NEWS in the Department of Mathematic
Lori Ziegelmeier - PhD final examination
Date: Wednesday, May 15, 2013
Place: Weber, 237
Time: 10:00 a.m.
Title: Tools and Techniques in Geometric and Topological Data Analysis
Advisor: Dr. Michael Kirby
Co-Advisor: Dr. Chris Peterson
Dr. James Liu
Dr. Bruce Draper
Abstract: In this dissertation, we consider several topics that are united by the theme of topological and geometric data analysis. First, we consider an application in landscape ecology using a well-known vector quantization algorithm to characterize and segment the color content of natural imagery. Color information in an image may be viewed naturally as clusters of pixels with similar attributes. The inherent structure and distribution of these clusters serves to quantize the information in the image and provides a basis for classification. A friendly graphical user interface called Biological Landscape Organizer and Semi-supervised Segmenting Machine (BLOSSM) was developed to aid in this classification. We consider four different choices for color space and five different metrics in which to analyze our data, and results are compared. Second, we present a novel topologically driven clustering algorithm that blends Locally Linear Embedding (LLE) and vector quantization by mapping color information to a lower dimensional space, identifying distinct color regions, and classifying pixels together based on both a proximity measure and color content. It is observed that these techniques permit a significant reduction in color resolution while maintaining the visually important features of images. Third, we develop a novel algorithm which we call Sparse LLE that leads to sparse representations in local reconstructions by using a data weighted $\ell_1$ norm regularization term in the objective function of an optimization problem. It is observed that this new formulation has proven effective at automatically determining an appropriate number of nearest neighbors for each data point. We explore various optimization techniques, namely Primal Dual Interior Point algorithms, to solve this problem, comparing the computational complexity for each. Fourth, we present a novel algorithm that can be used to determine the boundary of a data set, or the vertices of a convex hull encasing a point cloud of data, in any dimension by solving an optimization problem. In this problem, each point is written as a linear combination of its nearest neighbors where the coefficients of this linear combination are penalized if they do not construct a convex combination, revealing those points that cannot be represented in this way, the vertices of the convex hull containing the data. Finally, we exploit the relatively new tool from topological data analysis, persistent homology, and consider the use of vector bundles to re-embed data in order to improve the topological signal of a data set by embedding points sampled from a projective variety into successive Grassmannians.
Matthew Niemerg - PhD preliminary examination
Date: Wednesday, May 15, 2013
Place: Weber, 223
Time: 1:00 p.m.
Title: Gale Duality, Parameter homotopies, Monodromy, and Applications
Advisor: Dr. Dan Bates
Dr. Patrick Shipman
Dr. Chris Peterson
Dr. Chihoon Lee
Abstract: Numerical Algebraic Geometry (NAG) has recently seen significantly increased application among scientists and mathematicians as a tool that can be used to solve nonlinear systems of equations, particularly polynomial system. With the many recent advances in the field, we can now routinely solve problems that could not have been solved even 20 years ago. This preliminary report will give a brief introduction and overview of Numerical Algebraic Geometry and homotopy continuation methods; discuss heuristics for preconditioning fewnomial systems, as well as provide a hybrid symbolic-numerical algorithm for computing the solutions of these types of polynomials; introduce a new software module of Bertini named Paramotopy that is scientific software specifically designed for large-scale parameter homotopy runs; consider applications and algorithms utilizing that software; and finally explore how monodromy and constructing an ad-hoc homotopy on the fly can be used to solve systems instead of using adaptive multiprecision.
Dusty Ross - PhD final examination
Date: Thursday, May 16, 2013
Place: Weber 201
Time: 3:00 p.m.
Title: Open and Closed Gromov-Witten Theory of Three-Dimensional Toric Calabi-Yau Orbifolds
Advisor: Dr. Renzo Cavalieri
Dr. Chris Peterson
Dr. Jeff Achter
Dr. Erika Lunkenheimer
Motivated by string theory and enumerative geometry, Gromov-Witten theory has attracted a lot of attention in both mathematics and physics over the last two decades. The GW theory of toric CY 3-folds has a particularly efficient computational algorithm called the "topological vertex" which provides a local-to-global approach to conjectural correspondences related to GW theory. We introduce a generalization to orbifold targets, the "orbifold vertex", and discuss its applications to two such conjectural correspondences: Ruan's crepant resolution conjecture and the orbifold Gromov-Witten/Donaldson-Thomas correspondence.
FORT COLLINS - Colorado State University graduate programs remain among the nation’s best, according to rankings released by U.S. News and World Report in its 2014 Best Graduate Schools edition.
The professional program in the Department of Occupational Therapy in CSU’s College of Applied Human Sciences - designated a “Program of Excellence” by the state of Colorado - holds the No. 6 spot among similar programs nationwide, based on data collected for 2012.
Colorado State’s professional doctoral veterinary medicine program maintained the third slot in the rankings, a position it has held for more than a dozen years. It is also ranked third in the nation in federal research dollars
In addition to its strong showing in health disciplines, CSU’s graduate programs in science, engineering and business also were recognized as some of the best in the nation. Civil engineering and chemistry were both ranked in the top 50 as was the part-time MBA program in the College of Business. The University’s graduate programs in chemical, mechanical and electrical engineering; biological, computer and earth sciences; mathematics; physics; and social work all ranked in the top 100 in their respective categories.
Such strong graduate programs and a highly productive research faculty combine with a commitment to undergraduate education that places CSU 67th among public universities nationwide, according to U.S. News and World Report’s annual America’s Best Colleges rankings released in September 2012.
Colorado State has long been one of the nation’s top performing research universities. Despite significant cutbacks in federal funding in recent years, CSU has grown its annual research spending to about $330 million in Fiscal Year 2012. The research dollars set a new record high for the university and mark the fifth year in a row that spending has exceeded $300 million. This funding comes from a combination of federal, non-federal and local sources.
“Rankings such as these are a good, third-party barometer of how we are doing in the eyes of others. We will always continue to focus on our missions of providing a top-flight education to our students, conducting groundbreaking research and providing service to people throughout Colorado,” CSU President Tony Frank said. “Our job is to make Colorado State University the best public research university out there.”
In 2011-12, the eight colleges that make up CSU awarded more than 6,600 degrees, including 1,576 masters, 235 doctorates
**Reception following lecture in 117 Weber Building from 4:00-5:30pm.
The National Research Council offers outstanding fellowship opportunities for graduate, postdoctoral and senior researchers. See www.nationalacademies.org/ra for details and online application.
CSU Mail & More
CSU mail and more is a new service on campus that has been developed with our CSU students, faculty, and staff in mind to help you prepare, mail, and ship your letters and parcels. Products and services include: postage stamps, postage metering, UPS, FedEx, Faxing, Document Scanning, Package materials. CSU Mail and More is conveniently located with customer parking just a few short steps from their front door at 200 West Lake Street in the Central Receiving Building.
Summer Hours: Monday-Friday 7:00am-4:00pm (closed on all university holidays)
For more information:
2013 will be a special year on the Mathematics of Planet Earth
Here is the call from the International Mathematical Union: http://www.mpe2013.org/
The International Mathematical Union has started a blog on ranking mathematical journals:
Computational and Data-Enabled Science and Engineering in Mathematical and Statistical Sciences
View details at: http://www.nsf.gov/pubs/2012/nsf12018/nsf12018.jsp?WT.mc_id=USNSF_25&WT.mc_ev=click
FAll 2012 Department News Letter
To view, go to: http://www.math.colostate.edu/newsletter/2012%20fall/Newsletter%20FA12.html