STATMOS’ lead PI is Montserrat Fluentes, North Carolina State University, with Michael Stein of University of Chicago and Peter Guttorp of University of Washington as co-PIs. Barb Bailey and Rich Levine founded the SDSU node and Sam Shen helped set up the SIO node. The SDSU-SIO sub-network enables both SDSU and SIO students and faculty to receive STATMOS funding for collaborative research between the two institutions.

Shen leads the STATMOS interest group of nonstationary space-time process. Bailey directs the SDSU node of STATMOS. They both attended the STATMOS annual meeting at University of Chicago on July 31, 2016.

]]>San Diego State University welcomes 12 Presidential Graduate Research Fellows from around the world to the Aztec family. The competitive, merit-based campus program supports the recruitment of exceptional non-resident applicants to SDSU’s many graduate programs. Two of the awarded Research Fellows are members of the Mathematics & Statistics Department working as Math 252 TA’s. We welcome Stefan and Anja to San Diego and to SDSU.

**Stefan Ehard**

Hometown: Ulm, Germany

MS, Statistics

My university in Germany, the University of Ulm, is a partner institution of San Diego State University. For many years, some of the best graduate students in my university’s mathematics program have been coming to SDSU as part of an exchange program between the two institutions. This one-year program allows students to achieve both the American and German master’s degrees, making it highly attractive to me.

I earned my bachelor’s degree in pure mathematics at the University of Ulm in 2015. Thanks to a Fulbright Grant and the Presidential Graduate Research Fellowship, I am able to put my mathematical knowledge in an applied context at SDSU. I am particularly interested in stochastic modelling and statistics as they have many real-world applications, including in climate modelling at the Center for Climate and Sustainability Studies at SDSU. My research in statistics also compliments my focus on Actuarial Sciences and Insurance at the University of Ulm. My goal is to pursue a Ph.D. in Germany and eventually apply my academic work at a company that operates on a global level.

**Anja Schmidt
**Hometown: Ulm, Germany

MS, Applied Mathematics

I did my undergraduate study in mathematics and almost completed a master’s degree in pure mathematics at the University of Ulm in Germany. Participating in the exchange program of Ulm University, I chose to attend SDSU because the study program Applied Mathematics provides the opportunity to enhance my mathematical expertise by gaining insights into advanced and specialized areas of mathematics.

My interests are mostly in the fields of numerical mathematics, so I focus a lot on programming which is absolutely crucial at the present time. Being fascinated in finding solutions for unsolved problems just by using tools I have learned during my study time, I appreciate to broaden my horizon with regard to solve even harder problems. Therefore, I consider my stay at San Diego State University to become a highly valuable experience which promises to significantly enrich and improve my knowledge in mathematics and to proceed my personal development.

I’m very grateful to receive a Fulbright Grant, the Presidential Graduate Fellowship and a scholarship from Talanx Foundation. With this help, I am getting closer to my subsequent goal of pursuing a PhD in Mathematics.

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The GRFP provides three years of support for the graduate education of individuals who have demonstrated their potential for significant research achievements in STEM and STEM education. NSF especially encourages women, members of underrepresented minority groups, persons with disabilities, and veterans to apply.

This semester, San Diego State University welcomes National Science Foundation Graduate Research Fellow Matthew Voigt to campus.

**Matthew Voigt**

Hometown: St. Paul, Minnesota, Ph.D. in Math and Science Education

I chose SDSU because it’s a leader in the field of math and science education. I was blown away with the faculty’s hospitality and dedication to student learning.

My greatest educational accomplishment was having my research recognized by the National Science Foundation with a Graduate Research Fellowship. I am also proud of my undergraduate advocacy work for Lesbian. Gay, Bisexual and Transgender assistance and resource, which resulted in additional funding for LGBT safe space programs.

I hope to become a leader in the field of math education, through research and teaching. I would like to combine my experience as a computer programmer and educator to create dynamic new ways of exploring mathematics for both children and adult learners.

