Research Experience for Undergraduates (REU)
http://hdl.handle.net/2022/13432
2015-05-25T19:49:58ZModuli spaces of square-tiling deformations and single-tile real line tilings
http://hdl.handle.net/2022/13810
Moduli spaces of square-tiling deformations and single-tile real line tilings
Proffitt, Garrett
Classifying Single-Tile Periodic Tilings of the Real Line and Realizing the Deformation Spaces of Two and Three Square Periodic Tilings of the Plane through Combinatorial Structure.
2010-01-01T00:00:00ZOn the Combinatorics of Schubert Calculus
http://hdl.handle.net/2022/13533
On the Combinatorics of Schubert Calculus
Truong, Linh
2010-01-01T00:00:00ZThe Links Between Smale’s Mean Value Conjecture and Complex Dynamics
http://hdl.handle.net/2022/13532
The Links Between Smale’s Mean Value Conjecture and Complex Dynamics
Miles-Leighton, Hayley
In this paper we study the links between Smale’s Mean Value Conjecture (SMVC) and the convergence of critical points under iteration. We begin by introducing SMVC
and discussing what progress has been made towards proving this conjecture. From there we give a brief introduction to a few concepts in Complex Dynamics and Complex Analysis including conjugacy, conjugations by 1/z, and orbits. We then show that conjugacy conserves SMVC. At this point, we go through the quadratic case to show the patterns that we are looking for as well as to show a basic
structure of how this problem is being looked at. From there we look at the cubic case, going through SMVC for the cubic polynomial. We then introduce the Petal Theorem and show how it is used for the cubic case specifically. We conclude with the connections between the SMVC in the cubic case and the convergence of the same critical points explained and discuss future work.
2010-01-01T00:00:00ZTorsion Subgroups of CAT(0) Groups
http://hdl.handle.net/2022/13526
Torsion Subgroups of CAT(0) Groups
Ghadyali, Hamza; Dowlin, Nathan
Given a CAT(0) group G acting geometrically on a proper CAT(0)
space, we attempt to demonstrate that any torsion subgroup of G has
nite cardinality.
2010-01-01T00:00:00Z