University of Michigan, Ann Arbor
Department of Mathematics

1061 East Hall
734 763 0959
eisenst at umich dot edu

About me

CV

I am a second year graduate student interested in algebraic geometry, especially higher dimensional problems and questions on singular varieties. I am currently working on multiplier ideals with Professor Lazarsfeld.

Homework notes for 215

These notes are on the homework sets for the sections of 215 that I'm a TA for.

• Homework I.
• Homework II.
• Homework III.
• Homework IV.
• Homework V.
• Homework VI.
• Homework VII.
• Homework X.
• Homework XI.

Class notes

These notes come with no warranty of any kind, user beware. You may use them with only one stipulation: inform me of any mistakes you find. Ignore anything written in all caps, those are notes to myself. One day not too far from now I will go over these notes and whip them into some sort of readable shape.

• Syzygies of algebraic varieties.
• Singularities in analytic and algebraic geometry.

Past notes:

• Gromov-Witten theory.
• Algebraic Geometry II.
• Lie Groups.
• Differentiable Manifolds.
• Diophantine problems.
• Algebraic Geometry I.
• Commutative Algebra.
• Modular Forms.
• I am also taking algebraic number theory but I arrived in that class too late to catch up on notes.
• Number Theory Learning Seminar. This is likely to be full of mistakes since I do not really understand what this is talking about.

Articles

• Notes on elliptic curves.
  These notes were written over a year ago for a talk I gave at a seminar, as a summary of the first few chapters of Silverman's book on elliptic curves. They contain a few mistakes, some of which can be amusing.
• The sieve of Eratosthenes.
  This is an expansion and an elucidation of the section on the sieve of Eratosthenes in M. Ram Murty's book on sieves.
• The Selberg sieve.
  This is an expansion and an elucidation of the section on the Selberg sieve in M. Ram Murty's book on sieves.
• The existence and uniqueness of the Haar measure on a locally compact group.
  This is one of those theorems that everyone uses but noone bothers to prove. I wrote this up as a project for a graduate course on operator theory.
• Heights of algebraic points on surfaces, on the paper of Wolfgang Schmidt.
  This is an essay I submitted for a graduate course on Diophantine approximation. The beginning is a crash course in some very elementary theory of heights.
• A proof of Chen's theorem, with Adam Felix and Lalit Jain.
  Chen's theorem states that, eventually, every even number may be written as a sum of two numbers, one prime and the other having at most two prime factors. This is one of the two closest known approximations to the Goldbach conjecture, the other being Vinogradov's theorem that is proven via the circle method. These notes prove Chen's theorem in an almost self-contained fashion. All the foundational theorems of analytic number theory and the linear sieve are assumed. The exposition follows Nathanson's book. We never got around to fixing all the mistakes and typos found in these notes, reader beware.

Links

Chris Almost's website is an excellent collection of notes on many different subjects in mathematics.

Lalit's website contains some notes in number theory, especially the proof of the irrationality of Zeta(3).

James Milne's page is famous for the extraordinary collection of notes on number theory and related topics.

Alina Carmen Cojocaru has put up an essay written by M. Ram Murty that attempts to guide its reader in mathematical research.

Get Fuzzy should be self-explanatory.

Personal

I am a regular skydiver, although my recent participation in the sport has decreased to practically nothing due to time and monetary constraints. While in Canada, I skydive at Skydive Burnaby, a beautiful dropzone on lake Erie. We have the only full-time Twin Otter in Canada, it can take 24 people to 14,000' in about 20 minutes.

I am a (not strictly observant) Jew.

One fine day this page may contain some pictures not drawn by M.C. Escher.