LSU
Mathematics

# REU 2015 Topics

As noted in the description of the structure of the program, participant projects are collaboratively chosen at the end of the first week within the framework of the various topics presented during the first week. Project titles from past years are presented below and more detailed abstracts are available in the file attachments on this page.

2012 Projects

The attachment below on 2012 projects and references provides greater details on prospective 2013 projects as well. Please read the web page on the structure of the REU and note that you will be choosing your project at the end of the first week.

2011 Projects:

• Recursion in BRWT of Ribbon Graph Families
• Partial Twisting on $k$-cables
• Finding Solutions to GKS Systems Using Sage
• GKZ systems associated to two-dimensional root systems
• Arithmetic properties of Picard-Fuchs equations
• Picard-Fuchs equations, Apery-like sequences and irrationality
• Generic Polynomials for Groups of Small Degree
• Differential equations for families of curves of genus > 1
• Generic Polynomials for Triangular Groups over Finite Fields
• n-Pointed BRWT Polynomials
• Generic polynomials for p-groups in characteristic p
• Generating Functions for Geometric Groups
• BRWT of ribbon graph operations

# 2010 Projects:

• Permissible Plane Embeddings of Dessin Blow-ups

• Galois Invariance under Belyi-Extending Maps

• Calculating Picard Fuchs Differential Equations

• Differential Equations Satisfied by Families of Elliptic Curves

• Properties of Fibonacci Periods

• Relations in the Grothendieck Ring of Dessins

• Belyi Functions of Special Trees

• P-adic Convergence of the Ihara Zeta Function on Fractals

• Recursive Families of Dessin

• Dessins d'enfants: Symmetry and Quotient Dessins

• Belyi Extending Maps and Dessin d'Enfant

• Symmetric square DEs for the Beauville families of elliptic curves

For further details, you can read the abstracts in the 2010ProjectAbstracts file attachment below.

## 2009 Projects:

• Quasitree Expansion of the Bollob\'{a}s-Riordan Polynomial

• Dessins and Manturov bracket structures

• Non-congruence subgroups and modular forms

• Adams Operations on Chord Diagrams

• Dessins D'Enfants and Gassmann Triples

• Automata and Growth Functions for the Trefoil and $4_1$ Knots

• Cyclic Dessins

• Dessins & Chord Diagrams

• Handle-Slides on Single-Vertex Dessins

• Finding Fibered Covers of Non-Fibered Two-Bridge Knots

• Categorification of Krushkal's Fatgraph Polynomial

For further details, you can read the abstracts in the 2009ProjectAbstracts file attachment below.

AttachmentSize
projects2012.pdf247.99 KB
2010ProjectAbstracts.pdf137.48 KB
2009ProjectAbstracts.pdf111.06 KB
LSUdesc.pdf166.45 KB
how-to-draw-a.pdf225.14 KB
jwh2002b.pdf154.32 KB