# This Week's Events

## Seminars

Click on seminar heading to go to seminar page.

• ### Algebra Seminar

Monday September 18, 2017 at 13:30, Wachman Hall, Rm. 617
Introduction to categories, II

Vasily Dolgushev, Temple University

I will talk about adjoint functors, limits and colimits. I hope to give many examples. If time will permit, I will start talking about monoidal categories and monoidal functors.

• ### Analysis Seminar

Monday September 18, 2017 at 14:40, Wachman 617

Blair Davey, City College of New York

In the late 1960s, E.M. Landis made the following conjecture: If $u$ and $V$ are bounded functions, and $u$ is a solution to $\Delta u = V u$ in $\mathbb{R}^n$ that decays like $|u(x)| \le c \exp(- C |x|^{1+})$, then $u$ must be identically zero. In 1992, V. Z. Meshkov disproved this conjecture by constructing bounded functions $u, V: \mathbb{R}^2 \to \mathbb{C}$ that solve $\Delta u = V u$ in $\mathbb{R}^2$ and satisfy $|u(x)| \le c \exp(- C |x|^{4/3})$. The result of Meshkov was accompanied by qualitative unique continuation estimates for solutions in $\mathbb{R}^n$. In 2005, J. Bourgain and C. Kenig quantified Meshkov's unique continuation estimates. These results, and the generalizations that followed, have led to a fairly complete understanding of the complex-valued setting. However, there are reasons to believe that Landis' conjecture may be true in the real-valued setting. We will discuss recent progress towards resolving the real-valued version of Landis' conjecture in the plane.

• ### Probability Seminar

Tuesday September 19, 2017 at 15:00, UPenn (David Rittenhouse Lab 3C8)
Invasion percolation on Galton-Watson trees

Marcus Michelin, UPenn

Given an infinite rooted tree, how might one sample, nearly uniformly, from the set of paths from the root to infinity? A number of methods have been studied including homesick random walks, or determining the growth rate of the number of self-avoiding paths. Another approach is to use percolation. The model of invasion percolation almost surely induces a measure on such paths in Galton-Watson trees, and we prove that this measure is absolutely continuous with respect to the limit uniform measure as well as other properties of invasion percolation. This work in progress is joint with Robin Pemantle and Josh Rosenberg.

Tuesday September 19, 2017 at 16:00, Wachman 617

• ### Global Analysis Seminar

Wednesday September 20, 2017 at 11:40, Wachman 527

Max Reinhold Jahnke, University of São Paulo, Brazil

First, in order to understand the statement of a theorem by Bott we will see a brief exposition of the theory of cohomology of Lie algebras. As an application, we will see how to use it to prove that the study of the Dolbeault cohomology of left-invariant complex structures on semisimple compact Lie groups can be reduced to the study a purely algebraic problem: the study of Dolbeault cohomology of complex structures on semisimple compact Lie algebras. This approach was first used by Pittie.

• ### Big Problems / Big Ideas Seminar

Wednesday September 20, 2017 at 13:30, Wachman 617
Counting problems in geometry and group theory

Samuel Taylor, Temple University

We’ll explore the following two questions:

1) What geometric structures can be associated to a random 3-dimensional manifold?

2) How likely is it that two random elements of a group G commute?

Although these questions appear to be quite different, we’ll see how they fit into the common framework of counting problems in geometry group theory. Our talk will be a friendly overview of this framework and stress many problems — some of which have been recently answered and some of which are still open.

• ### Applied Mathematics and Scientific Computing Seminar

Wednesday September 20, 2017 at 16:00, 617 Wachman Hall

Heike Faßbender, Technical University Braunschweig, Germany

## Conferences

There are no conferences this week.