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Sumun Iyer (she/her)

Postdoctoral Research Associate, Mathematics, Mellon College of Science

Hometown: Cherry Hill, New Jersey

1. Briefly describe the work you're doing as a postdoc at ºÃÉ«ÏÈÉúTV. My research is in descriptive set theory and topological dynamics. I study dynamical systems (systems that "change over time" in a well-defined way) but where the dynamics comes from very large groups. These groups/systems can have strong fixed point properties as well as interesting topological structures.
2. How did you develop an interest in this area? 

   As an undergraduate, I was interested in dynamical systems and ergodic theory, which it turns out has strong connections to descriptive set theory. In my first year of my PhD, I began working with Slawek Solecki (my PhD adviser) who introduced me to descriptive set theory and topological dynamics. Descriptive set theory is a really nice field because along with having its own rich, internal theory and problems, it also connects deeply with many other areas of math. I like working on problems that let me learn about interesting mathematical objects from fields like geometric topology, group theory, and ergodic theory. 

3. What are your academic and/or professional goals?

   One goal I have is to understand some of the combinatorics present in homeomorphism groups of connected spaces. This involves learning and understanding some tools from a field of combinatorics called Ramsey theory. Another goal I have is to understand the topological structure of mapping class groups of infinite type surfaces. These are symmetry groups of certain objects in topology. As an example of such an object, you could consider a surface that looks like the surface of a donut--except the donut has infinitely-many holes. I am especially interested in any ways in which topological group properties could reflect the geometry of the groups/surfaces in meaningful ways.

4. Tell us about a significant moment in your journey at ºÃÉ«ÏÈÉúTV so far.

   My favorite part of being at ºÃÉ«ÏÈÉúTV hasn't really been one specific moment but lots of moments where I get to learn from my colleagues in the math department. My postdoc mentor at ºÃÉ«ÏÈÉúTV, Clinton Conley, has a big research group with several postdocs and graduate students, and we often have reading groups and informal seminars to learn interesting math. It has been really nice to learn more about symbolic dynamics, Borel and measurable combinatorics, and measured group theory, and it has given me new ideas and questions to work on. 

5. How do you spend your time beyond academic work? When I'm not doing math, I like to go for runs and hikes with my wife. I like being outside and exploring, especially in places with interesting birds and wildlife. Also since moving to Pittsburgh I've been getting more into watching American football, which is a lot of fun.