||East Hall 2852
I am currently a Ph.D. candidate, in my third year in the mathematics
department at the University of Michigan.
I am interested in algebraic geometry and commutative
algebra. My advisor is Mircea
Mustaţă. I was previously an undergraduate mathematics major at Princeton
University, where my advisor was
Summer Mini-Courses 2017
I am organizing a series of summer mini-courses taught by graduate
students in the mathematics department at Michigan. See the schedule.
- Math 215:
- Math 116:
Winter 2015, Fall 2015, Winter 2016.
- Math 115:
- Math 631, 632 (grading): Fall 2015, Winter 2016, Winter 2017.
- "Frobenius–Seshadri constants and characterizations of projective
- "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
K. Schaefer. Annals of Combinatorics 19.4 (2015), pp.
- "Characterizations of projective space and Seshadri constants in
arbitrary characteristic," Midwest Algebraic
Geometry Graduate Conference at University of Illinois at Chicago,
- "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 Berkeley-Stanford REU Joint Conference 2013, July 2013.
I have been LiveTeX-ing some classes and seminars at Michigan, and am
uploading them for other people to use. Matt Stevenson
is LiveTeX-ing notes for Bhargav Bhatt's course on Perfectoid spaces.
- 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
- D-modules and mixed Hodge modules. PDF (accessible for umich.edu
e-mail addresses; e-mail 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
- "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
The schedule with notes is still