This Friday at 3pm several Undergraduate Reseachers presented a project to faculty, Balasz Strenner and Dan Margalit, in the Skiles building.
The project which was organized by the SoM faculty members, was about curves on surfaces: One can encode a curve on a surface as a path connecting various points on a surface. Some paths are clearly not efficient: if we go from A to B, then B to C, we could have simply gone from A to C. On higher genus surfaces, paths can be inefficient in more complicated ways, but one can make a list of what the inefficient paths can look like and how they can be made more efficient.
The students designed a way to encode paths as a sequence of letters and numbers, and wrote a Python-implementation of the curve tightening process, which looks for inefficient subpaths of a path and replaces them with their efficient counterparts. This curve tightening problem is an ingredient of my Macaw project, which is an implementation of a quadratic time algorithm of Margalit, Yurttas and myself for the Nielsen-Thurston classification problem of mapping class groups of surfaces.
The Association for Women in Mathematics (AWM) has named Georgia Tech student Libby Taylor the recipient of the 2018 Alice T. Schafer Mathematics Prize. She will receive a B.S. in Mathematics from Georgia Tech in spring 2018, only two years after she graduated from Wheeler High School, in Marietta, Georgia.
Taylor’s advanced mathematical abilities have been evident since high school, according to School of Mathematics Emeritus Professor Tom Morley. As a high-school junior, Taylor took Morley’s third-year-college course Combinatorial Game Theory, and she led the team that applied the theory in interesting ways to Gomoku, the classic five-in-a-row game from China. Taylor’s work, Morley says, “showed mathematical maturity way beyond her age or educational background.”
As an undergrad at Georgia Tech, Taylor has been taking graduate-level courses and conducting original mathematics research. Hard working and highly motivated, she regularly attends research seminars, reads math books and papers voraciously, and eagerly gives talks at workshops and conferences in the U.S. and overseas. She learns as much as she can from discussions with graduate students, postdocs, and professors.
Professors describe Taylor as a strong, talented student with staggering potential, who is fearless in learning new topics, asks insightful questions, and is quick to pick up sophisticated ideas. Already she has six preprints published, one manuscript in preparation, and a chapter in a book about categorical representation theory called “Soergel Bimodules.”
“I have been continually impressed by her mathematical intellect, her initiative, and her ability to absorb mathematics,” says School of Mathematics Assistant Professor Jennifer Hom. “I look forward to seeing what Libby’s future holds.”
“The friendly atmosphere in the Georgia Tech School of Mathematics contributed greatly to my mathematical development,” Taylor says. “It has always been easy to find professors willing to help answer questions, suggest further reading, and discuss mathematical ideas with me. This environment is not present everywhere; this is something special about Georgia Tech.”
Taylor specifically credits her research mentors, Baker and School of Mathematics Professor William T. “Tom” Trotter, both of whom began advising Taylor on research projects when she was still in high school. “Their mentorship gave me a significant head start in my mathematical education and research,” Taylor says.
The Alice T. Schafer Mathematics Prize is named after the former president and founding member of AWM who contributed greatly to women in mathematics. The prize recognizes excellence in mathematics by an undergraduate woman.
Each year, AWM names a winner, a runner-up, and at least two honorable mentions. Among them are the following with Georgia Tech connections:
- Samantha Petti, 2015 runner-up and now a Ph.D. student at Georgia Tech
- Megan Bernstein, 2010 honorable mention and now a postdoctoral fellow at Georgia Tech
- Nicole Larsen, 2009 runner-up when she was an undergrad at Georgia Tech and now a research fellow at the Kavli Institute for Cosmological Physics at the University of Chicago
- Josephine Yu, 2003 runner-up and now an associate professor at Georgia Tech
AWM will recognize the 2018 winner, runner-up, and honorable mentions on Jan. 10, 2018, at the 2018 Joint Mathematics Meeting, in San Diego, Calif.
“This achievement has validated the work I have put into my education over the past few years,” Taylor says. “The accomplishments of past recipients motivate me to continue working hard to live up to their examples.”
Georgia Tech’s reputation and a family connection were the main factors that brought Iban J. Ariza all the way from Barcelona, Spain, to Atlanta, Georgia. Aspiring to be an industrial engineer, Iban knew that Tech has the top Industrial Systems Engineering program in the U.S.
