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GEOMETRY and PHYSICS on GRAPHS: This is the wiki for a geometry, physics, and graph theory NSF Research Experience for Undergraduates at Canisius College. Everyone is welcome to read our work but you must login to add things and to make changes. We offer login privileges to those in need; please contact us at the Canisius College Department of Mathematics and Statistics: [1] (http://www.canisius.edu/math/)
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Summer 2009
REU2009 is mentored by Stratos Prassidis and B.J. Kahng, with students Robert Abramovich (Johns Hopkins University), Greg Gauthier (Vanderbilt University), Laura Janssen (University of Nebraska), Jonathan Jaquette (Swarthmore College), Ann Johnston (Harvey Mudd College), Andrew Reynolds (University of California, Los Angeles), Mollie Stein (Barnard College), and Amelia Wallace (University of North Carolina).
Welcome to Canisius!
Here are some preliminary reports:
- Automata that Generate Triangular, Square, and Hexagonal Lattices by Gregory Gauthier
- Category Theory and Dynamical Systems by Jonathan Jaquette
- The Cuntz-Krieger Algebra of a Directed Graph by Andrew Reynolds
- Evaluating the Hecke Operator on Gamma by Gregory Gauthier
- Examples of topological dynamical systems embedded into symbolic dynamical systems by Jonathan Jaquette
- An Extended Example of Ihara Zeta Functions (unfinished) by Mollie Stein
- Generating the Truncated Icosahedron from Three Generators by Gregory Gauthier
- The Graph Algebra of a Box Product is not the Tensor Product of the Graph Algebras by Ann Johnston and Andrew Reynolds
- Group Extensions and The Heisenberg Group by Laura Janssen
- Hamiltonian Paths in Cayley Digraphs by Andrew Reynolds
- The Heat Kernel for Higher Dimensional Weighted Lattice Graphs by Robert Abramovic
- Analytic Functions and Infinite Hamiltonian graphs by Robert Abramovic
- The Ihara Zeta Function and the Riemann Zeta Function by Mollie Stein and Amelia Wallace
- Problem: Determining the Eigenvalues of an Infinite Hexagonal Lattice on a Torus by Gregory Gauthier
- A Reference to Some Common Binary Operations on Graphs by Ann Johnston
- Topological Dynamical Systems by Jonathan Jaquette
- Two methods to compute the Ihara Zeta Function by Mollie Stein
- Useful Code for Working with C*-algebras by Ann Johnston
Activities for REU 2009
Page listing the seminar talks given: Seminars09
We are also planning to have a joint mini-conference with the REU group at Rochester Institute of Technology. Tentative date is 7/22.
You can see the announcement for Summer 2009 at [2] (http://www.canisius.edu/~kahngb/reu/)
- Here is a link to some other research on random walks this summer Robert Makin
Summer 2008
REU2008 is mentored by Terry Bisson and B.J. Kahng, with students emily bargar (University of Chicago), Ari Binder (Williams College), Vivian Healey (University of Notre Dame), Rachel Hunter (Cornell University), Colin Klaus (Vanderbilt University), Brian Leary (Carnegie Mellon University), Josh O'Rourke (Reed College), and Gabrielle Paoletti (Canisius College).
Here is a list of major findings from our summer research:
- Tilings Vivian Healey
- Groupoids and Graphs Colin Klaus and Brian Leary
- Random Walks on Directed Multigraphs Ari Binder and Josh O'Rourke
- Zig-Zag Product information Brian Leary
- Hypergraphs emily bargar
- Simplicial Complexes Gabrielle Paoletti
- Box Products, Box Exponentials and Graph Covering Maps Rachel Hunter
List of Research Reports, Preprints, and Talk Slides from REU2008 can be found at: [3] (http://www.canisius.edu/~kahngb/reu/reuresults08.html)
Here are some preliminary reports from the first part of the summer:
- Isospectral Graphs emily bargar, Vivian Healey
- Cayley Graphs emily bargar
- Characteristic Polynomials of Adjacency Matrices of Families of Graphs emily bargar, Vivian Healey, Rachel Hunter, Brian Leary, Gabrielle Paoletti
- Fractals and Graphs Vivian Healey
- Abstracts for MathFest08
Here is a page listing links to papers, and lists of pdf files on one of the computers in our work room Some references for REU 2008
Here is a page listing conferences (and journals) Future Conferences for Student Presentations
You can see the announcement for Summer 2008 at [4] (http://www.canisius.edu/~kahngb/reu/reu08.html)
Summer 2007
REU2007 was mentored by Terry Bisson and Stratos Prassidis
with students Tim Doster,Alicia Hoffmann, Chelsey Cooley, Eric Lownes, Chloe Johnson, Stefan P. Sabo, Alissa Pioli, and Ben Lerman
(from left to right in the picture).
Here are some pages from the work this summer:
- New coverings from groups Alissa Pioli, Chelsey Cooley, Chloe Johnson.
- The Zig-Zag Product: Background and Examples... Stefan P. Sabo and Ben Lerman
- The Heat Kernel of the K-Regular Tree Eric Lownes and Stefan P. Sabo
- Fullerenes Alicia Hoffmann and Tim Doster
- Generalizing the Zig-Zag Product of Graphs Ben Lerman
- Preliminary work for Summer 2007
- Events for REU07
Summer 2006
- Summer 2006 Here is a link to a page with some overview on our activities.
The two projects for Summer 2006 were
Spectral gaps in groups and graphs, directed by Stratos Prassidis, and
Cayley graphs and coverings, directed by Terry Bisson.
Participating students were Clara Brasseur, Julia Lazenby, Taylor Coon, Allison Davis, Ryan Grady, Dominic Dotterrer, Samuel Cooper, and Joe Consiglio.
Summer 2005
Summer 2005 projects were Covers, Laplacians, and Growth on Graphs, directed by Stratos Prassidis, and
Characteristic polynomials and directed graphs, directed by Terry Bisson.
PICTURE (http://www2.canisius.edu/~prasside/reu_2005/pictures/PIC1.JPG)
Participating students in 2005 were Jordan Volz, Diane Lunman, Angelo Chandler, Robert Marciniak, Tricia Profic, Brian Meagher, David Mittiga, and Jack Wessel.
Space for this website has been generously provided by Dr. Dewey J. Bayer, Professor of Psychology, Canisius College.
National Science Foundation (REU listings): [5] (http://www.nsf.gov/crssprgm/reu/list_result.cfm?unitid=5044)
American Mathematical Society (REU listings): [6] (http://www.ams.org/employment/reu.html)
Here is a link to Buffalo Blue Bicycles, a local bike-sharing project [7] (http://www.buffalobluebicycle.org/)
