| Title | Description
|
| 2-Categorical
affine symmetries of quantum enveloping algebras | We produce
2-representations of the positive part of affine quantum enveloping
algebras on their finite-dimensional counterparts in type A_n. These
2-representations naturally extend the right-multiplication
2-representation of U_q^+(sl_(n+1)) on itself and are closely related to
evaluation morphisms of quantum groups. We expect that our
2-representation exists in all simple types and show that the
corresponding 1-representation exists in type D_4.
|
| Characterization
of
saturated graphs related to pairs of
disjoint matchings | Continuation of the paper below. We
first show that graph decompositions into paths and even cycles provide
a new way to study this ratio. We then use this technique to
characterize the graphs achieving ratio 1 among all graphs that can be
covered by a certain choice of a maximum matching and maximum disjoint
matchings. Published in the Illinois Journal of Mathematics.
|
| Pairs of disjoint
matchings
and related classes of graphs | We study the ratio, in a
finite graph, of the sizes of the largest matching in any pair of
disjoint matchings with the maximum total number of edges and the
largest possible matching. Previously, it was shown that this ratio is
between 4/5 and 1, and the class of graphs achieving 4/5 was completely
characterized. Here, we show that any rational number between 4/5 and 1
can be achieved by a connected graph. Furthermore, we prove that every
graph with ratio less than 1 must admit special subgraphs. Part of an
undergraduate research project while I was at UIUC.
|
| Magnetic
Ergostars, Jet
Formation, and Gamma-Ray Bursts: Ergoregions versus Horizons | We
perform the first fully general relativistic, magnetohydrodynamic
simulations of dynamically stable hypermaassive neutron stars with and
without ergoregions to asses the impact of ergoregions on launching
magnetically-driven outflows. Part of an undergraduate research project
(in the physics department)
while I was at UIUC. Published in Physical Review D.
|
