Jay Hineman will be visiting the department to give a talk about applying for jobs in academia and industry. Jay is a 2012 UKY Math PhD alumni who now works for a company called Geometric Data Analytics, Inc.

Title: Riemann-Like, Super-Lebesgue

Abstract: The gauge integral is a slight modification of the definition of the Riemann integral that addresses some deficiencies in the Riemann and Lebesgue integrals. We define and examine some examples of gauge integration, and illustrate some of its advantages over the Riemann and Lebesgue integrals.

Title: Mathematicians Have Always Been... Interesting

Abstract: Have you ever looked around a room of mathematicians and thought, "Wow, what a collection of people!"? And what about math itself? There are scores of strange things that come up all the time. It turns out that neither of these phenomena is a new development; there are many obscure (and not so obscure) historical examples of intriguing mathematicians who came up with weird math. In this lighthearted trip through the last 3000 years, we will explore and appreciate some of these accomplishments.

Title: Introduction to Quantum Computing

Abstract: This talk will be about basic notions in Quantum Computing such as quantum bits, quantum gates, entanglement, and measurements. I will describe and discuss Quantum Teleportation, and if time permits, I will give a short overview on Quantum Error-Correction.

Title: Just your average American: How NPR inspired me to learn about Orbifolds

Abstract:   First introduced by Satake as V-manifolds, Orbifolds, are generalizations of manifolds and can be thought of as a quotient space with isolated singularities. Orbifolds are found in many areas of mathematics including geometry, topology, music theory, and string theory. In this talk, we will build up to and introduce orbifolds, discuss some examples, and explore the juicy history of pinball. 

P.S. - If you would like to read about how the name came to be, it is quite entertaining: 

"The origin of the word “orbifold”: the true story. Near the beginning of his graduate course in 1976, Bill Thurston wanted to introduce a word to replace Satake’s “V-manifold” from [12]. His first choice was “manifolded”. This turned out not to work for talking - the word could not be distinguished from “manifold”. His next idea was “foldimani”. People didn’t like this. So Bill said we would have an election after people made various suggestions for a new name for this concept. Chuck Giffen suggested “origam”, Dennis Sullivan “spatial dollop” and Bill Browder “orbifold”. There were many other suggestions. 5 The election had several rounds with the names having the lowest number of votes being eliminated. Finally, there were only 4 names left, origam, orbifold, foldimani and one other (maybe “V-manifold”). After the next round of voting “orbifold” and the other name were to be eliminated. At this point, I spoke up and said something like “Wait you can’t eliminate orbifold because the other two names are ridiculous.” So “orbifold” was left on the list. After my impassioned speech, it won easily in the next round of voting."

- From Lectures of Orbifolds and Reflection groups by Michael W. Davis

As always, pizza will be there at 4 and the talk will start at 4:15. 

Title:    Non-Vanishing Homology of the Matching Complex

Abstract:     A matching on a graph G is any subgraph where the maximum vertex degree is 1.  Since edge-deletion preserves the property of being a matching, the set of all matchings on G forms a simplicial complex M(G).  We will survey results on the lowest non-vanishing homology group for M(K_n) and, time permitting, discuss the extension of these results to more general graphs.  ​This is a practice talk for my qualifying exam, but no prior familiarity with simplicial complexes nor homology is assumed.

Pizza at 4:00 p.m., talk at 4:15 p.m.

Title:  Derangements, discrete Morse theory, and the homology of the boolean complex

Abstract:  The boolean complex is a construction associated to finite simple graphs. We summarize a matching which shows that this complex is homotopy equivalent to a wedge of spheres, and the number of these spheres is related to the boolean number, a graph invariant. To better understand this structure, we use a correspondence between derangements and basis elements and compute the homology of the boolean complex for several specific examples. A basic knowledge of discrete Morse theory may be helpful but is not necessary.

Pizza at 4:00 p.m., talk at 4:15 p.m.

Title:  An Introduction to Differential Forms

Abstract:  The theory of differential forms is a beautiful subject that has particular importance in geometry, topology and physics.  Our focus will be on how differential forms provide a better approach to multi-variable calculus.  Specifically, we will see that many ostensibly unrelated results are unified using differential forms.  Time permitted, we will introduce de Rham cohomology, a cohomology theory based on differential forms.

Title:  Gauss's Golden Theorem (Quadratic reciprocity)

Abstract:  For which odd primes is the congruence $x^2\equiv 0 \mod p$ soluble? The quadratic reciprocity is a marvelous theorem in number theory that deals with this question. We will present examples and a proof of the quadratic residue law (Time permitting).

Title:  Coding Theory and Subspace codes

Abstract:  In this talk I will give a basic introduction into the ideas of coding theory and subspace codes. Then I will give a few examples of constructions of subspace codes and show a theorem which can be used to link these codes. I will end on the idea of decoding particularly the linkage construction. This should be an introductory talk, no previous coding theory knowledge required.