Join the department in congratulating Eric Katz, an Assistant Professor, who received an NSF CAREER award for his proposal entitled "Tropical and Diophantine Geometry"
From the NSF description:
"The PI will apply tropical geometry techniques to resolving long-standing problems in combinatorics and diophantine geometry."
"With collaborators, the PI will incorporate algebraic geometric methods (particularly Hodge theory, positivity, and genericity) into geometric combinatorics with the goal of understanding the possible face numbers of certain polyhedral complexes. By refining established techniques, he will investigate sharper inequalities among face number which will elucidate combinatorial structures. He will also deepen the commutative algebraic underpinnings of his recent work on matroids. In Diophantine geometry, he will study bounds on the number of rational and torsion points on curves. Following the methods of Buium and Kim, with collaborators, he will examine functions on curves of bad reduction that vanish on points of arithmetic interest and bound their zeroes. This involves elaborating analogies between classical and p-adic analytic geometry”
The proposal has an educational outreach component:
"The PI will engage in educational and outreach activities including the following: the broadening of his department's honors program; community outreach presentations; mentorship of students from underrepresented groups; graduate advising; and exposition”