2014-2015 Colloquium Series
This Colloquium Series is sponsored by the Math and Computer Science Department. Unless otherwise noted, all talks take place in Jepson Hall, Room 109 at 4 p.m.
Starting at 3:30 p.m. refreshments will be served in the lounge outside of Jepson 212 prior to all talks.
More talks will be added as they are scheduled. Please check back.
A great opportunity to learn about collaborative research with faculty and fellow students!
Hilary Briggs, Cathy Shi, Xiwen Zhou, Weizhi Wu, Melisa Quiroga-Herra, Amber Young (Mentors Dr. Kathy Hoke & Dr. Joanna Wares)
Tedi Aliaj, Sam Bell, John Clikeman, Hayu Gelaw, Uthaipon Tantipongpipat (Mentor Dr. Jim Davis)
Fiona Lynch (Mentor Dr. Lester Caudill)
Yi Guo & Zezhong Chen (Mentor Dr. Bill Ross)
Ningxi Wei & Xinchun Liu (Mentor Dr. Della Dumbaugh)
Ahn Tran (Mentor: Dr. Charlesworth)
Marie Fernandez (Mentor: Dr. Lawson)
Francisco Cuevas and Lingmiao Qui (Mentor: Dr. Shaw)
Jennifer He, Andy Choi, Hadi Abdullah, Omar Farooq, John Keto, Alex Beman (Mentor: Dr. Szajda)
Interested in doing something special during the summer?
Come and see what we have done!
Title: Automated Mathematical Conjecture-making
Abstract: It is now possible for a computer to generate conjectures that are designed to address or advance specific mathematical questions. Computers are already of fundamental utility in many areas of mathematics--and they will soon assistant mathematicians in ways that many have believed to require human intelligence.
We have developed a program, based on a heuristic of Fajtlowicz, that can be used to make invariant-relation or property-relation conjectures for any kind of mathematical object. We will explain how the program works; and illustrate the use of the program mainly in graph theory research---some number theory, matrix theory, game theory, and linear programming conjectures will also be presented.
The program is open source and can be used be students to initiate---via the process of generating conjectures, finding counterexamples, and re-generating conjectures---studies of new mathematical subjects, and even mathematical research. This is joint work with Nico Van Cleemput (Ghent University).
Title: Matrices and Topology
Abstract: In this talk we consider the set of n by n matrices and ask various topological questions about certain of its subsets. The idea is that to answer such questions we need to use various results from linear algebra. We are thus exposed to a connection between two different areas of mathematics. This talk is accessible to anyone who knows linear algebra and basic convergence results for real numbers and n-dimensional Euclidean space.
Title: The Fluid Dynamics of Jellyfish Swimming and Feeding
Abstract: The jellyfish has been the subject of numerous mathematical and physical studies ranging from the discovery of reentry phenomenon in electrophysiology to the development of axisymmetric methods for solving fluid-structure interaction problems. In this presentation, we develop and test mathematical models describing the pulsing dynamics and the resulting fluid flow generated by the benthic upside down jellyfish, Cassiopea spp., and the pelagic moon jellyfish, Aurelia spp. The kinematics of contraction and distributions of pulse frequencies were obtained from videos and used as inputs into numerical simulations.
Particle image velocimetry was used to obtain spatially and temporally resolved flow fields experimentally. The immersed boundary method was then used to solve the fluid-structure interaction problem and explore how changes in morphology and pulsing dynamics alter the resulting fluid flow. For Cassiopea, significant mixing occurs around and directly above the oral arms and secondary mouths. We found good agreement between the numerical simulations and experiments, suggesting that the presence of porous oral arms induce net horizontal flow towards the bell and mixing.
For Aurelia, maximum swim speeds are generated when the elastic bell is driven at its natural frequency.
Title: Torsion Points of Elliptic Curves
Abstract: An elliptic curve is a geometric object with an especially rich mathematical structure. These curves are involved in applications that vary from Wiles' proof of Fermat's Last Theorem to secure web browsing, and the challenge of working with them has captured the interest of mathematicians from Weierstrass to Serre. Despite their complexity, elliptic curves and their basic properties may be defined using only high-school algebra, and many relevant questions can be stated with little additional background. For this reason, they are in a rare position to provide an accessible glimpse of modern mathematics.
This talk will provide an introduction to elliptic curves and then focus on questions related to a class of points known as torsion points. No special mathematical background will be required.
Title: Pi Day Celebration