## University of Sydney Algebra Seminar

# Evgeny Mukhin (Indiana University-Purdue University Indianapolis)

## Friday 9 May, 12:05-12:55pm, Place: 373

### Counting real solutions

Given a system of algebraic equations with real coefficients, it is much easier to count complex solutions than real. I will explain a new way to get information on a number of real solutions. My algebraic equations come from problems in Schubert Calculus. For example, given a monic real polynomial w(x) of degree 2d, count the number of pairs of monic real polynomials f(x) and g(x) of degrees d+1 and d, the subleading coefficient of f(x) is zero, such that and f'g-fg'=w. I will explain that such questions can be studied by means of representation theory and integrable systems. This talk is based on a joint project with V. Tarasov (IUPUI).