Kirsten Wickelgren – Colloquium “Mathematics in jury selection and mathematics employment for young students”
Abstract: In many states in the US, a pool of qualified jurors is assembled and then lawyers are allowed to strike a certain number of jurors from the pool, in the sense that the lawyers are allowed to remove the juror from the subset of people who will ultimately decide the outcome of the trial. Strikes can be used for any reason, except a discriminatory reason: A lawyer can strike a juror because “She looked at me in a way I don’t like.” A lawyer cannot strike a juror based on their race or gender. This talk will discuss work done on the mathematics of jury selection in a program called “Mathematics Employment Experience for High School Students.”  High School students in the US are usually between 13 and 18 years old. 

Kirsten Wickelgren – Seminar talks
“Gromov–Witten invariants in A1-homotopy theory”
Abstract: Gromov-Witten invariants count curves in a given homology class on a space passing through cycles representing other given homology classes. For example, the number of complex degree d rational plane curves passing through 3d-1 points is such an invariant. It is independent of the generically chosen points over the complex numbers. (There is 1 line through 2 points, 1 conic through 5, 12 rational degree 3 curves through 8…) Fixed answers to such questions are obtained by  working over an algebraically closed field like the complex numbers. Some of the solutions may be real, or integral, or defined over Q[i], but the fixed count does not see the difference. We use A1-homotopy theory to give arithmetically meaningful counts of rational curves and investigate their properties. This talk will discuss joint work with Erwan Brugallé,  Chongyao Chen, Jesse Kass, Marc Levine, and Jake Solomon. 

 “A1-homotopy theory and the Weil Conjectures”
Abstract: In a celebrated paper from 1948, André Weil proposed a beautiful connection between algebraic topology and the number of solutions to equations over finite fields: the zeta function of a variety over a finite field is simultaneously a generating function for the number of  solutions to its defining equations and a product of characteristic  polynomials of endomorphisms of cohomology groups. This talk will describe the Weil conjectures and then enrich the zeta function to have  coefficients in a group of bilinear forms using A1-homotopy theory. The  enrichment provides a connection between the solutions over finite fields and the associated real and complex manifolds.  The new work in this talk is joint with Tom Bachmann, Margaret Bilu, Wei Ho, Padma Srinivasan, and Isabel Vogt.