now incorporated into "Uniform bounds on
symbolic powers in regular rings."
 "Projectivity of the moduli of curves," coauthored with R. Cheng and C.
Lian, in collaboration with Y. Kovacheva and M. Marinescu. Stacks
Project Expository Collection (SPEC). London Mathematical Society
Lecture Note Series, Vol. 480. Cambridge: Cambridge University Press,
2022, pp. 1–43. doi:
10.1017/9781009051897.003.
Thesis

Seshadri Constants and Fujita's Conjecture via Positive Characteristic
Methods. arXiv:1905.03839.
Published version:
http://hdl.handle.net/2027.42/149842
or https://search.proquest.com/docview/2273364341.
Corrected version:
PDF or
PDF of only corrections.
Organization
 Purdue University Algebraic Geometry Seminar (coorganized with Deepam Patel and
Yilong Zhang).
Fall 2022–.
 AMS Fall Eastern Sectional Meeting 2020,
Special Session on Algebraic Singularities in Arbitrary Characteristic
(coorganized with Rankeya
Datta). On Zoom, October 3–4, 2020.
 eCARs: Early Commutative Algebra Researchers
(coorganized with Alessandra Costantini and Kyle Maddox).
On Zoom, June 27–28, 2020.
Research Talks
 University of Michigan Algebraic Geometry Seminar, October 2023.
 Recent
Trends in Algebraic Geometry, Mathematisches Forschungsinstitut
Oberwolfach, June 2023.
Report.
 MPS
Conference on Higher Dimensional Geometry, Simons Center, May 2023.
 Morgantown Algebra
Days 2023, West Virginia University, April 2023.
 IIT Bombay Virtual
Commutative Algebra Seminar, March 2023.
Recording.
Notes.
 University of Utah
Algebraic Geometry Seminar, February 2023.
 Tsinghua University Algebraic
Geometry Seminar, December 2022.
 Tokyo University Algebraic
Geometry Seminar, December 2022.
 Purdue University Commutative Algebra Seminar, November 2022.
 University of Illinois–Chicago Algebraic Geometry Seminar, October 2022.
 Purdue University Algebraic Geometry Seminar, September 2022.
 Seminar at Waseda University, May 2022.
 AMS Spring Central Sectional Meeting 2022 formerly at Purdue University, Special
Session on Recent Developments in Commutative Algebra, March
2022.
 Commutative and
Homological Algebra Market Presentations, January 2022.
Recording.
Notes.
 Zoom Algebraic
Geometry Seminar, January 2022. Recording.
 University of Illinois–Chicago Algebraic
Geometry Seminar, October 2021.
 Tokyo University/Kyoto University,
Joint Algebraic Geometry Seminar,
May 2021.
 City University of New York
Commutative Algebra & Algebraic Geometry Seminar,
March 2021. Recording.
 Princeton University Algebraic Geometry Seminar, March 2021.
 Stony Brook University Algebraic
Geometry Seminar, February 2021.
 Stanford University
Algebraic
Geometry Seminar, January 2021.
Recording and notes.
 Fellowship
of the Ring, October 2020.
Recording and notes.
 AMS Fall Eastern Sectional Meeting 2020 formerly at Pennsylvania State
University, Special
Session on Geometry and Arithmetic of Algebraic Varieties, October
2020.
 Experimental Talks in
AG, June 2020.
Worksheet.
 Joint
NU/UIC/UofC algebraic geometry and commutative algebra seminar,
June 2020. Notes.
 University of California, Berkeley Commutative Algebra and Algebraic Geometry Seminar, January 2020.
 Pennsylvania State University Algebra and Number Theory Seminar, December 2019.
 Purdue University Commutative
Algebra Seminar, December 2019.
 École Polytechnique Fédérale de Lausanne
Groups,
Arithmetic and Algebraic Geometry Seminar, November 2019.
 MiniWorkshop:
Seshadri Constants, Mathematisches Forschungsinstitut Oberwolfach,
November 2019. Report.
 University of Connecticut Algebra Seminar, October 2019.
 Yale University Algebraic and Tropical Geometry Seminar, October 2019.
 Princeton University Algebraic Geometry Seminar, October 2019.
 Princeton University New Faculty Talks, October 2019.
 KUMUNUjr
2019, University of Nebraska–Lincoln, 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 at the University of
Arkansas, Special
Session on Advances in Birational Geometry, November 2018.
 AMS Fall Central Sectional Meeting 2018 at the University of Michigan,
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, University of Illinois–Chicago, April 2017.
 Mathematics Department Open House, Princeton University, May
2014.
 Berkeley–Stanford REU Joint Conference, Stanford University, July 2013, with
T. Duff and
K. Schaefer.
Slides
Lecture Notes
I LiveTeXed some classes and seminars at Michigan, and
uploaded 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
 "The property of being Japanese (aka N2) is not local,"
written with R. Datta, February 22, 2020. PDF.
 "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. Now incorporated into my Ph.D. thesis
as Theorem 5.5.8.
PDF.
 "Fsingularities for nonFfinite rings," formerly
an appendix to arXiv:1809.01217,
August 2018. Now incorporated into my Ph.D. thesis
as Appendix A.
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
 "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 organized 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.
Any opinions, findings, and
conclusions or recommendations expressed in this material are those of the
author(s) and do not necessarily reflect the views of the National Science
Foundation.