Thursday, June 18, 2015
The Early Researcher Award program (ERA) is administered by the Province of Ontario. The ERA program helps promising and recently-appointed Ontario researchers build their research team of graduate students and postdoctoral fellows.
The title of Professor Eric Katz's funded project was Tropical Geometry: Structure and Degeneration. Eric works in combinatorial algebraic geometry and number theory by way of tropical geometry. Currently, he is interested in finding combinatorial analogues of Hodge theory to address positivity questions in combinatorics and using degeneration methods to give uniform bounds for the number of rational and torsion points on algebraic curves. He has also brought Hodge theory techniques to bear on enumerating lattice points of polytopes in joint work with Alan Stapledon. Research highlights include the proof with June Huh of the Rota-Heron-Welsh conjecture for representable matroids and uniform bounds for the number of rational points for algebraic curves of low Mordell-Weil rank with Joseph Rabinoff and David Zureick-Brown.
The title of Professor Laura Sanità's funded project was New Algorithmic Approaches for Network Design Problems. Laura's research focuses on algorithmic problems originating from theoretical computer science and applied mathematics. One of her primary research topics is the development of approximation algorithms for fundamental combinatorial optimization and integer programming NP-hard problems. She is also interested in studying the polyhedral structure given by the set of feasible solutions of optimization problems. Algorithmic and polyhedral techniques are important tools, frequently employed to design solvers for large-scale industrial optimization problems.