Have you heard of M.C. Escher? Origami?

He is said to have created more mathematicians than any other person in history, through his numerous books and long-running recreational math column in Scientific American. Widely revered among mathematicians, Gardner passed away in 2010. However his influence and legacy continue to inspire us to approach seemingly intractable problems from unconventional angles.

Title:  The combinatorial structure behind the free Lie algebra

Abstract:  We explore a beautiful interaction between algebra and combinatorics in the heart of the free Lie algebra on n generators: The multilinear component of the free Lie algebra Lie(n) is isomorphic as a representation of the symmetric group to the top cohomology of the poset of partitions of an n-set tensored with the sign representation. Then we can understand the algebraic object Lie(n) by applying poset theoretic techniques to the poset of partitions whose description is purely combinatorial. We will show how this relation generalizes further in order to study  free Lie algebras with multiple compatible brackets.

Hosted by the Graduate Student Council.  All are welcome to come mingle over coffee, tea, and cookies!

Title:  Eilenberg-MacLane Spaces

Abstract:  A space X is a K(G,n)  if \pi_n(X)=G and \pi_i(X)=0 if i\neq n. An interesting aspect is that the homotopy type of a CW comples K(G,n) is uniquely determined by G and n. We will investigate the construction of K(G,1), otherwise known as BG, for an arbitrary (discrete) group G, the homology of K(G,1) spaces, and the infinite symmetric product SP(X).

Title:  Duals of Skew θ-Constacyclic Codes

Abstract:  We generalize cyclic codes to skew θ-constacyclic codes using skew polynomial rings. We provide a useful tool for exploring these codes: the circulant. In addition to presenting some properties of the circulant, we use it to re-examine a theorem giving the dual code of a skew θ- constacyclic code first presented by Boucher/Ulmer (2011). This talk includes work with Dr. Heide Gluesing-Luerssen.

Title:  Extremal functions in modules of systems of measures

Abstract:  We study Fuglede’s p-modules of systems of measures in condensers in the Euclidean spaces. First, we generalize the result by Rodin that provides a way to compute the extremal function and the 2-module of a family of curves in the plane to a variety of other settings. More specifically, in the Euclidean space we compute the p-module of images of families of connecting curves and families of separating sets with respect to the plates of a condenser under homeomorphisms with some assumed regularity. Then we calculate the module and find the extremal measures for the spherical ring domain on polarizable Carnot groups and extend Rodin’s theorem to the spherical ring domain on the Heisenberg group. Applications to special functions and examples will be provided. Joint work with Melkana Brakalova and Irina Markina.

Lyman break galaxies (LBGs) are often used as prototypes to construct
strongly star-forming galaxies, since the Lyman break signature is
straightforward to identify at z>3 from the ground. However, at z~2,
the Lyman break is located in the UV wavelength range and can only be
observed from space. Until the launch of GALEX, large (wide-field)
ground-based proxy selection methods for LBGs had to be used, which
produce measurable differences from true LBG samples. We will use deep
GALEX and ground based U-images to select a true Lyman break sample of
z~2 LBGs, and investigate the nature of galaxies which produce the IR
background.

The GALEUS (GALaxy Evolution UV Survey) will use public wide-deep data
to study the physical properties of UV-selected star-forming galaxies
at z~2. We propose to investigate the contribution of UV and IR
luminous galaxies to the population of LBGs, using UV to FIR data (0.16
to 500~microns) observed by GALEX, Spitzer, and Herschel, with
supporting optical/IR data from HST+ACS and ground-based surveys. I
will show preliminary results based on spectral energy distributions.

With the recent discovery of the Higgs boson at the Large Hadron Col-

lider, the mechanism through which fundamental particles acquire mass in

the Standard Model of particle physics is now complete. However, the vast

majority of the visible mass of the universe resides in protons and neutrons

which are not fundamental, but composite particles of the quarks and glu-

ons whose interactions are described by Quantum Chromodynamics (QCD).

These strong interactions are responsible for 99% of the proton and neutron

masses, and therefore these bound states of quarks and gluons provide an

ideal laboratory to study QCD and elucidate our understanding of visible

matter in the universe. To that end, one of the primary goals of the STAR

experiment at the Relativistic Heavy Ion Collider is to use spin as a unique

probe to unravel the internal structure and the QCD dynamics of the nucleon

by studying high-energy polarized proton collisions. In this talk, I will dis-

cuss what we have learned about the origin of the proton's spin, emphasizing

recent developments in gluon and antiquark polarization.