**Tom Oldfield**

**Office:** RLM 11.130

**E-mail: **toldfield@math.utexas.edu

About Me:

I am a second year graduate student in mathematics at the University
of Texas at Austin, where my advisor is Sean Keel. I am
interested in a broad range of topics within algebraic and complex
geometry, particularly those involving moduli spaces. My
undergraduate work was completed at the University of Cambridge
(which is why I pronounce maths with an "s"), where I also completed
the part III course in 2015.

### Teaching:

M408C - Differential and
Integral Calculus [Fall 16]

M408D - Calculus Refresher
[Fall 16]

M325KH - Honours Discrete
Mathematics [Spring 16]

M408D - Calculus Refresher
[Spring 16]

M408C - Final Exam Review
[Fall 15]

M408C - Differential and Integral
Calculus [Fall 15]

Seminars
I've helped to run:

A
reading seminar for algebraic
geometry (Also previously in Summer 2016)

A study
group in commutative
algebra,
joint with Richard
Hughes (Fall 2015)

**Things that I've
done:**

**The Hilbert Schemes of Points in
Projective Spaces: (2015) **During my time on the part
III course, I decided to write this essay under the supervision of
Dr. John Ottem. The
spirit of the part III essay is to take multiple sources with a
common theme and weave a coherent narrative out of them. I chose
to begin with a proof of the existence of the Hilbert scheme and a
discussion of some of it's properties, and to conclude by proving
some of the more important facts about the Hilbert scheme of
points using the Hilbert-Chow morphism.
**On the cohomology ring of
compact hyperk****ähler
manifolds: (2014)** In the Summer of 2014 I was awarded
funds to take part in the Bridgwater Summer Undergraduate Research
Program working under the guidance of Dr. Charles Vial
in Cambridge. By performing computations with some elements of the
Chow group derived from the Beauville-Bogomolov form, I hoped to
extend a result proved jointly by Vial and Dr. Mingmin Shen
about a particular decomposition of the Chow groups of certain
hyperkähler varieties of K3^[2] type. Although the immediate
generalisation turned out not to hold, I was able to establish
several smaller results.
**IAS/PCMI
Undergraduate Summer School on Geometric Analysis:****
(2013)** PCMI and the IAS
jointly run a summer session every year, with programs for a huge
number of different types of people interested in mathematics,
including programs for active mathematics researchers,
undergraduate students and even mathematics teachers. Each year
has a different theme, and in 2013 the theme was Geometric
Analysis. I found that this was a great way to be introduced to
the subject as an undergraduate and would highly recommend
applying to the program if you find next years topic to be of
interest to you.

**About This Site:**

It was created on 25/08/2015 so that I could give the students in my
first TA appointment (beginning 26/08/2015) somewhere to go to find
my contact information. Hopefully it will soon develop into
something better looking and more substantial. I have similar hopes
for myself.