Mathematics

A Mathematical View of Biology and Diversification

Vanessa Rivera-Quiñones (Illinois Math)

Abstract: Have you ever wondered about the meaning of the phrase "survival of the fittest"? To an evolutionary biologist, fitness simply means reproductive success and reflects how well an organism is adapted to its environment. How systems adapt over time has been a central question in Biology and other Life-Sciences. While I will focus on the theory of Adaptive Dynamics, there are many areas of mathematics that have contributed to our understanding of adaptation. In this talk, I will give an overview of how we can use mathematical models to understand adaptation as an evolutionary process and its relationship to creating and preserving diversity. If time permits, I will also address the connections between this theory and my own research in disease modeling.

Poisson Manifolds and their Stacks

Joel Villatoro (UIUC)

Abstract: The categorical notion of a differentiable stack and the theory of Lie groupoids are related by the concept of Morita equivalence. To any Lie groupoid, we can associate a differentiable stack so that Morita equivalence of Lie groupoids corresponds to an isomorphism of stacks. There is also a closely related notion of Morita equivalence of Poisson manifolds. We can then ask if there is a way to associate a stack to a Poisson manifold such that a similar property holds. In this talk I will introduce a 'site' which answers this question. I will also give a few concrete examples of the kinds of geometric phenomena captured by stacks over this site.

Teleportation

Marius Junge (Department of Mathematics, University of Illinois)

Abstract: Teleportation is real, and has a clear mathematical explanation. Don't worry, nobody will be 'beamed up' and then 'lost in space' during this talk. Instead, we will study the nice collection of matrices responsible for teleportation and superdense coding. This will required us to dive into some aspects of quantum mechanics. The aim of this talk is to understand that there is plenty of abstract mathematics to be discovered in the interface of operator algebra theory and quantum information theory.

Embedding of Heisenberg group in L_1

Jeremy Tyson (UIUC)

Abstract: We continue proving the non-embedding result