Welcome to my home page. Last updated May 9, 2018   I am a professor emeritus of mathematics at the University of Minnesota. In plain english, this means that I retired at the end of the 2008-09 school year. For now, my plan is to actively maintain my interactive pictures of polyhedra and algebraic surfaces. Other parts of this web page will be updated from time to time, as needed.   My main research areas are Algebraic Geometry and  Commutative Algebra. I have taught graduate courses in areas related to my research interests, and undergraduate courses in a wide range of subjects. Materials related to my research and to some of my courses are linked below.   Please scroll down or click on one of these links to view these materials and related links: Current research interests & publication list   Some mathematical materials  {Click here for expanded descriptions.} Interactive pictures of polyhedra and algebraic surfaces. Curve sketches Lecture notes, etc.   Online presentations April 16, 2009 Duluth Colloquium April 26, 2007 IMA presentation April 3, 2006 Math Club presentation   at the University of Minnesota February 23, 2005 lecture at UNAM Morelia Conferencia de 23 de febrero 2005 a UNAM Morelia       ( en español)   Courses I have taught Algebraic geometry courses Math 5385          (Computational Algebraic Geometry) Math8203/4/5          ( Algebraic Geometry    Fall/Winter/Spring 1997/98) Linked items include the course syllabus, suggested references, notes from some of the lectures, and assigned exercises. Other courses   Academic advising for IT Lower Division students I participated in this activity from the Fall of 1993 through the spring of 2008 -- the end of the period when IT faculty officially had a role in academic advising for IT students in lower division.  Note:  IT (Institute of Technology) was the previous name of the College of Science and Engineering (CSE). I recommend the following page for current information on academic advising and related matters for CSE students :         IT Lower Division Program homepage.   Although it's out of date right now, you're also welcome to visit my previous advising info page.   1997 Mumford Symposium pictures   Comments and inquiries to: roberts@math.umn.edu

• In Algebraic Geometry I am interested in projective embeddings of algebraic varieties, projections of embedded varieties, and enumerative questions about singularities of varieties and mappings.
   
• In Commutative Algebra I am interested in determinantal ideals, and ideals and algebras generated by monomials. Some of my work in this area is connected with the representation theory of the general linear group. In the past I have studied rings of invariants of linear algebraic groups acting on regular rings.
   
• My publication list is linked here.

• Some sketches of algebraic curves
  The pictures are presently static, but I hope that it will be possible to develop a Java application which will make it possible for the viewer to manipulate them.
  • REU project report One-parameter families of algebraic curves in Matlab
    by Rory Mulvaney, University of Minnesota, TC
  
  Note: I'm not participating in the summer REU program this year. If you're interested in learning about current summer REU opportunities, please click on the following link:
   
  • School of Mathematics Summer 2001 REU page
     
• Some pictures of objects in 3-dimensional space
  The pictures are based on software developed at The Geometry Center, formerly here at the University of Minnesota.   [The Geometry Center is now closed, but their homepage is now located and maintainted at the University of Illinois.]

  You can move the pictures by grabbing them with the mouse. (Your viewer needs to be Java enabled . . . )

  • Pictures of regular and semi-regular polyhedra
  • Pictures of a few algebraic surfaces    
     
• Lecture notes from my introductory graduate level algebraic geometry course
   
• The class homepage from my computational algebraic geometry course
   

The opinions expressed in this page are strictly those of the page author. The contents of this page have not been reviewed or approved by the University of Minnesota.