In addition, his father, Carlos Ariza, got an M.S. in Industrial Engineering and a Master of Business Administration at Tech. “He continues to be full of praise for Tech,” Iban says of his father.
An avid soccer and golf player, Iban is graduating with a B.S. in Discrete Mathematics. He completed high school at LaSalle Bonanova, in Barcelona, Spain. “During my high school years, I was constantly challenged to reach new goals and to learn as much as I could in preparation for my university studies,” Iban says. “My high school helped me ease into the demanding environment that is Tech.”
What is the most important thing you learned at Georgia Tech?
To always get your sleeping hours. ALWAYS.
Most people think that Georgia Tech will cut down your hours of sleep and cause a lot of stress because of the demanding workload. I believe you can do anything with proper organization.
Is your method of study time consuming? Is there a better way to learn? Can you absorb more information in a shorter time by using techniques x,y,z? Freshmen students should be looking at how to improve their study methods.
Learn how to learn, then actually learn. But my main recommendation would be to always get your sleep.
What surprised you most at Georgia Tech?
It came as a huge surprise to me when I learned that Tech hosted the Summer Olympic Games in 1996, especially because Barcelona, my hometown, hosted them in 1992.
I was also surprised to experience the wide diversity and inclusion from different organizations on campus. Moreover, it is a good feeling to know that you’re in one of the top universities in the country and that you’re learning with some of the best professionals in their fields of study.
Which professor(s) or class(es) made a big impact on you?
I consider a class to be impactful if I ended up enjoying the subject more than when I started taking it. Among the classes I enjoyed more in the end are probability and statistics taught by Professor Plamen Iliev; quantum computing, by Professor Brian Kennedy; and calculus, by Prov. Stavros Garoufalidis.
Most of my computer science classes – such as algorithms, data structures, and operating systems – were impactful, as was my research mentor, Professor Lew Lefton.
What is your most vivid memory of Georgia Tech?
All the soccer days that I spent with friends.
When I first came to Tech, I played indoor soccer every Friday. That is where I met most of my current friends and best friends. Now, we post our game highlights on Facebook and meet almost every day for about two hours. It feels amazing. Soccer is called the “Beautiful Game” for good reasons.
A shout-out to my intramural team, called Root 19! We have won three Independent Soccer Intramural tournaments, two India Club Tournaments, and countless other competitions. To them, I say: “Guys, we’ve left a legacy in this university. Hopefully, we'll get a statue someday!”
What was the most valuable outcome of your participation in experiential learning activities?
My first internship, during freshman year, helped me understand that industrial engineering was not my passion. After careful thought, I decided to change my major to discrete mathematics.
But as a self-learner, I was passionate about many subjects – including chemistry, biology, and physics. I almost transferred to physics and chemical engineering before deciding on mathematics. There is a lot to think about when changing your major field of study, so talk to your advisors. They provide great insight.
What advice would you give to incoming freshmen at Georgia Tech?
I would encourage students to start working and applying for internships in their early years. Get a feeling of what the market needs and the common jobs for someone with your degree.
- Find your passion; talk to your advisors to learn if your passion aligns with the job market
- Always get seven to eight hours of sleep
- Eat healthy
- Go out with friends at least once a week
- Find a way to relieve stress: sports, yoga, walking, traveling
- Avoid 8 AM classes
- Make use of professors’ office hours
- Stay motivated
- Stay happy and laugh everyday
- Learn how to invest
Where are you headed after graduation?
Georgia Tech has done a great job to prepare me for my future. I currently have a couple of offers to work as a software engineer with Fortune 500 companies, but I am still interviewing with other companies.
Georgia Tech has great computer science and mathematics programs. However, what you really need to educate yourself in is your passion and your ability to think creatively and solve real-world problems. Much of the high-demand workforce skills come from self-learning or continued learning, which arise from motivation, commitment, and a need to improve our world.
