Life in graduate school is a matter of solving challenging problems, playing games, and drinking coffee from French Press for second-year Mathematics Master’s student Alex Troesch. Alex received a B.S. in Mathematics and Physics from the College of Creative Studies at UCSB in 2011. As an undergraduate student, Alex received multiple awards for academic excellence in Mathematics and Physics.
Alex took the time from his busy graduate schedule to respond to a few questions about his research in geometric group theory, his experience as an undergraduate teacher, and how his interests in math, physics, and technology intersect. Read on to learn more about Alex’s accomplishments.
Tell us a little about your research and how you came to choose the topic.
I am working in geometric group theory. In particular, I study how complicated symmetries can be broken down into simple reflections and how this structure can help us understand large collections of symmetries. I became involved in this topic because I have always been drawn towards aesthetically pleasing mathematics and the study of symmetry is a natural point of interest. Additionally, these problems are closely related to problems of algorithm design and computational complexity due to their extremely combinatorial nature. This requires the use of extensive computer software to help us understand the transformations involved. A large part of my thesis work has been developing software tools to help us perform calculations for particularly difficult examples of symmetries.
How do your interests in math, physics, technology, and the future intersect with your experiences as a researcher and teacher?
For my teaching, I always try to be a little bold in my discussions with students. I try to say things which may surprise them and make them want to look a little bit closer at the topic. I feel that technology plays an essential role in the way we communicate and to teach effectively we need to be aware of the lessons that this interplay can teach us, because communication is at the heart of any good teaching experience. For example, I have experimented with videoconferencing for office hours via Google+ in order to encourage students to participate and ask questions even if they can’t make it in person. The notions of ubiquitous and wearable computing can have potentially far-reaching changes for how we communicate, and these changes should not be ignored.
While the needs of modern technology have often informed directions for applied research in math and physics, more and more areas of pure math are becoming relevant to modern engineering; a recent example of this is topological data analysis. I like to think about the shape of things to come and what role my ideas can play in it, since anyone trained to think clearly and creatively has the potential to make a big difference in the world.
What has graduate student life been like for you?
After struggling with a very heavy course load for a few years, to be without the constant strain of lectures and grueling problem sets is a welcome change. It has been hard to balance my time between learning what I need to know for my thesis and learning what sparks my interest at that very moment. I have been prone to delve deep into the bowels of Wikipedia and the 2nd floor of the Davidson library. Sometimes a late night coffee can turn into an early morning snack. I can get a bit carried away.
What has been a source of motivation or drive for you in your graduate studies?
After I finish at UCSB, I would like to go on and get a Ph.D. in mathematics. So, in a direct way, my desire to continue my education provides me with motivation. Also, the moment when you can see a problem or idea in a new way provides me with a great sense of accomplishment. Sometimes these little victories can be few and far between, but they certainly keep me motivated to work and think about hard problems and difficult concepts.
Name an accomplishment you are most proud of and why.
I was allowed to design and teach a lower division seminar course on topology and modern geometry through the College of Creative Studies during my final undergraduate year and it was a great experience. It was a challenge to piece together a thread of interesting ideas and to get a chance to truly see what life is like from the other side of the classroom. I’m not sure what the students thought of the course, but I am definitely proud of the work and thought I put into it.
What do you do to relax? Any hobbies, collections, pastimes, favorite places to go, favorite things to do? Along these same lines, what makes you happy?
I have become an avid player of modern board games such as Dominion, 7 Wonders, and Ticket to Ride. I find it very easy to get wrapped up in a board game, which helps put me at ease and allows me to completely focus on the moment of playing a great game with friends. A nice cup of coffee from the French Press downtown is a sure way to put a smile on my face.
What is one thing people would be surprised to know about you?
I think people would be surprised to know that I think Pinkie Pie is the best pony.
What do you hope to be doing 5 or 10 years out of graduate school?
I am torn between pursuing a traditional research position at a university and pursuing a career in industry since I am still unsure of where my immediate goal, getting my Ph.D., will take me. All I know is that if in a few years' time I am surrounded by enthusiastic and creative problem solvers I will find a way to be happy with how everything turns out.
Do you have any advice for current grad students?
We are all in this business of making new knowledge together, and it’s a hard business where insight and motivation can come from unlikely places - so be ready.