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Junior Colloquium – 2018-2019

Thursday, April 11, 2019
TITLE: Geometric Constraints Everywhere
SPEAKER: Meera Sitharam, University of Florida
TIME: 3:40 PM-4:35 PM
ROOM: Ayres 405
The talk will tour 3 modeling scenarios:  supramolecular self-assemblies (such as viruses), sticky-sphere clusters, and material microstructure (composite, or designed for 3D printing).

Happily, as this talk will argue, much of the theory of geometric constraints, combinatorial rigidity and configuration spaces – already heavily utilized in macroscale modeling –  is well-suited to the micro and nanoscale.

Thursday, March 22, 2019
TITLE: Optimal control techniques applied to management of natural resource models
SPEAKER: Suzanne Lenhart, University of Tennessee and National Institute for Mathematical and Biological Synthesis (NIMBioS)
TIME: 3:40 PM-4:35 PM
ROOM: Ayres 405
Optimal control techniques have been used to investigate management strategies in a variety of models for natural resources. Two applications involving FISH and FIRE will be discussed, incorporating the economic impacts.  Harvesting of fishery stock has led to habitat damage. We present a model with spatiotemporal dynamics of a fish stock and its habitat. Techniques of optimal control of PDEs are used to investigate the harvest rates that maximize the discounted value while minimizing the negative effects on the habitat. The number of large-scale, high-severity forest fires occurring is increasing, as is the cost to suppress these fires. We incorporate the stochasticity of the time of a forest fire into our model and explore the trade-offs between prevention management spending and suppression spending.

Thursday, January 31, 2019
TITLE: Statistics, Topology and Machine Learning for Data Analysis
SPEAKER: Farzana Nasrin, University of Tennessee
TIME: 3:40 PM-4:35 PM
ROOM: Ayres 405
Analyzing and classifying large and complex datasets are generally challenging. Topological data analysis, that builds on techniques from topology, is a natural fit for this. Persistence diagram is a powerful tool originated in topological data analysis that allows retrieval of important topological and geometrical features latent in a dataset. Data analysis and classification involving persistence diagrams have been applied in numerous applications such as action recognition, handwriting analysis, shape study, image analysis, sensor network, and signal analysis. In this talk I will provide a brief introduction of topological data analysis, focusing primarily on persistence diagrams. The goal is to provide a supervised machine learning algorithm, the classification, on the space of persistence diagrams. This framework is applicable to a wide variety of datasets. I will present applications in material science, specially classification of crystal structures of High Entropy Alloys.

Thursday, November 29
TITLE: A Panel Discussion on Research Opportunities for Undergraduates in Mathematics and Other STEM Fields
TIME: 3:50 PM – 4:35 PM
ROOM: Ayres 405
This discussion is co-organized with the Math Club.

Thursday, October 18
TITLE: Old analogies in the Calculus of Variations – The Brachistochrone
SPEAKER: Marco Mendez, University of Chicago
TIME: 3:40 PM-4:35 PM
ROOM: Ayres 405
I will tell the story of the Brachistochrone problem. This is one of the oldest variational problems and can be solved only using elementary calculus. I will present in detail Johann Bernoulli’s clever solution, which is based on Fermat’s principle and a variational analogy between mechanics and optics. If time permits, I will briefly discuss a more recent analogy between the theory of phase transitions and minimal hypersurfaces, which will be the subject of my talk in the Geometric Analysis Seminar.

Thursday, October 11
TITLE: Introduction to L-functions
SPEAKER: Daniel Shankman, Purdue University
TIME: 3:40 PM-4:35 PM
ROOM: Ayres 405
L-functions are mysterious complex analytic functions whose zeroes and poles are connected to the behavior of prime numbers.  The most famous L-function is the Riemann zeta function.  First, I will prove some things about the Riemann zeta function in order to investigate the convergence of the infinite sum 1/2 + 1/3 + 1/5 + 1/7 + etc. of the reciprocals of the prime numbers.  Then I will define a Dirichlet L-function and use it to prove that there are infinitely primes of the form 4n+1.  There is a much easier way to prove this, without using any analysis, but the method which I will present, using L-functions, can be generalized to show that there are infinitely many prime numbers of the form an + b, where a and b are integers without any prime factors in common.  This generalization is a theorem originally proved by Dirichlet in 1837, and there is no known proof of this which does not use analysis.