|Index||This week||Schedule & abstracts||Past talks||Organizer notes||Graduate page|
|Jan 16||Priya Prasad||Organizational Meeting|
|We're seeking out speakers for this year's Graduate Student Colloquium.|
|Jan 23||Jonathan Taylor||On the Diameter of a Family of Graphs|
|We present the definition of a connected domination critical graph. We then proceed to show that the diameter of any such graph is bounded by its connected domination number. Furthermore, we give examples of graphs with diameter d, connected domination number k, and $2 \leq d \leq k$, with the exception of $d=3$ and k even.|
|Jan 30||Angel Chavez||Lie Groups (with Applications)|
|I will give an elementary and brief introduction to the notion of a Lie group. I will provide several examples of Lie groups. Finally, I will conclude with some nice applications to physics.|
|Feb 6||Matt Thomas||Analyzing Conceptual Gains in Introductory Calculus with Interactively-Engaged Teaching Styles|
Research in mathematics and physics education indicates that students in interactively engaged classrooms are more successful on tests of basic conceptual knowledge than students in traditional lecture-based classrooms. Despite this, undergraduate mathematics courses are largely dominated by lectures in which students take a passive role. While studies involving tools such as Peer Instruction and the Force Concept Inventory have encouraged changes in the ways introductory physics is taught, changes in mathematics instruction have not occurred to the same extent.
Using the recently developed Calculus Concept Inventory together with video and audiotape analysis of introductory Calculus classes, we investigate specific aspects of Interactively-Engaged teaching and determine which aspects of Interactively-Engaged teaching are most correlated with conceptual learning.
In this presentation, I will describe the coding protocol that was developed for the 15 videos, using 5 instructors. I will also present results demonstrating the relationship between types of interactions occurring in the classroom and conceptual learning, as measured by the Calculus Concept Inventory.
|Feb 13||Nick Henscheid||An Introduction to Optimal Transport Theory|
|The goal of this talk is to introduce the audience to the tools of optimal transportation theory and to briefly mention some of its more striking applications. The theory dates to a simple variational problem posed by Gaspard Monge in 1781, but it has in the past 30 years bloomed into a powerful technique that continues to illuminate a wide variety of problems in both pure and applied mathematics. Among these applications are fluid dynamics, geometric inequalities, differential geometry, economics, nonlinear PDE, dynamical systems, image processing, star formation, optics, mathematical biology, and even the state of the early universe. Basic familiarity with real analysis is assumed.|
|Feb 20||Nellie Gopaul||Statistical Techniques for Neuron Classification from 2-d Morphological Characteristics|
|Finding groups within data has applications to a variety of interesting (and job-rich) fields such as handwriting recognition, gene-expression categorization and insurance fraud detection. In this talk, I will describe several pattern-detection algorithms and show their results when applied to a data set of fruit fly neurons. Come for the bagels, stay for the kernel tricks.|
|Feb 27||Michael Bishop||Quantum Mechanics in Bernoulli Disorder|
|Quantum mechanics is a theory developed to explain both particle and wave-like properties of small matter such as light and electrons. The consequences of the theory can be counter-intuitive but lead to mathematical and physical theory rich in fascinating phenomena and challenging questions. The theory asks many seemingly unrelated questions: If an electron travels through an imperfect copper wire with random impurities, how do the random impurities affect the electron's travel? If measurement of individual particles is theoretically impossible, should models explicitly identify particles? What are the implications of changing this in a given mathematical model? How do quantum mechanical systems differ when particles interact? The list of questions goes on and on. My research studies these systems in random environments, asking questions about the interplay in quantum multi-particle systems between the localization due to a random external potential and the delocalization due to a weak and repulsive interaction. This talk will introduce the subject and outline my mathematical results for single-particle behavior and multi-particle mean-field behavior for ground states in Bernoulli-distributed disorder.|
|Mar 6||Gleb Zhelezov||Solving PDEs Using Bacteria|
|PDE models of physical processes often have the unphysical property of blowing up in finite time. In this talk, we will discuss how to apply a particle method (similar to the particle-in-cell method) for overcoming this issue in a model which describes the propagation of mold feeding on bacteria. Necessary tools, like the Fokker-Planck equation, will be introduced. As in other graduate colloquium talks, applications to physics will be pushed off to the last slide and not discussed.|
|Mar 20||Ryan Coatney||The Gauss Circle Problem|
|The Gauss circle problem is one of the earliest, and perhaps simplest, problems from the early days of analytic number theory. Simply stated, the Gauss circle problem is deriving an estimate for $N(r)$, the number of integer lattice points inside a circle of radius $r$. We will discuss the importance of this problem and several generalizations that have been studied in the past 150 years.|
|Mar 27||Mandi Schaeffer Fry||Irreducible Representations of Finite Groups of Lie Type: On the Irreducible Restriction Problem and Some Local-Global Conjectures|
This is a "dry-run" for my defense! I'll begin by trying to make sense of the title, and then talk about the two main problems in my dissertation, in which I investigate various problems in the representation theory of finite groups of Lie type, with primary focus on the symplectic group $Sp(6, 2^a)$:
Given a subgroup $H \lt G$ and a representation $V$ for $G$, we may view $V$ also as a representation for $H$. However, even if $V$ is an irreducible representation of $G$, $V$ may (and usually does) fail to remain irreducible as a representation of $H$. We classify all pairs $(V,H)$, where $H$ is a proper subgroup of $G=Sp_6(q)$ with $q$ even, and $V$ is a representation of $G$ in characteristic other than 2 which is absolutely irreducible as a representation of $H$. This problem is motivated by the Aschbacher-Scott program on classifying maximal subgroups of finite classical groups.
The local-global philosophy plays an important role in many areas of mathematics. In the representation theory of finite groups, the so-called ``local-global" conjectures relate the representation theory of $G$ to that of certain proper subgroups, such as the normalizer of a Sylow subgroup. One might hope that these conjectures could be proven by showing that they are true for all simple groups. Though this turns out not quite to be the case, some of these conjectures have been reduced to showing that a finite set of stronger conditions hold for all finite simple groups. We show that $Sp_6(q)$, $q$ even, is ``good" for these reductions.
|Apr 10||Priya Prasad||Encouraging Students to Think Mathematically|
|Recently, K-12 schools nationwide have begun adopting the Common Core Standards for Mathematics. In the Common Core, there is a list of 8 Mathematical Practices that students should develop. This talk introduces those practices and offers suggestions for how university instructors (such as TAs) can encourage them in their courses.|
|Apr 17||Megan McCormick||Hurwitz numbers and integrals over the unitary group|
|In the late 1800s, Hurwitz posed the following question: Given a set of fixed ramification points on the 2-sphere with fixed ramification types, how many non-isomorphic ramified coverings are there? This problem has not been solved in full generality, but Hurwitz himself and others since him have found formulas to enumerate specific classes of such coverings. The Hurwitz numbers, as they are now called, show up in many areas of mathematics. I will go into detail about how they are related to calculating derivatives of integrals over the unitary group.|
|Apr 24||Michael Bishop, Martin Leslie, Mandi Schaeffer Fry, Matt Thomas||Job search panel|
|Planning to graduate in the next one, two or three years (or ever)? Wondering about the job search process? Talk to four grad students who have successfully navigated the system and are about to start a variety of jobs!|
|May 1||Eric New||Title TBD|
|Abstract to be determined.|