Adam Boocher
Department Of Mathematics, 
University Of Notre Dame, 
Notre Dame, IN 46556

Mailbox: Hayes-Healy 255  
Phone: (574) 276-0534
Email: aboocher@nd.edu

I am currently a senior honors math major at the University of Notre Dame. My mathematical interests currently lie in commutative algebra and algebraic geometry and I am currently writing a thesis in commutative algebra on the Eisenbud-Mazur conjecture (cool stuff!). I have written a few expository and research papers, which are linked to below. I recently co-organized the conference Undergraduate Work in Mathematics at Notre Dame.

Apart from mathematics I enjoy traveling, movies, and can often be heard whistling for many hours of the day. I am also a competitive Scrabble and bridge player and am current club president of the Notre Dame Scrabble Club and Math Club. To see my previous webpage (as well as the theater curtain I had in my room in 2005-2006) click here.

Research

  • In Summer 2005 I participated in the Notre Dame REU. Working with Prof. Misha Gekhtman, my partner Brad Froehle and I studied the topic of Totally Positive Matrices. Our paper, "On generators of bounded ratios of totally positive matrices" will appear in Lin. Alg. & Appl.
  • In Summer 2006 I was at the Claremont Colleges REU where I worked under the supervision of Prof. Jim Hoste (Pitzer College) with Jay Daigle (Pomona College) and Wenjing Zheng (U. California Berkeley) on the subject of Lissajous knots. We were able to find bounds for the number of knot types of Lissajous knots of certain frequencies. For an expository look at our research, the following links are for the poster we presented at the Joint Math Meetings in Janurary 2007, and the presentation we gave at the Claremont Colleges in August. This is really cool stuff!
    • Poster - "Sampling of Lissajous and Fourier Knots"; our poster from the Joint Math Meetings 2007.
    • Presentation - A beamer presentation given July 28, 2006 at the Claremont Colleges
    • Notre Dame Talk - A shorter presentation given September 30, at Notre Dame
    • Preprint
  • In the Summer of 2007 I worked at the Williams College REU under the guidance of Prof. Susan Loepp. Our group studied completions of excellent unique factorization domains. Our paper can be found below as can a pdf for a short presentation we gave on this research and a poster too.
  • An Excellent Poem: I wrote a short poem about the methods we used in our proofs for constructing these excellent rings. It's mathematically accurate and meant to be humorous, but I'm not sure if the humor extends much past those in our group... Enjoy!

    • Expository Papers

    Algebraic Geometry: In the Spring of 2007 I organized an undergraduate seminar in algebraic geometry aimed at sophomore level honors students. I have prepared a set of lecture notes to accompany the seminar.
    Lecture Notes
    Seminar Syllabus

    Free Resolutions This was meant to be a later chapter in the algebraic geometry notes, but I haven't gotten around to combining them yet. These may be a bit rough but carry one to the start of free resolutions and computing Hilbert functions of monomial ideals.



    Koszul Complexes - A short expository paper on Koszul Complexes to accompany a series of talks I gave at the Commutative Algebra seminar.

    Tietze Extension Theorem - An expository paper on the Tietze Extension Theorem and the entrance paper to the Notre Dame SUMR program.

    Commutative Algebra Notes A start to some typed notes on introductory commutative algebra. These mainly follow Atiyah & MacDonald and contain some solutions to the homework problems.