The Tech Topology Conference brings together established and beginning researchers from around the country for a weekend of mathematics in Atlanta. Check back soon for more details. We are pleased to announce this year's speakers:
- Tori Akin (Duke University)
- Lei Chen (University of Chicago)
- Diana Hubbard (University of Michigan)
- Tye Lidman (North Carolina State University)
- Ciprian Manolescu (UCLA)
- Emmy Murphy (Northwestern University)
- Balázs Strenner (Georgia Tech)
The 2017 conference features a session of five-minute lightning talks.
If you are interested in giving such a talk (on behalf of your work or someone else’s) please see the "Registration and Support" page.
Deadline for submitting proposals for Lightning Talks is October 31.
organizers: J. Etnyre, J. Hom, P. Lambert-Cole, J. Lanier, C. Leverson, D. Margalit, and B. Strenner
Supported by the NSF and the Georgia Institute of Technology
SoM at Joint Mathematics Meeting 2018
The Joint Mathematics Meeting is the largest Mathematical yearly event in the USA. In 2018, it will take place in San Diego and attract more than 5000 participants.
Mathematics in Georgia Tech is featured in some of the plenary events: One of the Lectures devoted to current achievements will be given by Prof. Crochow reporting on work of Prof. Croot and others: "The Cap Set Conjecture, The Polynomial Method, and Applications (after Croot-Lev-Pach, Ellenberg-Gijswijt, and others)."
Prof. D. Randall, adjunct in mathematics will give a plenary talk on "Emergent Phenomena in Random Structures and Algorithms."
More information about the Joint Mathematics Meeting in: http://jointmathematicsmeetings.org/jmm
At the start of his class on differential equations, Rafael de la Llave invites students to watch a mesmerizing demonstration.
He hangs two one-inch-diameter hex nuts from a clothesline through strings of the same length. With both hex nuts at rest, the School of Mathematics professor taps one slightly.
Given the slight energy input, the nut moves. In a while, the nut at rest also starts to swing. Eventually, a dance commences, the two hex nuts gracefully oscillating as they transfer energy from one to the other.
When more oscillators are involved, beautiful geometric patterns emerge, as this video shows.
Designers of space missions can harness the dynamics creating these dazzling motions to save fuel. “If we could make the mathematical details very explicit, we can make these work to our advantage,” de la Llave says. “We could move spacecraft with very small amounts of fuel. We could extend the life of satellites – or send robots to the moon – inexpensively.”
NASA recently awarded a $100,000 grant to de la Llave, Marian Gidea of Yeshiva University, and Rodney Anderson of NASA’s Jet Propulsion Laboratory (JPL)to take the first steps to realize the potential of mathematics to lower the fuel cost of space travel. The project – “Accelerating Diffusion to Enable Rapid Tour Design” – has a duration of one year.
As part of the project goals, this week in the Skiles Building, space mission designers from JPL and mathematicians from Georgia Tech and Yeshiva University are gathering for a four-day workshop. The participants will work together with the mathematical tools of the Arnold diffusion mechanism and trajectory design. The goal is to incorporate what is also known as the “butterfly effect” – which is the ability of minuscule changes to cause gigantic effects in certain systems – into space mission design.
“If we want to go around jumping from moon to moon, applying these new advances in mathematics can help us get there at much, much lower cost, making such a mission so much more doable.”
The Arnold diffusion mechanism is the underlying mathematical concept. Both de la Llave and Gidea are world-renowned experts in this field.
“In a nutshell, the Arnold diffusion mechanism states that small amounts of force, applied at the right moments, can produce large effects over time,” Gidea explained last year. “A familiar example is pushing a playground swing: with a tiny push on the swing each time it comes back to you, the amplitude of the swing will keep increasing.
“In the case of space missions, this small forcing translates into firing the rocket’s engine at the right place and the right moment to accelerate in orbit when the natural dynamics is slow.” Other possible small forcings could be the tugs of gravitational tides induced by stars, planets, moons, and even asteroids.
At other times, “the spacecraft will coast along the space superhighway at zero cost,” Gidea said.
“Celestial bodies are moving all the time,” de la Llave says. “And they generate forces that depend on time. If you can ride the wave of those forces, then you can move and accelerate using just the gravitational forces of astronomical objects.”
