Junior Colloquium
The Junior Colloquium is a series of talks intended for students interested in mathematics or related subjects. Usually offered every other Thursday at 3:35 in Ayres Hall, the talks attract students from a variety of majors on the UT campus. The JC always 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) should go to listserv.utk.edu and add his/her e-mail address to the JRCOLL listserv. The archives of JC speakers, titles, and abstracts are available here.
For those interested in speaking, the ground rules for speakers at the JC are as follows:
1. Talks should be accessible to anyone with a
good understanding of basic calculus.
2. Talks should appeal to a wide audience, which often includes engineering
and other non-math majors.
3. Talks should NOT be surveys of areas of mathematics or career talks.
4. Faculty may give talks as often as they wish, but the same talk may not be
given in two consecutive years (keep your notes for future use!).
The regular meeting time is Thursday at 3:30 pm in Ayres 215, roughly every other Thursday. 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.
Below is the JC schedule so far this year--it will be updated as future talks are scheduled.
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 Ken Stephenson in the Math Department for more information.
Thursday, November 12
TIME: 3:35 – 4:35 p.m.
ROOM: HBB 102
SPEAKER: Professor Conrad Plaut
TITLE: “A pair of geometric inequalities”
ABSTRACT: We will consider two questions: (1) What is the maximum area that can be bounded by a closed curve of length 1 in the plane, and which curves, if any, realize this maximum? (2) What is the maximum area of a convex surface in 3-space having diameter 1, and which surfaces, if any, realize that maximum? (I will explain what a convex surface is—the concept is very simple and intuitive). The answer to the first question was known to the Greeks, although it wasn’t until the latter half of the 19th century that the statement was really proved, by Weierstrass. The answer to the second question is still unknown. In 1955 A.D. Alexandrov conjectured that the area is bounded above by pi/2, and he exhibited a very simple surface that realizes this area. But this surface, unlike the circle, is not smooth, and not even really a convex surface. At the present time it is not even known whether there is a maximum area, or, if there is one, if it is realized by a smooth surface. After almost 55 years this very interesting question is still waiting to be solved.
Thursday, October 29
TIME: 3:35 – 4:35 p.m.
ROOM: HBB 102
SPEAKER: Professor Suzanne Lenhart
TITLE: “The power of optimal control: from confining rabies to improving CPR”
ABSTRACT: This talk will present optimal control of two examples which are discrete in time. The first example involves difference equations that model cardiopulmonary resuscitation. The goal is to design an external chest and abdomen pressure pattern to improve the blood flow in the heart in standard CPR procedure. The second example is an epidemic model for rabies in raccoons on a spatial grid. The goal is to find the optimal distribution pattern for vaccine baits to slow the spread of the disease.
Thursday, October 22
TIME: 3:35 – 4:35 p.m.
ROOM: HBB 102
SPEAKER: Dr. Sharon Bewick, NIMBioS
TITLE: Modeling Local Community Responses to Climate Change
ABSTRACT: I will be talking about the development of a mechanistic mathematical framework that models both competitive and mutualistic interspecific interactions with the goal of interpreting community dynamics and altered community structure under a warming regime. In particular, I will focus on climatic change as it affects ant communities in the temperate forests of eastern North America. To that end, the primary interspecific interactions that I will be discussing will relate to competition between ants for food resources.
Previous models have considered competitive interactions between ants in terms of dominance-discovery tradeoffs. Certainly, global climate change may perturb both the dominance relationships between species and/or the discovery abilities of individual species, and this may have predictable consequences on community composition. More recently, however, several empirical studies have suggested that a dominance-thermal tolerance tradeoff may be more important than a dominance-discovery tradeoff, at least in the temperate forests of eastern North America. With this tradeoff, the impact of global climate change is even more obvious. I will therefore discuss the development of mechanistic mathematical models that capture the features of dominance-thermal tolerance tradeoffs and the possibility of using these models to predict community composition, both under current climatic conditions and under a warming regime. Finally, I will briefly touch on aspects related to modeling the impact that the ant community has on the plant community through ant-plant seed dispersal mutualisms.
Thursday, October 8
TIME: 3:35-4:35 p.m.
ROOM: Haslam Business Building, 102
SPEAKER: Assistant Professor Fernando Schwartz
TITLE: A taste of differential geometry: The Gauss-Bonnet theorem
ABSTRACT: Will give a proof of one of the most beautiful theorems in differential geometry. Vector calculus is the only prerequisite for this talk.
Thursday, September 17
TIME: 3:35 -- 4:35 p.m.
ROOM: HBB 102
SPEAKER: Dr. Blair D. Sullivan, Oak Ridge National Laboratory
TITLE: "Why Graph Theory is Strongly-Connected"
ABSTRACT: Worried about the job market, but still want to be a mathematician? Perhaps graph theory is just what you need. Come hear how it prepares you for a diverse set of careers - including matchmaking, mapmaking, and truck driving! On a more serious note, this talk will provide a motivated introduction to graph theory, highlighting several active research areas, connections to other branches of mathematics, and real-world applications (including Facebook, as illustrated above).
Thursday, September 10
TIME: 3:35 – 4:35 p.m.
ROOM: HBB 102
SPEAKER: Professor Mark Meerschaert, Michigan State University
TITLE: “The Fractal Calculus Project”
ABSTRACT: Fractional derivatives are almost as old as their integer-order cousins. Recently, fractional derivatives have found new applications in engineering, physics, finance, and hydrology. In physics, fractional derivatives are used to model anomalous diffusion, where a cloud of particles spreads ...expanded abstract
The entire talk will be accessible to advanced undergraduate students.