Tom Oldfield

Office: RLM 11.130

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.


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 hyperkähler 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.