The department would like to welcome Dr. Dhruv Ranganathan, from MIT, who will be giving a talk on Wednesday, 2/15/17, from 11:00-12:00 in SCP 229.

**Abstract and Bio:**

Among the most basic objects that one can study in geometry are arrangements of lines in the plane —configurations of straight lines and points with specified incidence conditions, like “this subset of four lines intersect at that point”. The set of all configurations of lines satisfying chosen incidence conditions is a simple example of an object known as a moduli space, a concept that appears naturally in geometry, representation theory, physics, and even genetics. I’ll try to explain a remarkable phenomenon displayed by these spaces of arrangements of lines, known as “Mnev Universality”, which states that these simple configuration spaces of lines encode in them the same complexity as arbitrary Diophantine polynomial systems. This is a fancy way of saying that these spaces of configurations can become “as complicated as any object defined by polynomials”. Time permitting, I’ll also explain some consequences of this for moduli spaces in algebraic geometry.

Dhruv Ranganathan is presently a CLE Moore Instructor at the Massachusetts Institute of Technology and a member of the Institute for Advanced Study. He earned his PhD in mathematics from Yale University in 2016 and a BS in mathematics from Harvey Mudd College. Dhruv’s research centers around combinatorial algebraic geometry, an age old tradition that turns difficult problems in algebraic geometry into impossible problems in combinatorics. He has a passion for working with students, and has mentored numerous undergraduate and high-school research projects since early in graduate school. To become a mathematician, he cast aside what would have been certain successful careers in countless sports, as well as likely starring roles in Hollywood movies. As a firm proponent of quantum mechanics and the many-worlds interpretation of it, he likes to believe that there is a parallel universe version of himself in which these sacrifices weren’t made.