Arizona Summer Program 2010

Undergraduate Research in Geometry

July 5-30, 2010

PROGRAM: Participating students will experience a taste of what life is like for a research mathematician. They will work in groups on projects, interact with senior mathematicians, present results in a mini-conference, possibly publish a paper, and interact with undergraduates from around the country.

TOPICS OF RESEARCH: Research will be in the general areas of geometry and differential equations. Some projects will be related to discrete geometry and others will be related to geometries on Lie groups. We expect projects will have both an experimental and a theoretical component. For more on the projects, click here.

FACULTY AND SUPERVISORS:

• David Glickenstein, Director: University of Arizona.
  
• Andrea Young, Deputy Director: University of Arizona.
  
• Tracy Payne: Idaho State University.
  
• Mike Jablonski: University of Oklahoma.
  

GRADUATE STUDENT MENTORS:

• Daniel Champion, University of Arizona
• Yuliya Gorlina, University of Arizona
• Alex Henniges, University of Arizona
  
• Danny Maienschein, University of Arizona
• Michael Williams, University of Texas at Austin
  

• Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes by Andrew Marchese and Jacob Miller
• Prescribing Curvature for Piecewise-Flat Triangulated 3-Manifolds by Howard Cheng and Peter McGrath
• Log-linear ODEs and Applications to the Ricci Flow for Homogeneous Spaces by Michael Kreisel and Mary Russell
• The Ricci bracket flow by Kevin Kozlowski and Brennan Vincent
• Mathematics of source unfolding by Joe Crouch, Mark Doss, Taylor Johnson, Kira Kiviat, and Justin Lanier
• Source unfolding algorithm by Joe Crouch, Mark Doss, Taylor Johnson, Kira Kiviat, and Justin Lanier

• Constant Scalar Curvature Metrics on Boundary Complexes of Cyclic Polytopes by Andrew Marchese and Jacob Miller
• Prescribing Curvature for Piecewise-Flat Triangulated 3-Manifolds by Howard Cheng and Peter McGrath
• Homogeneous log-linear ODEs and applications to the bracket flow by Michael Kreisel and Mary Russell
• The Ricci bracket flow on solvable Lie groups by Kevin Kozlowski and Brennan Vincent
• Visualizing piecewise flat manifolds by Joe Crouch, Mark Doss, Taylor Johnson, Kira Kiviat, and Justin Lanier

SCHEDULE:

• Week 1.
• Week 2.
• Week 3.
• Week 4.
  

NOTES/HANDOUTS/ANNOUNCEMENTS:

• Introduction to piecewise flat manifolds.
• Latex demonstration files
• ams_article_template.tex
• refs_template.bib
• ball1.pdf
• balls2.JPG
• Matlab files
• ricci2d.m
• solvericci3d.m
• xcf.m
• solvexcf3dfunddompic.m
• Beamer demonstration files
• Danny's beamer page
  
• Poster demonstration files (based on template by Nathaniel Johnson and Jacobs University).
  
• Sample poster
• Sample poster .tex file
• Image for sample poster
• This .sty file extends the beamer package to work for posters.
• This .sty file contains the theme which controls the look of the poster
• Yuliya's poster page
  
• Applying to grad school
  
• Sample Resume: .docx or .pdf
• Bill Velez's slides: .docx or .pdf
• Dave's assorted tips for applications.
  
• Young Mathematicians Conference at the Ohio State University. Application deadline is August 2.

Click here for a downloadable poster.