The Arnold diffusion mechanism is rooted in the Kolmogorov-Arnold-Moser (KAM) theorem. The theorem provides a general framework for understanding what happens when a simple physical system is modified slightly, according to School of Mathematics Professor Howard “Howie” Weiss. “Rafael and others played a big role in extending the KAM theorem,” Weiss says. “Rafael is extremely modest. He is probably the world’s leader in this business.”
Design of space mission routes historically has been based mostly on patching orbits of conical geometry. Recent mathematical advances in the Arnold diffusion mechanism have uncovered other geometries that reveal new potential pathways leveraging the gravitational dynamics in space. Adding small maneuvers at precise times and locations to the pathways found via the Arnold diffusion mechanism could significantly drop the cost of space missions.
While de la Llave and Gidea work on the mathematics, JPL’s Anderson will focus on applying the mathematical methods to mission concepts. Anderson is an expert on the application of dynamical systems theory to trajectory design problems. He is the coauthor of a 2013 NASA monograph that explores the use of low-energy paths to transfer a spacecraft from Earth to its moon.
One space endeavor of great interest is to visit the moons of Jupiter systematically, de la Llave says. “If we want to go around jumping from moon to moon, applying these new advances in mathematics can help us get there at much, much lower cost, making such a mission so much more doable.”
Story Collider: Part 1 - Lew Lefton tries to succeed as both a math professor and a math comedian
Lew Lefton is a faculty member in the Georgia Tech School of Mathematics and the Assistant Dean of Information Technology for the Georgia Tech College of Sciences. He also has the role of Assistant Vice President for Research Cyberinfrastructure at Georgia Tech. Lefton co-founded and is the acting executive director of Decatur Makers, a family-friendly makerspace in downtown Decatur. He is on the board of the Southeast Makers Alliance and has been involved as a co-producer of Maker Faire Atlanta since 2014. Lefton has a bachelor of science degree in math and computer science from New Mexico Tech, and a Ph.D. in mathematics from the University of Illinois. He moved to Decatur in 1999. Lefton is also an accomplished and experienced comedian who has done stand up and improv comedy for more than 30 years.
34th SEAM PRELIMINARY ScheduleFriday, March 23, 2018.8:30 Registration, coffee, bagels9:10 Elisabeth Werner10:00 Break10:10 Parallel sessions of 20-min talks11:00 Coffee break11:30 Krystal Taylor12:20 Lunch1:40 Benjamin Jaye2:30 Coffee break3:00 Parallel sessions of 20-min talks3:50 Coffee break4:20 Yumeng Ou5:10 End of talks of Day 1Saturday, March 24, 2018.8:30 Coffee, bagels9:10 Marianna Csiornei10:00 Break10:10 Dmitriy Bilyk11:00 Coffee break11:30 Parallel sessions of 20-min talks12:20 Lunch1:40 Brett Wick2:30 Coffee break3:00 Session in honor of Joe Ball5:30 End of talks6:30 DinnerSunday, March 25, 2018.8:30 Coffee, bagels9:10 Stefan Richter10:00 Coffee break10:30 Parallel sessions of 20-min talks
Recently the AMS published a book written by Michael Damron and two co-authors, titled 50 Years of First-Passage Percolation.
First-passage percolation (FPP) is a fundamental model in probability theory that has a wide range of applications to other scientific areas (growth and infection in biology, optimization in computer science, disordered media in physics), as well as other areas of mathematics, including analysis and geometry. FPP was introduced in the 1960s as a random metric space. Although it is simple to define, and despite years of work by leading researchers, many of its central problems remain unsolved.
In this book, the authors describe the main results of FPP, with two purposes in mind. First, they give self-contained proofs of seminal results obtained until the 1990s on limit shapes and geodesics. Second, they discuss recent perspectives and directions including (1) tools from metric geometry, (2) applications of concentration of measure, and (3) related growth and competition models. The authors also provide a collection of old and new open questions. This book is intended as a textbook for a graduate course or as a learning tool for researchers.
See the CoS full story here:
Michael Damron is an Associate Professor in the SoM at Georgia Tech, who has been highly active in the fields of Continuous and Discrete Probability, has been awarded several teaching awards including the LexisNexis Dean’s award from Georgia Tech in 2016, and is mentoring several post-docs and graduate students here at Tech. This is Michael's second book.