I follow Ravi Vakil's rules about
letters of recommendation. Please read them if you want me to write you a letter.
Graduate students
Julie Rana → University of Minnesota.
Julie wrote a thesis
about the boundary of the Kollár-Shepherd Barron-Alexeev's compactification of the moduli space of quintic surfaces.
This required finding new bounds on indices of singularities of stable surfaces,
extending deformation theory results of Horikawa to the stable case,
representation-theoretic analysis of flops on the minimal resolution, etc.
See her paper A boundary divisor in the moduli space of stable quintic surfaces.
Julie was awarded a Distinguished Thesis award at UMass.
Tassos Vogiannou.
Tassos is developing a theory of spherical tropicalization, extending the usual tropicalization
procedure (in the spirit of [15], [17], and Section 2 of [20]) to the case when the ambient variety is spherical.
Alex Levin → University of Vermont.
Alex proved that the dual simplicial complex of the Naruki space of cubic surfaces (see [20]) is
shellable, and in particular homeomorphic to a bouquet of 3-dimensional spheres.
This neat result was unfortunately never published.
Ilya Scheidwasser → Northeastern University.
Ilya's
Capstone thesis contains some
combinatorial information about hypertrees not covered in [22].
Ilya's C++ program found all hypertrees with
7,
8,
9,
10, and
11 vertices
(note that irreducible hypertrees are called "strong hypergraphs" in Ilya's thesis).
Charles Boyd. Charles found that the Craighero--Gattazzo quintic surface is not reduced in characteristic 7.
This observation lead to [26].
Nate Harman→ MIT.
Most of Nate's REU results on combinatorics of hypertrees, and especially spherical hypertrees, were incorporated in [22].
Nicky Reyes → UT Austin.
Nicky's experiments helped a great deal to classify extremal P-resolutions in Section 4 of [24].
Stephen Obinna. Stephen is working on blow-ups of toric surfaces in the spirit of [25].
I enjoy working with undergraduate students and typically hire one student every year.
If you are interested in working with me, contact me early to see if we are a good match.
My preference is to do a summer REU followed by writing an Honors thesis.
All my undergraduate projects are directly related to my own research.
You will be asked to do a lot of computer experimentation to satisfy my curiosity
about various matematical objects, so programming skills
(Mathematica, C++, etc.) are required. Notice that
I do not consider writing a paper based on your results as a priority unless you get superb results,
which of course is rare at this early career stage. But you will get a taste of serious research.
Often I will incorporate your calculations in my papers. We will also learn a lot of mathematics,
in particular we will read Miles Reid's Undergraduate Algebraic Geometry
as part of the project, so you are encouraged to start reading it early solving all exercises.
Some students then start reading Shafarevich's Basic Algebraic Geometry
or even Hartshorne's Algebraic Geometry.
So far nobody has attempted to read Grothendieck's EGA, maybe you will be the first?