In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

Processes in nature can often be described by equations. In many non-trivial cases, it is impossible to find the exact solutions to these equations. However, some equations are much simpler to deal ...

Combinatorial algebraic geometry sits at the intersection of discrete mathematics and algebraic geometry, exploring the deep interplay between algebraic structures and combinatorial methodologies.

Thom polynomials measure how global topology forces singularities. The power of Thom polynomials predestine them to be a useful tool not only in differential topology, but also in algebraic geometry ...

Enumerative Geometry, Gromov-Witten theory, reduced invariants, quasimap invariants, toric geometry.

I received my PhD from the University of Michigan in 2009. I was a postdoc at Imperial College, london from 2009-2011, and an NSF postdoc at Columbia University from 2011-2013. I was an assistant ...