Abridged Version

Invited Talks

  1. Visualizing the Limiting Behavior of Iterated Conformal Mappings (Mar 2015), Department Lectures, Department of Mathematics and Computer Science, Rhode Island College. (slides | TeX Stylesheet)
    Abstract
    The aim of this talk is to discuss Curt McMullen's lim software, a tool which allows users to visualize the limiting behavior of iterated Möbius transformations. Overall, the talk will be broken into (roughly) three parts: First, there will be a (generally self-contained) review of the necessary mathematical background; next, the softwar itself will be discussed with special emphasis on what's happening "behind the scenes"; finally and as time permits, there will be a discussion regarding some limitations (get it?!) and possible generalizations of the software.

    The talk will be accessible to anyone with undergraduate exposure to complex analysis and elementary group theory and will contain a diverse enough collection of information to appeal to those interested in either math or computer science. Everyone is welcome.

Local & Miscellaneous Talks

  1. The FunctionSpaces Project: (A Step Towards) Making Abstraction Computable (Aug 2015), FunctionSpaces Team + UIUC Math Faculty. (slides)
    Description
    For most of the 2015 year, the math component of my "math content developer" position at Wolfram consisted of the FunctionSpaces project, an atttempt to "teach" WolframAlpha (W | A) about function spaces. This presentation was the second of my company-related presentations of the progress of the project and was targeted at a "local" (to Urbana) professoriate to elicit responses, feedback, etc.
  2. Computability in Pure Mathematics: An Entity-Property Framework for Function Spaces (Mar 2015), WolframAlpha Scientific Content Group. (slides)
    Description
    For most of the 2015 year, the math component of my "math content developer" position at Wolfram consisted of the FunctionSpaces project, an atttempt to "teach" W | A about function spaces. This presentation was the first of my company-related presentations of the progress of the project.
  3. The Quest for Reebless Foliations in Sutured 3-Manifolds (Dec 2014), Advanced Topics Exam (ATE), Florida State University. (slides)
    Description
    This is the presentation component of my ATE and is intended to present the boiled-down version of the details of my prospectus and hence of Gabai's '83 article concerning the existence of Reebless foliations in a large class of 3-manifolds admitting sutured manifold hierarchies. The document details the basics of foliation theory as well as defining sutured manifolds (including hierarchies & decompositions), foliation depth, and a (very (very)) condensed presentation of the proof of one of Gabai's big theorems.
  4. Sutured Manifold Hierarchies and Finite-Depth Foliations (Nov 2014), Topology Seminar, Florida State University. (slides)
    Description
    This will be an introductory talk centered on notions related to finite-depth foliations on 3-manifolds. In this talk, the term "depth" will be defined relative to foliations and numerous examples will be given to help illustrate the concept. In addition, an introduction to sutured manifolds will be given including their decompositions and hierarchies thereof. The talk will conclude with a short summary of results contained in the seminal work of Gabai, one of which includes an algorithm for constructing finite-depth foliations on certain classes of sutured 3-manifolds. Overall, the talk will be very low-level and will feature lots of pictures.
  5. Curvature and the Shape of Space (Oct 2014), 2nd Annual Florida State University Math Fun Day. (slides)
    Description
    A slideshow summarizing various higher geometry concepts for the public / non-mathematicians. A projection was looped onto a wall; no oral presentation was given.
  6. Type Inferencing and Predictability: Probabilistic Models and the Wolfram Demonstrations Project (Aug 2014), 2014 Wolfram Science Summer School, Bentley University, Boston MA. (slides)
    Description
    I spent the majority of the 2014 summer school working with a mentor (Taliesin Beynon) on a project which uses the Wolfram Language (aka Mathematica or M-) to input approximately 5,000 notebooks from the Wolfram Demonstrations Project, to analyze which M- symbols people use and nest most frequently, and to graphically analyze these results. The technology used herein was approached as a building block for potential implementation of a "predictive text" feature in future versions of M-.
  7. An Introduction to Generalized (Complex) Geometry (Apr 2014), Complex Analysis Seminar, Florida State University. (slides)
