We will discuss arithmetic restriction phenomena and its relation to Waring's problem, focusing on how recent work of Wooley implies certain restriction bounds.
I will discuss some p-adic (and mod p) criteria ensuring that an elliptic curve over the rationals has algebraic and analytic rank one, as well as some applications.
The talk will survey some results about smooth and topological 4-manifolds obtained via surgery, and discuss some contrasting information provided by gauge theory about smooth finite group actions on 4-manifolds.
Familiar species; humans, mammals, fish, reptiles and plants represent only a razor’s edge of the Earth’s immense biodiversity. Most of the Earth’s multicellular species lie buried in soil, inside of plants, and in the undergrowth, and include millions of unknown species, almost half of which are thought to be fungi. Part of the amazing success of fungi may be the elegant solutions that they have evolved to the problems of dispersing, growing and adapting to changing environments. I will describe how we using both math modeling and experiments to discover some of these solutions. I will focus on (i) how cytoplasmic mixing enables some species to tolerate internal genetic diversity, making them better pathogens and more adaptable, and (ii) how self-organization of these flows into phases of transport and stasis enables cells to function both as transport conduits, and to perform other functions like growth and secretion.