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Department of Mathematics & Statistics


Academic Year 2017-2018

Speaker: Dr. Jireh Loreaux, SIUE

When: Friday Dec 1, 3:30 pm - 4:30 pm

Where: PH 0405

Title: Diagonalization of matrices and the Pythagorean Theorem


There is a natural interpretation of the Pythagorean Theorem in terms of elementary linear algebra. While this interpretation is straightforward, it leads to a much more general statement in operator theory with surprising consequences. In this talk, we explore the relationship between these statements and the diagonalization of matrices by means of a unitary matrix which is a small perturbation of the identity. As part of this presentation I will present a problem which is suitable for an undergraduate research project.

Speaker: Dr. Gabe Spalding of Illinois Wesleyan University

When: Friday, October 20th from 4:00 - 5:00 pm, happy hour to follow

Where: PH 1302

Professor Spalding received his Ph.D. in Applied Physics from the Harvard School of Engineering and Applied Sciences. His research tries to be serious, but is routinely rephrased in terms of playful sci-fi references, from creating a functional sonic screwdriver to Star Trek-style holodecks (computer-generated holograms that are not merely ethereal images; they have corporeal substance) and acoustic tractor beams (research awarded a 2014 Platypus Award from Mental Floss magazine and named a “Top 10 Breakthrough" of the year by Physics World magazine). His 2016 work on Faster-Than-Light Imaging experimentally demonstrated creation and annihilation of spot pair images (where one moves forward in time and the other backwards). If that's not spooky enough for you, check out his work on "Ghost Imaging" using quantum mechanically entangled photon pairs, where the photons incident upon the detecting camera have never interacted with the object imaged. He works, as an activist, to develop and support lab instruction.

Speaker: Dr. Jim Gill of Saint Louis University

When: Friday, September 22, 4:00-5:00pm, happy hour to follow

Where: EB 0165

Title: Finite Dimensional Random Objects

Abstract: We discuss research by several investigators into random objects made of infinitely many smaller pieces and their geometry.  It turns out that many of them have a planar geometry due to a strange property of finite dimensional metric spaces.

Academic Year 2016-2017

Speaker: Dr. James Parish

When: Friday, Apr 21, 2017, 3:00-4:00pm, happy hour to follow

Where: Vadalabene Center Room 2306

Title: Simple Closed Geodesics on Rectangular Prisms


The study of geodesics – locally shortest paths – has been a significant topic in geometry for a very long time. On smooth surfaces, it is a complicated matter of analysis, involving the solution of a pair of nonlinear differential equations. In the last few decades, the study of geodesics on polyhedra has attracted considerable attention. Here, geodesics are easy to construct; they are composed of line segments crossing the faces of the polyhedron, with passage from one face to the next occurring in a predictable fashion. Attention has focused on the identification of closed geodesics, which return to their initial point and direction; the techniques have an algebraic and combinatorial flavor. In this talk, I will discuss geodesics on rectangular prisms – boxes, so long, so wide, and so high – and provide a complete description of simple (i.e., non-self-intersecting) closed geodesics on these polyhedra.

Speaker: Dr. Andrew Neath

When: Wednesday, Mar 29, 2017, 6:00-7:00pm, happy hour to follow

Where: Vadalabene Center Room 2007

Title: Statistical Modeling for Replication Studies


There is growing concern over the number of scientific findings accepted as truth which then realize failure when the study is replicated. Traditional statistical inference is designed as a look back to how data originates. Perhaps we need to take a better look in anticipation of what data we will we see next. This talk will provide examples of some interesting aspects of statistical problems in analyzing replication studies, and some thoughts on how the information from a single study fits together with what we learn from replication attempts.

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