# This Week's Events

## Seminars

Click on seminar heading to go to seminar page.

• ### Algebra Seminar

Monday February 20, 2017 at 13:30, Wachman Hall Rm. 617
Maximum nullity, zero forcing, and power domination

Chassidy Bozeman, Iowa State University

Zero forcing on a simple graph is an iterative coloring procedure that starts by initially coloring vertices white and blue and then repeatedly applies the following color change rule: if any vertex colored blue has exactly one white neighbor, then that neighbor is changed from white to blue. Any initial set of blue vertices that can color the entire graph blue is called a zero forcing set. The zero forcing number is the cardinality of a minimum zero forcing set. A well known result is that the zero forcing number of a simple graph is an upper bound for the maximum nullity of the graph (the largest possible nullity over all symmetric real matrices whose (ij)-th entry (for distinct i and j) is nonzero whenever {i,j} is an edge in G and is zero otherwise). A variant of zero forcing, known as power domination (motivated by the monitoring of the electric power grid system), uses the power color change rule that starts by initially coloring vertices white and blue and then applies the following rules: 1) In step 1, for any white vertex w that has a blue neighbor, change the color of w from white to blue. 2) For the remaining steps, apply the color change rule. Any initial set of blue vertices that can color the entire graph blue using the power color change rule is called a power dominating set. We present results on the power domination problem of a graph by considering the power dominating sets of minimum cardinality and the amount of steps necessary to color the entire graph blue.

• ### Analysis Seminar

Monday February 20, 2017 at 14:40, Wachman 617
Differentiability and rectifiability on metric planes

Guy David, Courant Institute, New York University

Since the work of Cheeger, many non-smooth metric measure spaces are now known to support a differentiable structure for Lipschitz functions. The talk will discuss this structure on metric measure spaces with quantitative topological control: specifically, spaces whose blowups are topological planes. We show that any differentiable structure on such a space is at most 2-dimensional, and furthermore that if it is 2-dimensional the space is 2-rectifiable. This is partial progress on a question of Kleiner and Schioppa, and is joint work with Bruce Kleiner.

• ### Colloquium

Monday February 20, 2017 at 16:00, Wachman 617
2-Segal spaces and the Waldhausen S-construction

Julia Bergner, University of Virginia

The notion of a 2-Segal space was recently defined by Dyckerhoff and Kapranov, and independently by Galvez-Carrillo, Kock, and Tonks under the name of decomposition space. Unlike Segal spaces, which encode the structure of a category up to homotopy, 2-Segal spaces encode a more general structure in which composition need not exist or be unique, but is still associative. Both sets of authors above proved that the output of the Waldhausen $S_\bullet$-construction is a 2-Segal space. In joint work with Osorno, Ozornova, Rovelli, and Scheimbauer, we look at a discrete version of this construction whose output is a 2-Segal set. We show that, via this construction, the category of 2-Segal sets is equivalent to the category of augmented stable double categories. In this talk, I'll introduce 2-Segal sets and spaces, discuss this result and a conjectured homotopical generalization, and, time permitting, look at some other interesting features of 2-Segal spaces.

• ### Probability Seminar

Tuesday February 21, 2017 at 15:00, UPenn (David Rittenhouse Lab 3C8)
Large deviation and counting problems in sparse settings

Shirshendu Ganguly, Berkeley

The upper tail problem in the Erdös-Rényi random graph $G \sim G(n,p)$, where every edge is included independently with probability $p$, is to estimate the probability that the number of copies of a graph $H$ in $G$ exceeds its expectation by a factor $1 + d$. The arithmetic analog considers the count of arithmetic progressions in a random subset of $Z/nZ$, where every element is included independently with probability $p$. In this talk, I will describe some recent results regarding the solution of the upper tail problem in the sparse setting i.e. where $p$ decays to zero, as $n$ grows to infinity. The solution relies on non-linear large deviation principles developed by Chatterjee and Dembo and more recently by Eldan and solutions to various extremal problems in additive combinatorics.

• ### Geometry and Topology Seminar

Wednesday February 22, 2017 at 14:30, Wachman 617
Minimal surfaces with bounded index

Davi Maximo, University of Pennsylvania

Abstract: In this talk we will give a precise picture on how a sequence of minimal surfaces with bounded index might degenerate on a given closed three-manifold. As an application, we prove several compactness results.

• ### Applied Mathematics and Scientific Computing Seminar

Wednesday February 22, 2017 at 16:00, 617 Wachman Hall