Mathematics Instructor, Hieu Do, has written about his discoveries in pseudo-Anosov mapping. Genus 3 is a structure as the above, only with three openings in the form.
Chandra Healy; Dancer, Teacher and Writer
Chandra Healy is a Dance Instructor at Truckee Meadows Community College who enjoys conveying her enthusiasm for creativity in movement to her students.
Healy’s BFA, Dance Performance and Choreography degree was earned at the University of Nevada, Las Vegas, and she has worked as both a teacher and a professional dancer.
Her written articles have been published in the Las Vegas Informer, an online magazine.
“Performing Arts in America: A Timeless Tale of Future Trends Affecting the Arts," conveys the issues that today’s dance industry faces, especially in regards to funding for the dance arts through private and public sectors.
Another of Healy’s articles is entitled “Lights, Camera, Action: Looking through the Lens One Dance at a Time." It reveals the work behind the camera for dance performances. Healy describes and analyzes the current practices of filming dancers in motion. She has also written a review of a major two-day dance festival in Nevada, “Turns, Leaps & Jumps: Dance Choreographers take Stage at the 15th Annual Las Vegas Dance in the Desert Festival.”
Healy has a passion for writing about dance because she’s able to explore and analyze the creativeness of the choreography.
“I like to bring the fundamentals of dance to others through the expressiveness and true beauty that dance offers,” she said.
Healy teaches dance appreciation courses at TMCC. For more information, she can be reached by TMCC email.
Joseph Gonzalez Honors Veterans with WWI Pilot Story Presentation
Joseph Gonzalez is a veteran of the United States Marine Corps, and TMCC Professor Emeritus in History, Political Science and Law. His PhD is from the University of California, Santa Barbara with a specialty in modern British and European history. Gonzalez retired in June 2015 after 43 years of community college teaching, with 10 years at TMCC.
His presentation “Improbable Ace: A Pilot in World War I” at the February 2016 meeting of the national World War One Historical Association was so well-received that he was asked to also present it for the TMCC Community. The TMCC History Club asked for Gonzalez to present his work at their April 2016 meeting, as well.
The research work and slide presentation is a detailed look at the unpublished memoirs of Captain J.E. Doyle, RFC/RAF, D.F.C., a flyer during the War. The Royal Flying Corps (RFC) was the air force of the British Army during that time period.
Gonzalez said that his interest piqued as he learned how the veterans displayed continued courage upon returning home.
“My engagement with the Great War’s air combat grew out of a larger concern for the veterans of that conflict,” he said. “Captain Doyle lost his leg in the latter days of the war, and despite being an ace, an officer, and significantly wounded, he struggled to find his place in the postwar world. All of the veterans of the 1914-1918 war are now gone, but the effort to remember the sacrifice of those who serve in subsequent conflicts remains. We must remember, so that we can honor all who served.”
To inquire about requesting Gonzalez to speak at a meeting or event, please contact him by TMCC email.
Hieu Do Says it is Awesome to Find More Questions to Answer
Hieu Do is a new mathematics instructor at TMCC this academic year, having previously earned his PhD from Oregon State University in June 2016.
His original discovery in two-dimensional mapping was published in the November 2016 issue of the prestigious national Journal of Modern Dynamics.
Do’s article was peer refereed. Peer refereeing is a rigorous process where a committee of about four or five referees review a paper that has been submitted for publishing in a journal, verifying it for accuracy and analyzing writing style. They suggest any edits that would make the content more engaging to general and academic reading audiences. For Do’s article, the refereeing process took more than seven months. They suggested mostly cosmetic changes, he said.
His work concerns Ergodic theory. The word Ergodic originates from two Greek words; ergon meaning work, and odos is path. Ergodic theory is a branch of mathematics that studies what is known as "dynamical systems" and often involves probability and statistics. Dynamical systems are mathematical models of structures such as the flow of water in a pipe. More specifically, Ergodic theory studies dynamical systems with an invariant measure. One example of an invariant measure can be shown by thinking of the globe—when traveling from the Earth's North Pole to the South Pole, the measure would be the same traveling through the Eastern Hemisphere as through the Western Hemisphere.
Shapes such as a donut are known as genus 1, and forms such as a waterpark inner tube float with two holes are genus 2. For these structures, any time a straight line is the center as the object is twisted, there is stretch factor and shrinking factor in the measurements on each side of the straight line.
“In my paper, we give explicit examples describing constructable surfaces with clear descriptions of such flows whose invariant measure is zero, and that is why this work is valuable to the Journal,” Do said.
He added that scholars like to push knowledge as much as possible in a theoretical way. The knowledge may be applicable for real life purposes in the future. He added that more research is needed in pseudo-Anosov to find and see more patterns.
“For me, the interesting thing is not the answer, it’s discovering more questions that you want to answer,” he said.
For the mathematically savvy, below is the academically-oriented explanation of Do’s article, “New infinite families of pseudo-Anosov maps with vanishing Sah-Arnoux-Fathi invariant.”
“We show that an orientable pseudo-Anosov homeomorphism has vanishing Sah-Arnoux-Fathi invariant if and only if the minimal polynomial of its dilatation is not reciprocal,” Do said. “We relate this to works of Margalit-Spallone and Birman, Brinkmann and Kawamuro. Mainly, we use Veech's construction of pseudo-Anosov maps to give explicit pseudo-Anosov maps of vanishing Sah-Arnoux-Fathi invariant. In particular, we give a new infinite family of such maps in genus 3.”
Coming up in the Accomplished Authors Series
- Viki Kappel Spain
- Jill Channing
- Scott Miller
For more information about the Accomplished Authors and Presenters series, please contact Marketing and Communications at 775-673-7087.