**Junior Colloquium**

The Junior Colloquium is a series of talks intended for students interested in mathematics or related subjects, started in the fall of 2002. The JC takes place roughly every other Thursday at 3:30 in the fourth floor colloquium room of Ayres Hall. The JC attracts a large and diverse audience, and students at all levels (and even faculty) are invited to attend. Anyone interested in receiving e-mail announcements about the JC (who is not already on the UTKMATH, seminarlist or pmail e-mail lists) will find information on the Tennessee Today web site or on our weekly seminar list.

For those interested in speaking, here are some hints about what is expected:

1. Talks should be accessible to anyone with a good understanding of basic calculus. If substantial portions of the talk require a higher level of mathematics then the necessary background should be mentioned in the abstract.

2. Ideally, talks should appeal to a wide audience, which often includes engineering and other non-math majors.

3. Faculty may give talks as often as they wish--keep your notes/slides for future use! However, the same talk may be given at most once in any two consecutive years.

4. It is OK to use a talk to advertise an area of mathematics or a career field, but the main purpose of the talk should be to to tell an interesting story about problem(s) in pure or applied mathematics.

Anyone who would like to receive notices about the JC should go to listserv.utk.edu and add his/her e-mail address to the JRCOLL listserv.

Previous subjects have ranged from quaternions to soap bubbles to tornadoes, and previous speakers have included UT faculty and invited visitors from other universities. Potential speakers should contact Dr. Ken Stephenson in the Math Department for more information.

**Thursday, March 8**

Title: Asymptotic error analysis

** Speaker: Brian Wetton, University of British Columbia **Time: 3:40 PM-4:35 PM

Room: Ayres 405

When computing numerical approximations to problems with smooth solutions using regular grids, the error can have additional structure. The historical example of the Euler-McLaurin formula for the approximation of integrals with the trapezoidal rule is shown. This expansion can be used to justify Richardson extrapolation of the approximations leading to the Romberg integration formula. For approximation of differential equations, similar error expansions can be derived. For standard methods on uniform grids, an expansion for the error can be constructed that is regular in the grid spacing. For some other methods, numerical artifacts (boundary layers and errors that alternate in sign between adjacent grid points) can also be present. Identifying the types of errors that are generated by a given scheme and the order at which they occur is called Asymptotic Error Analysis. Several examples are shown, including the error analysis of cubic spline interpolation which is shown to have numerical boundary layers. A numerical artifact from an idealized adaptive grid with hanging nodes used to approximate a simple elliptic problem is presented.

Join us for Pizza in A 408 at 3:15, but bring your drink.

**Thursday, February 8**

Title: How to teleport a goat in five easy steps

**Speaker: Remus Nicoara, University of Tennessee **

Time: 3:40 PM-4:30 PM (Arrive at 3:20 for pizza in Ayres 408)

Room: Ayres 405

We will discuss the mathematics behind the (theoretical) quantum teleportation of a goat. An important role in this process is played by Hadamard matrices, which are chessboard-like patterns of colors satisfying certain rules. Other applications of Hadamard matrices will also be presented.

**Thursday, November 2**

Title: Zombie Attack! Modeling the Dynamics of a Zombie Apocalypse

**Speaker: Dr. Christopher Strickland, UTK **

Time: 3:40-4:35pm

Room: Ayres 405

Abstract: In this talk, I present several differential equation models for zombie invasion and analyze them to determine the fate of mankind. Largely based off the 2009 paper "When Zombies Attack!: Mathematical Modelling of an Outbreak of Zombie Infection" by Munz et al., this talk will serve as an introduction to epidemiological modeling and present basic dynamical systems analysis for nonlinear systems. It will be of particular interest to any students currently taking MATH 231 or especially MATH 431, since the simplest zombie model is easily analyzed by hand and can serve as an example of Jacobian eigenvalue/eigenvector methods. There will also be plenty of zombie pictures.

Pizza will be served in A 408 @ 3:15, bring your drink.

**Thursday, October 12**

Title: Transionospheric Synthetic Aperture Imaging

**Speaker: Dr. Erick Smith, US Naval Research Laboratory**

Time: 3:40-4:35pm

Room: Ayres 405

* Note: Math majors who would like to join the speaker for a lunch or dinner (to be scheduled) should get in touch with Ken Stephenson, kstephe2@utk.edu.

Synthetic Aperture Radars (SAR) use microwaves to image the surface of the Earth (or other planets) from above, usually by airplanes or satellites. From the standpoint of mathematics, SAR imaging is an inverse problem of reconstructing certain characteristics of the target from the information contained in the radio waves reflected off this target. It can be done at nighttime and even through cloud cover. Radars that operate in the UHF and VHF bands, with frequencies of hundreds of MHz, also can penetrate foliage and the ground to see more, but if the radar is located on a satellite, images in these frequencies are also susceptible to distortions caused by the ionosphere, a dynamic region of the atmosphere containing a high concentration of ions and free electrons.

In this talk, we will look at problems associated with spaceborne synthetic aperture imaging in these frequencies and the mathematical ways to correct for the distortions, with the primary methodology stemming from asymptotic analysis and perturbation theory. This is done without prior knowledge of the current state of the ionosphere, which is both inhomogeneous and anisotropic as well as constantly changing in time and having both deterministic and stochastic components. We also look at anisotropy in the target and how certain material parameters can be determined from the phenomenologically constructed scattering matrix. Besides mathematicians, the presentation should also be of interest to those with physics and electrical engineering backgrounds.

Published earlier this year and the basis for this talk, Transionospheric Synthetic Aperture Imaging is a follow-up to the speaker’s 2013 dissertation, SAR Imaging Through the Earth’s Ionosphere, incorporating the contents of the dissertation as well as work that came before it and afterwards.

**Thursday, September 21**

Title: Generatingfunctionology

**Speaker: Carl Wagner, UTK**

Time: 3:40 pm – 4:35

Room: Ayres 405

Abstract: We'll see how multiplying various power series leads to the solution of many interesting problems in enumerative combinatorics.

Pizza will be served at 3:20 in A 408. Please bring your own drink.

**Thursday, September 7**

Title: TBA

**Speaker: Sergey Gavrilets, Distinguished Professor, EEB/Math**

Time: 3:40 pm – 4:35, Arrive at 3:15 for pizza

Room: Ayres 405

Pizza will be served at 3:15 in A 401. Please bring your own drink.

Previous Junior Colloquiums: