What area(s) of scholarship are you most interested in?
I study pure mathematics and I am interested in algebraic geometry and homotopy theory. Homotopy theory is the study of shapes, which are cut out by polynomial equations (like x^2+y^2=z^2). The ubiquity of such shapes unifies ideas from various areas of mathematics such as number theory and complex analysis. The latter is the systematic study of shapes up to "bending and stretching" 鈥 here the rules are such that a coffee cup and a donut are indistinguishable. One of the themes of modern mathematics is that ideas from homotopy theory can shed light on questions and objects in algebraic geometry. This is quite surprising as algebraic geometry tends to view shapes in a rigid way.
My most recent research is on motivic cohomology. In a sense, motivic cohomology is a very sensitive probe which takes in a complicated algebro-geometric shape and spits out observable data that mathematicians can use to try and rebuild the shape - or at least understand it better.
How did you become interested in that area?
Everything kind of began when I was an undergrad at the University of Chicago. I was attracted to the extreme abstraction of homotopy theory, but soon learned that the power of mathematics comes from examples. I think it was a conversation with Professor Matthew Emerton that changed my entire perspective on this. Algebraic geometry was then the area that I found most rich. Sometimes I feel that examples in the subject tells the story of an entire universe! Most of my work since grad school has then been about understanding algebraic geometry from a homotopy-theoretic lens.
What course(s) will you be teaching this year?
This fall, I will be teaching undergraduate differential topology and point-set topology at UTSC. Both form the initial motivation for modern homotopy theory. In spring, I will teach a graduate class at the St. George campus on p-adic motives which is a topics class on certain aspects of motivic cohomology.
What are you looking forward to most about joining the 澳门六合彩开奖接口 community?
The community seems really close and tight-knit which I think will give me the opportunity to get to know well the students at UTSC, as well as my colleagues. The campus is also really pretty and I am looking forward to running and biking under the autumn foliage in the forest.
What are you reading/watching right now?
I am reading Elena Ferrante's 鈥淢y Brilliant Friend,鈥 partly because the New York Times named it the best book of the 21st century, partly because apparently no one knows who she is!