*See full report: http://newscenter.sdsu.edu/sdsu_newscenter/news_story.aspx?sid=75750*

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Dylan is a deep thinker with innovative ideas. His sales and marketing experience have been primarily internet based with profitable success. Passionate about the protection of the environment, Dylan continues to educate his peers on solution based ideas. He is a proven leader as captain of his basketball team and a team player in all aspects of his life. Also currently a USPA licensed skydiver and skydiving coach at Sky San Diego, Dylan has a passion for living by the motto, “live life to the fullest”. He recognizes entrepreneurship as a pathway to achieving his personal goals and making the world a better place for all. His goal for the future is to become a serial entrepreneur and positively impact the world through my endeavors.

]]>MS Applied Mathematics

THESIS DEFENSE

Monday, August 15, 2016

2:00pm GMCS 418

*Pseudo-Spectral Continuation Methods for the Planar Hamiltonian Korteweg-de Vries Equation*

Abstract:

The aim of this thesis was to develop a pseudo-spectral continuation scheme for periodic orbits of planar Hamiltonian dynamical systems. Traditionally, numerical continuation of Hamiltonian periodic orbits is performed by way of shooting methods. While we build our analysis on the more traditional approach, we remove any integration required by the shooting method in favor of solving the Hamiltonian dynamical system directly at every point along the continuation branch.

This thesis considers the Korteweg-de Vries (KdV) equation to build the pseudo-spectral continuation scheme. We first derive the standard KdV equation and build the corresponding Hamiltonian dynamical system. We then consider an unfolding parameter and a phase condition to ensure that we converge to unique solutions. Finally, we show that using the pseudo-spectral continuation method, we are able to solve for solutions along the continuation branch much faster and with a higher level of accuracy than shooting methods.

Thesis Committee:

Christopher Curtis, Thesis Chair, Department of Mathematics & Statistics

Peter Blomgren, Department of Mathematics & Statistics

Calvin Johnson, Department of Physics

THESIS DEFENSE

*The Inclusion-Exclusion and Mixing Ratio Conjectures From the Ingleton Inequality*

Abstract:

The Ingleton Inequality, which is based on a vector space theorem and adapted to entropy functionals by Matus, plays a role in describing the entropy region for four discrete random variables, depending on whether or not it is satisfied. The entropy regions that are defined by entropic vectors for discrete random variables are not known, in general. For , recent work has been accomplished by Mao and Boston in characterizing this space of -dimensional entropic vectors. They study how *group-characterizable* entropic vectors sometimes yield violations of the Ingleton Inequality/Ratio, thus expanding the understanding of this region. We discovered a decomposition of the Ingleton Ratio into what we dub the Mixing Ratio and the Inclusion-Exclusion Ratio, which resembles the inclusion-exclusion principle from set theory. We propose two conjectures based on the simpler Inclusion-Exclusion and Mixing Ratios, attempting to streamline the search for Ingleton Inequality-violators. Examples of these violators are reproduced in order to provide support for our conjectures. Characterizing the entropy region associated with discrete random variables is related to determining the maximum communication rate of a network coding system that uses discrete random variables. Characterizing this region for arbitrary remains an open problem.

Thesis Committee:

Michael O’Sullivan, Thesis Chair, Department of Mathematics & Statistics

Carmelo Interlando, Department of Mathematics & Statistics

Jean mark Gawron, Department of Linguistics

Turbulence mitigation algorithms have gained a lot of attention in the last decade and several algorithms are now available. Unfortunately, since this problem is generally involved in Defense applications, there is no common dataset to assess such algorithms. The purpose of Gilles’ grant is to create a free open dataset of observations acquired through atmospheric turbulence. A camera with different lenses will be purchased to run several scenarios of interest for the Defense community. The project involves an undergraduate student and we expect to use the proximity of the desert to make several observation by the end of the Summer. It is expected that this dataset will be released online by the end of 2016. Pictured: Nicholas Ferrante (SDSU), and Dr. Gilles.