Algèbre et géométrie

Let G be a connected locally compact group with a left Haar measure μ, and let A,B ⊆ G be nonempty and compact. Assume further that G is unimodular, i.e., μ is also the right Haar measure; this holds, e.g., when G is compact, a nilpotent Lie group, or a semisimple Lie group. In 1964, Kemperman showed that μ(AB) ≥ min {μ(A)+μ(B), μ(G)} . The Kemperman inverse problem (proposed by Griesmer, Kemperman, and Tao) asks when the equality happens or nearly happens. I will discuss the recent solution of this […]

This talk describes the connection between /strong minimality/ of the differential equation satisfied by an complex analytic function and the real and imaginary parts of the function being /Pfaffian/. The talk will not assume the audience knows these notions previously, and will attempt to motivate why each of them are important notions in various areas. The connection we give, combined with a theorem of Freitag and Scanlon (2017) provides the answer to a question of Binyamini and Novikov (2017). We also answer a question of Bianconi (2016). We give what […]