# ACGT Seminar

The Algebra, Combinatorics, Geometry, and Topology (ACGT) Seminar meets on Tuesdays at 12:45-2:00pm in Room 164 of the Adel Mathematics Building. If you are interested/willing to give a talk, please contact Dana C. Ernst, ACGT Coordinator.

# Schedule Spring 2015

Note that talks are listed in reverse chronological order.

### Semisimple Lie algebras

Dates: March 24, March 31, April 7, April 14, 2015

Speaker: Thomas Holtzworth (NAU)

Abstract: In this series of talks we will discuss semisimple Lie algebras.

### A weak image of the matroid of the braid arrangement, realizable in characteristic two

Date: March 10, 2015

Speaker: Michael Falk (NAU)

Abstract: Motivated by applications in the theory of (higher-degree) resonance varieties, we give a new (or perhaps newly rediscovered) construction of a rank-reducing weak map of the matroid $M(K_n)$ of the complete graph (which coincides with the matroid of the reflection arrangement of type $A$). The weak image arises naturally as a minor of the projective space over $\mathbb{Z}_2$.

### The simple singularities

Date: March 3, 2015

Speaker: Michael Falk (NAU)

Abstract: We give an elementary introduction to the basic ideas in the ADE classification of simple singularities, with the eventual goal to expose the appearance of Weyl groups in singularity theory. In this first installment we discuss isolated singular points of complex hypersurfaces and the Milnor fibration.

### Groups with all order subsets dividing the order of the group

Date: February 17, 2015

Speaker: Bret Benesh (College of Saint Benedict & Saint John’s University)

Abstract: Consider the symmetric group $S_3$ acting on three letters. It has one element of order $1$, three elements of order $2$, and two elements of order $3$. Notice that for each order, the number of elements of that order (one, three, and two, respectively) divides the order of the group, which is $3!=6$. This is not always true, as there are two elements of order $3$ in $\mathbb{Z}_3$. Groups with this property are called “perfect order subset groups,” or POS groups. We will discuss the basics of POS groups and some classification theorems about POS groups.

### Symmetries of tetravalent metacirculant graphs of type III

Dates: February 3, February 10, February 24, 2015

Speaker: Ben Lantz (NAU)

Abstract: I will discuss my thesis work done with Dr. Wilson last spring and examine symmetries in metacirculant graphs and what a metacirculant graph is. I’ll talk about how Linking Ring structures are used to help classify these graphs. Then I’ll focus on some of the problems and questions that we encountered during our research.

### The Orlik-Solomon algebra: differential forms and cohomology

Dates: January 20, January 27, 2015

Speaker: Michael Falk (NAU)

Abstract: We give a short proof of the isomorphism of the Orlik-Solomon algebra of a complex arrangement with an algebra of differential forms, and of the latter with the (De Rham) cohomology of the complement. As a corollary of the latter isomorphism, the complement is a formal space (in the sense of Sullivan). The proof uses a long exact sequence from elementary algebraic topology and the no-broken-circuit basis of the OS algebra.