||Fine Hall 310
I am currently a Postdoctoral Research Fellow at Princeton University,
funded by the National Science Foundation.
My mentor is János
I am interested in algebraic geometry and commutative
algebra, especially in positive characteristic.
I was previously a Ph.D. student at the University of Michigan, where my advisor was Mircea Mustaţă.
Teaching (at the University of Michigan)
- Math 115:
Fall 2014, Fall 2017.
- Math 116:
Winter 2015, Fall 2015, Winter 2016.
- Math 215
(teaching assistant): Spring 2016.
- Math 631, 632 (grading): Fall 2015, Winter 2016, Winter 2017.
- Michigan Math and Science
Scholars (course assistant): "Art and Mathematics" and
"Mathematics of Cryptography," Summer 2019.
Research (also on arXiv)
- "Permanence properties of F-injectivity," coauthored with Rankeya
- "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.
- "Frobenius–Seshadri constants and characterizations of projective
space." Mathematical Research Letters 25.3 (2018), pp.
- "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,
A. Nesky, and
Annals of Combinatorics 19.4 (2015), pp.
Seshadri Constants and Fujita's Conjecture via Positive Characteristic
- Pennsylvania State University Algebra and Number Theory Seminar, December 2019.
- Purdue University Commutative Algebra Seminar, December 2019.
- École Polytechnique Fédérale de Lausanne
Arithmetic and Algebraic Geometry Seminar, November 2019.
- University of Connecticut Algebra Seminar, October 2019.
- Yale University Algebraic and Tropical Geometry Seminar, October 2019.
- Princeton University Algebraic Geometry Seminar, October 2019.
2019 at the 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,
- AMS Fall Southeastern Sectional Meeting 2018 at the University of
Session on Advances in Birational Geometry, November 2018.
- AMS Fall Central Sectional Meeting 2018 at the University of Michigan,
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.
Algebraic Geometry Graduate Conference at the University of Illinois–Chicago, April 2017.
- Mathematics Department Open House at Princeton University, May
- Berkeley–Stanford REU Joint Conference at Stanford University, July 2013, with
T. Duff and
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
- 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
- MATH731, Topics in Algebraic Geometry: Berkovich Spaces, taught by Mattias Jonsson (see
- Learning seminar on Deligne's Weil II theorem, Summer 2016,
organized by Bhargav
Bhatt (see plan).
- MATH731, Topics in Algebraic Geometry: Perverse
Sheaves, taught by Bhargav
Bhatt (see course website). 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,
- "F-singularities for non-F-finite rings," formerly
an appendix to arXiv:1809.01217,
- "F-modules 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
Carl Lian, and
with guidance from
Stacks Project Workshop,
- "D-modules and mixed Hodge modules," Fall 2016 and Winter
- "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 mini-course 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.
- "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.
- "Using Grothendieck groups to define and relate the Hilbert and Chern
polynomials axiomatically," final project for MATH631, Fall 2014.
- "Fiber Bundles in Analytic, Zariski, and Étale Topologies," senior thesis, Spring 2014. PDF
- "An elementary proof of the classification of vector bundles on
P1 and line bundles on
Pn," Fall 2013. PDF
- "Counting exceptional curves on blowups of
P2," Fall 2013.
- "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 Mini-Courses 2016 and 2017
I organized 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
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