**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. Dustin Cartwright in the Math Department for more information.

**Thursday, February 27th**

Title: Least-area Polyhedral Tiles of Spaces

*Speaker: Frank Morgan, Williams College*

Time: 3:40 pm

Room: Ayres 405

Abstract: * *The cube is the least-area unit-volume polyhedron of six sides. What about other numbers of sides? We'll discuss what's known and make some guesses about other cases.* *

**Thursday, February 20th**

Title: Classification and Symmetries of Knots**
Speaker: Morwen Thistlethwaite
**TIME: 3:40 pm

ROOM: Ayres 405

Abstract: For the topologist, a (classical) knot is a smooth simple closed curve in 3-dimensional space. Two knots are equivalent if one can continuously deform one to the other: stretching and bending are allowed but cutting is prohibited. We can picture a knot as a length of rope with its ends glued together, and with a small amount of practice we can draw pictures of knots, seemingly making the subject approachable. However, knot theory is teeming with problems that are easy to ask and very hard to solve. Even the problem of deciding whether two given knots are equivalent can be tricky, and has caught people out over the years. A very useful approach is to transform a knot theoretical problem into a (hopefully)

easier problem in algebra. Some of the simpler algebraic invariants will be presented.

**Thursday, February 6th**

Title: The Traveling Salesman Problem**
Speaker: Vyron Vellis
**TIME: 3:40

ROOM: Ayres 405

Abstract: One of the most famous problems in computer science is the Traveling Salesman Problem (TSP) which asks the following question: “Given a finite list of cities, what is the shortest possible route a traveling salesman has to take to visit each city?”. The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. In analysis, we asked ourselves a more general question: “Given again a list of cities (possibly infinite, even uncountable, or better, a continuum!), when can our traveling salesman travel them all in finite (optimal, in some sense) time?”. This question (known as the Analyst’s TSP) has been one of the core questions of geometric measure theory and its applications span almost all fields of modern analysis. In this talk, we will discuss this problem, its solution and related results.

**Thursday, November 14th**

TITLE: Bose-Einstein condensation of an Ideal Gas

**SPEAKER: Maximilian Pechmann**

TIME: 3:40 PM

ROOM: Ayres 405

Abstract: A Bose-Einstein condensate is a state of matter of a Bose gas and an exotic quantum phenomenon. It was theoretically predicted by Bose and Einstein in 1924, but was long considered a mathematical curiosity without practical use. However, since the experimental observation of such a condensate in 1995, Bose-Einstein condensation is a field of research of great interest. Although this phenomenon is well understood from a physical point of view, its mathematically rigorous description is still incomplete. We present a mathematical precise treatment of the Bose-Einstein condensation in the simple case of an ideal Bose gas in a box.

**Thursday, October 10**th

Title: Hydrocode Modeling of Impact Craters

* Speaker: Wendy Caldwell*,

*Arizona State University*Room: Ayres 405

Time: 3:35pm

Abstract: Asteroid 16 Psyche is the largest M-type (metallic) Main Belt Asteroid (MBA). Radar albedo data indicate Psyche’s surface is rich in metallic content, but estimates for Psyche’s bulk structure vary widely. Psyche has two large impact structures in its Southern hemisphere. In this work, we present results from 2D and 3D simulations of the formation of these craters using the FLAG hydrocode, developed and maintained by Los Alamos National Laboratory. FLAG has been verified and validated for impact cratering simulations, with good agreement to theoretical and experimental results. Through quantitative comparison of the simulated crater dimensions with measured values, our models suggest that Psyche is largely composed of porous, metallic material. In addition, our work indicates that the impacts were likely oblique, with angles at least 45 degrees from vertical.

Previous Junior Colloquiums: