Colloquium 05/01: Dylan Jager-Kujawa on Automated Propositional Logic Proofs using Gentzen Deduction Trees

On Monday, May 1, at 3:30 pm in Math Building 357, Dylan Jager-Kujawa will be giving a presentation on computer aided proofs titled Automated Propositional Logic Proofs using Gentzen Deduction Trees as part of an Honors Project. This talk is open to all faculty and students.

Abstract: In the mid 1930s, Gerhard Gentzen devised an algorithm to prove propositional logic theorems. Gentzen’s method is similar to previous algorithms, in that it attempts to search for counterexamples to disprove a theorem, however it differs in that it breaks propositions into a number of sequents, each containing assumptions and conclusions.

While this results in a somewhat more intuitive proof, it has the added benefit of being very well suited to implementation by a computer. The use of trees, as well as a well-defined set of permitted operations, makes implementation of this algorithm far more natural than those of Gentzen’s peers. (Flyer in PDF form)

 

 

 

Colloquium 04/26: Dr. Jacob Turner on Going With the Flow: Statistical Considerations in Cell Composition Analysis

As part of the R. W. Yeagy Colloquium Series, Wednesday, April 26 at 3:00 PM in Math Building 357, Dr. Jacob Turner will be speaking about “Going With the Flow: Statistical Considerations in Cell Composition Analysis.”

Abstract: Flow cytometry (FCM) is a single cell technology that is routinely applied to quantify and evaluate cell populations present in biological samples.  In a typical FCM study, thousands of cells are used to determine the proportion of important cell subpopulations and the difference in the proportions between diseased groups or drug treatments is often hypothesized.  The process of identifying cell populations has been rigorously explored; however, the statistical analysis of data derived from these processes has not received much attention.  This presentation will introduce the general process of an FCM experiment, illustrate some of the distributional properties exhibited by FCM derived data, and summarize an alternative modeling and testing procedure. (flyer in PDF form)

Colloquium 04/10: Lizzy Huang on Harmonic Maps with Repulsive Potentials

As part of the R.W. Yeagy Colloquium Series, on Monday, April 10 at 2:30pm in Math Building 357, Lizzy Huang will speak on Harmonic Maps with Repulsive Potentials.

Abstract: Many questions in topology and physics can be expressed in terms of finding a function f  between a curved space M (the domain) and another curved space N (the target) which minimizes a natural energy functional: \int_M |df|^2. Functions that minimize this energy are called harmonic maps. One method to obtain a harmonic map is to consider a family of maps  which follow a path of ‘steepest descent’. In this talk, I will discuss a modification of this approach in which an unbounded potential energy is added to the total energy. Then I will discuss the behavior and singularities of the limiting maps in cases of special significance to topology. I will only assume knowledge of multivariable calculus and linear algebra for this talk.

Colloquium 04/07: Dr. David Lax on “An Order Filter Model for the Algebraic Relations Defining the Grassmannian and its Cousins”

As part of the R.W. Yeagy Colloquium Series, Dr. David Lax will be speaking at 1:30pm on Friday, April 7 in Math Building 357 on An Order Filter Model for the Algebraic Relations Defining the Grassmannian and its Cousins.

Abstract: The Grassmann manifolds consist of planes in a vector space and have coordinates given by determinants. These coordinates are naturally partially ordered, and the relations among the coordinates are straightening laws–meaning they respect this order.  For any of the Grassmann manifolds’ cousins, the ‘minuscule flag manifolds,’ we present a model for its coordinates that uses colored partially ordered sets and some straightening laws shared by these coordinates.

Colloquium 3/8: Ryan Jensen on Topological Data Analysis

On Thursday March 9th at 2 PM in Math Building 357, Ryan Jensen from the University of Tennessee will be talking about “Topological Data Analysis”.

Abstract: What is the shape of the following collection of data points (original image from Persistence Theory: From Quiver Representations to Data Analysis by Steve Y. Oudot)?

 

It depends on the “scale” from which the points are viewed. From a very small scale, all that is visible is a point; from a larger scale, there are multiple “B’s”; at an even larger scale, an “A” appears; finally, when viewed from a great distance, there is nothing but a blob.

In this talk we will give an introduction (accessible to undergraduates) to persistent homology, which is a tool from algebraic topology used to study the shape (homology) of data and through which scales that shape persists. We will look at the persistent homology of the above example as well as real life examples, including the shape of protein distribution in medicated cells. Finally, we will briefly discuss new results from large scale geometry which could be useful in determining other persistent properties of a data set.

Colloquium 03/06: Travis Russell on “Abstract Characterizations in Operator Theory and Some Applications”

On Monday March 6th from 2:30-3:30 PM in Math 357, Travis Russell from the University of Nebraska will be talking about “Abstract Characterizations in Operator Theory and Some Applications.”

Abstract characterizations occur frequently in mathematics. Roughly speaking, an abstract characterization is a way of extracting the essential structure of a mathematical object that normally exists in a highly structured and complex setting. In this talk, I will provide an overview of some abstract characterizations that occur in the theory of operator spaces. I will illustrate how quantum physics has motivated some of these ideas and how these ideas are now contributing to the theory of quantum computation. (Flyer in PDF form)

Colloquium 2/27: Quinn Morris on “From Theory to Practice: Boundary Value Problems and Prokelesia Arginata”

As part the R.W. Yeagy Colloquium Series, Mr. Quinn Morris will be talking about “FROM THEORY TO  PRACTICE: BOUNDARY VALUE PROBLEMS AND PROKELISIA ARGINATA at 2:30 PM on Monday February 27th in Math 357.

Abstract: In a first course in ordinary differential equations, one often treats initial value problems and is able to show existence & uniqueness of solutions when f is “nice”. In this talk, we will instead consider boundary value problems, and observe that even for very “nice” functions f, existence and uniqueness is a much more complicated question. In the second half of the talk, we will discuss some boundary value problems arising from population models with density dependent dispersal on the boundary. The NSF-funded study of these models is on-going work with a group of undergraduates, graduate students, and faculty at three universities. (flyer in PDF form)