    Abstract
    The purpose of this talk is to introduce and briefly survey Nigel Hitchin's generalized geometry. This relatively new and blossoming field has proven to be of particular interest in recent years, both with pure mathematicians and theoretical physicists alike. Overall, the talk will contain some brief overview-type results about the general setup of Hitchin's geometry including basic facts, preliminary results (largely without proof), and some discussion about how these ideas generalize the usual differential geometry. Included will be ideas about generalized complex geometry, and it will be shown (in various depths) how results from the geometry of complex manifolds can be generalized to this new setting. As time permits, some ideas about future ideas and additional research thereon may be discussed.
  8. Limit Sets and Applications to Foliations (Apr 2014), Graduate Student Seminar, Florida State University. (slides)
    Abstract
    The purpose of this talk is to discuss various aspects of limit sets with an emphasis (towards the end) to foliation theory. In particular, some basic framework will be laid, followed by a brief topical discussion of Curt McMullen's lim software for graphing limit sets of Möbius groups. As time permits, there will be some discussion about possible extensions of lim and applications to foliation theory. The talk will be given with very few techincal details and will be generally accessible to a casual audience.
  9. Limit Sets and Their Applications (Feb 2014), Topology Seminar, Florida State University. (slides)
    Abstract
    The purpose of this talk is to discuss various aspects of limit sets. In particular, some basic framework will be laid, followed by a somewhat more in-depth discussion of Curt McMullen's lim software for graphing limit sets of Möbius groups. If time permits, there will be some discussion about possible extensions of lim and applications to foliation theory. The talk will be given with very few techincal details and will be generally accessible to a casual audience.
  10. Hyperkähler Manifolds (Nov-Dec 2013), Florida State University. (slides)
    Description
    Short presentation on Hyperkähler manifolds as part of a Fall 2013 FSU course on complex manifolds. Because of time constraints, talk was limited to definitions, examples, and one "proof".
  11. Foliations of Riemannian Manifolds (Nov-Dec 2013), Florida State University. (slides)
    Description
    Short presentation on foliations as part of a Fall 2013 FSU course on Riemannian geometry. Contrary to the title, the topic involved almost no Riemannian geometry whatsoever and instead focused on proving the Frobenius theorem equating integrability with complete integrability and involutivity.
  12. Constructing Complex Manifolds Using Lie Groups (Oct 2013), Complex Analysis Seminar, Florida State University. (slides)
    Description
    This was an ill-prepared discussion on the result and consequences of Prop 2.1.13 of Huybrechts' book which states that the quotient of a free and proper action of a complex Lie group $G$ on a complex manifold $M$ is again a complex manifold. The talk was very elementary and was very bad.
  13. Complex Structures on Manifolds (Oct 2013), Complex Analysis Seminar, Florida State University. (slides)
    Description
    A very basic introduction to complex structures on manifolds. The talk focused on definitions and examples, many of which came from Huybrechts' book.
  14. Function Theory in Polydiscs I & II (Spring 2012), Bowling Green State University. (slides)
    Description
    A two-part in-class presentation summarizing foundational results from Rudin's book Function Theory in Polydiscs.
  15. Investigation of the Qualtitative Behavior of the Equilibrium Points for a Modified Lotka-Volterra Model (2009), given 4 times in various Georgia locations. (slides)
    Description
    A presentation given several times summarizing my undergraduate research efforts.

Posters

  1. Continued Fractions: What They Are, Why They're Important, and Who Really Cares? (Nov 2013), 1st Annual Florida State University Math Fun Day. (poster | handout)
    Description
    A poster/handout combination designed to show basic definitions and properties of continued fractions. These items were the focal point for conversations to be had with general audience, non-mathematician visitors throughout the day. Note that the Wolfram logo is used to signify that some of this information was learned during my 2013 summer internship with Wolfram wherein we "taught" WolframAlpha stuff about continued fractions.
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