REU at MHC: PREVIOUS YEARS

• Ramsey theory (Jillian McLeod)
• Number theory (Margaret Robinson)

• Gauss' conjecture on equivalence classes of quadratic forms with positive discriminant (Giuliana Davidoff)
• Polynomial Knots (Alan Durfee and Donal O'Shea)

• Polytopes and toric varieties (Jessica Sidman)
• Number theory (Margaret Robinson)

• Polynomial and rational knots (Alan Durfee and Donal O'Shea)
• k-Regular Expander Graphs (Giuliana Davidoff)

• Polynomial knots (Alan Durfee and Donal O'Shea)
• Number Theory (Margaret Robinson)

• Markov Chain Monte Carlo. (George Cobb together with Yung-Pin Chen of Lewis and Clark College)
• Ramanujan graphs.(Giuliana Davidoff)

• Difference sets in groups (Harriet Pollatsek)
• Polynomial knots. (Alan Durfee and Donal O'Shea)

• Exponential Sums and Local Zeta Functions (Margaret Robinson)
• Models of turbulence (Mark Peterson)

• Polynomial knots (Alan Durfee)
• Error-correcting codes (Giuliana Davidoff)

• Algorithmic proofs of the Quillen-Suslin theorem (Donal O'Shea).
• P-adic analysis and local zeta functions (Margaret Robinson)

• Curvature of algebraic singularities (Donal O'Shea).
• Weight distributions of certain generalized codes (Giuliana Davidoff).

• Curvature of algebraic singularities (Alan Durfee)
• Local zeta functions (Margaret Robinson)

• Difference sets in groups (Harriet Pollatsek)
• Limiting tangents and normals to singularities of algebraic surfaces (Alan Durfee and Donal O'Shea).

• Topics in comparative number theory (Giuliana Davidoff).
• Varational methods for solution of PDE's (Lester Senechal).

• Igusa's local zeta function (Margaret Robinson)
• Critical points of real polynomials (Alan Durfee)
• Laplacian growth (Mark Peterson)

• Bootstrap Estimation of Eigenvalues in Principal Components Analysis (Janice Gifford).
• Curvature and Limits of Normals to Surface Singularities (Donal O'Shea)
• Steepest Descents with Sobolev Norm (Lester Senechal).

• Counting Critical Points of Real Polynomials in Two Variables (Alan Durfee)
• The Red Blood Cell Shape (Mark Peterson)
• Extremization in Function Spaces (Lester Senechal).

• Bootstrap Estimation of Eigenvalues in Principal Components Analysis (Janice Gifford).
• Limits of Tangent Spaces (Donal O'Shea)
• Time Dependent Evolution of Planar Domains (Mark Peterson)

Support for 1988-1990 was provided by National Science Foundation grant DMS-8804962, support for 1992-1994 by NSF grant DMS-920084, support for 1995-1997 by NSF grant DMS-9424077, and support for 1998-2003 by NSF grant DMS-9732228.

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