We introduce quivers, path algebras and their representations. Then, in the case when our ground field is algebraically closed, we discuss a particular Morita invariant of path algebras arising from finite quivers, the Ext quiver of the category. Through examples we see how to compute the Ext quiver using quiver representations and techniques from linear algebra. We aim to keep the talk accessible to undergraduate and graduate students alike.

Ryan Bianconi UI Mathematics PhD...

From a summer REU at the University of Minnesota, we constructed a solvable lattice model for the dual weak symmetric Grothendieck polynomials in hopes of using such a model to prove related properties of these polynomials, including Cauchy identities and branching rules. We also considered a similar lattice model construction for the weak symmetric Grothendieck polynomials in hopes of proving a Cauchy identity, concluding with a negative result. Moreover, we expand on previous work by...

Digital signatures are an important feature in any encryption/decryption scheme, as it provides a message with integrity, authenticity, and nonrepudiation. The problem occurs when long messages are being exchanged and signatures that are just as long need to be verified. By using hash functions, a ”fingerprint” of the message can be used instead of the message itself for verification, making the process computationally inexpensive. If we consider a single iteration of a general hashing...

John Reppy

The analysis of structure in three-dimensional images is increasingly valuable for biomedical research and computational science.  At the same time, the computational burden of processing images is increasing as devices produce images of higher resolution (e.g., typical CT scans have gone from 128^3 to roughly 512^3 resolutions).  With the latest scanning technologies, it is also more common for the values measured at each sample to be multi-dimensional rather than...

Every ten years, the Census Bureau conducts the Census, a nation-wide tallying of every single individual living in the United States. In addition to helping governments and researchers manage land, understand population trends, and distribute resources, the Census is essential to a key democratic function: drawing electoral districts. The process of drawing electoral districts, called “redistricting,” divides every state in the United States...