Calendar

Feb
1
Thu
Colloquium: Leslie Hogben (Iowa State U.) @ Post 127
Feb 1 @ 3:00 pm – 4:00 pm

Speaker:
Leslie Hogben
Iowa State University and American Institute of Mathematics

Title:
Power domination and zero forcing: Using graphs to model real-world problems

Abstract:
A graph $G = (V, E)$ is a set of vertices $V = {1, dots , n}$ and set of edges $E$ of
two element sets of vertices. A graph can be used to model connections between
vertices, such as airline routes between cities, internet connections, a quantum
system, or an electric power network.
Power domination and zero forcing are related coloring processes on graphs.
We start with a set of vertices colored blue and the rest colored white. We apply
a color change rule to color the white vertices blue. A set of blue vertices that
can color all vertices blue by using the power domination color change rule (or
zero forcing color change rule) is called a power dominating set (or a zero forcing
set). Finding a such set allows us to solve various problems, and a minimum
such set can provide an optimal solution.
In an electric power network, a power dominating set (blue vertices) gives
a set of locations from which monitoring units can observe the entire network.
In a quantum system, a zero forcing set (blue vertices) gives a set of locations
from which the entire system can be controlled.
This talk will describe power domination and zero forcing processes on
graphs and some of their applications.

Feb
2
Fri
Logic seminar: David Ross
Feb 2 @ 2:30 pm – 3:20 pm

This semester the Logic Seminar continues at a new day and time, Fridays at 2:30 in Keller 314.

For the first meeting this Friday I will (probably) speak about _Skolem polynomials_:

Abstract:
Over 100 years ago Hardy proved that a certain large class of real functions
was linearly ordered by eventual domination. In 1956 Skolem asked
whether the subclass of integer exponential polynomials is *well*-ordered
by the Hardy ordering, and conjectured that its order type
is epsilon_0. (This class is the smallest containing 1, x, and closed
under +, x, and f^g.) In 1973 Ehrenfeucht proved that the class is
well-ordered, and since then there has been some progress on the order
type.

The proof of well-ordering is rather remarkable and very short, and I
will attempt to expose it (which is to say, cover it) in the hour.

David Ross

Colloquium: Pamela Harris (Williams)
Feb 2 @ 3:30 pm – 4:30 pm
Feb
9
Fri
Logic seminar: Mushfeq Khan
Feb 9 @ 2:30 pm – 3:30 pm

Mushfeq Khan will speak on amenability and symbolic dynamics.
As usual the seminar is in Keller 314.

Talk Story with Pavel Guerzhoy
Feb 9 @ 3:30 pm – 4:30 pm

A Talk Story in Number Theory.

There is a childish misconception that the occupation of a professional mathematicians
is to operate with very big numbers. That is presumably primarily applicable to those who
do Number Theory. In this talk, I will show that this sometimes may be not too far from truth.

The talk is supposed to be entertaining and is directed to grad students willing to get a rough idea
about what it takes (and what it may give) to choose Number Theory as a research speciality.

Feb
13
Tue
Number Theory Seminar: Claus Sorensen (UCSD) @ To be determined
Feb 13 @ 2:30 pm – 3:30 pm

Speaker: Claus Sorensen (UCSD)
Title: Local Langlands in rigid families
Abstract: The local Langlands correspondence attaches a representation of GL(n,F) to an n-dimensional representation of the Galois group of F (a local field). In the talk I will report on joint work with Johansson and Newton, in which we interpolate the correspondence in a family across eigenvarieties for definite unitary groups U(n). The latter are certain rigid analytic varieties parametrizing Hecke eigensystems appearing in spaces of p-adic modular forms. These varieties carry a natural coherent sheaf and we show that its dual fibers are built from the local Langlands correspondence by taking successive extensions; even at the non-classical points. Our proof employs certain elements of the Bernstein center which occur in Scholze’s trace identity. The first half of the talk is intended for a general audience with a limited background in number theory.

Feb
16
Fri
Logic seminar: David Webb
Feb 16 @ 2:30 pm – 3:30 pm

Continuing the theme of symbolic dynamics, I will demonstrate a proof of Simpson’s result that “Entropy = Dimension” for N^d and Z^d, and discuss some of Adam Day’s work generalizing these results to amenable groups.

Feb
23
Fri
Logic seminar: Umar Gaffar @ Keller 314
Feb 23 @ 2:30 pm – 3:30 pm

This week Umar Gaffar will give Shelah’s proof of the following result:

Let $\lambda$ be the cardinality of an ultraproduct of finite sets. If $\lambda$ is infinite then $\lambda=\lambda^{\aleph_0}$.