# Algebra, Geometry, and Cryptology Seminar Fall 2017

Fall 2017
Fridays, 3:00-3:50
Location: MB124

The Algebra, Geometry and Cryptology (AGC) Seminar meets on selected Fridays, dates indicated below. The seminar is organized by Zach Teitler <zteitler@boisestate.edu>.

• Taking the seminar for credit
The seminar may be taken for credit as Math 498. For information about receiving credit, contact zteitler@boisestate.edu.
• Everybody is welcome!
Everybody interested is welcome to attend and participate! Enrollment for credit is not required. We welcome students to attend and present in the seminar. Attending seminars and colloquium presentations is an excellent way to learn about research topics and senior thesis topics.
• AGC Seminar mailing list
Announcements of upcoming seminars are sent by email to all interested participants. To be added to the AGC Seminar mailing list, contact zteitler@boisestate.edu.

### August 25:

Open problems & Planning

### September 1:

Topology Seminar
Jens Harlander, Boise State University
The Geometric Realization Problem

### September 8:

Scott Andrews, Boise State University
The $q,t$-Catalan numbers
The Catalan numbers $C_n$ enumerate many different combinatorial objects, including triangulations of an $(n+2)$-gon, 123-avoiding permutations, and Dyck paths. There are two $q$-analogues of the Catalan numbers, both of which turn out to be specializations of the more general $q,t$-Catalan numbers. In this talk I will introduce the Catalan numbers and the idea of a $q$-analogue of a number and I will define the $q,t$-Catalan numbers.

### September 15:

Topology Seminar
Uwe Kaiser, Boise State University
A Survey of the Volume Conjecture in Knot Theory

### September 22:

Zach Teitler, Boise State University
Recent* advances in Waring rank and apolarity

### September 29:

Topology Seminar
Jens Harlander, Boise State University
Groups, Homology, and Bias

### October 6:

Zach Teitler, Boise State University
High-rank and maximum-rank geometry

### October 13:

Aaron Bertram, University of Utah
The Tropical Nullstellensatz
The (weak) Hilbert Nullstellensatz states that if a system of polynomial equations in several variables has no complex solutions then the equation $1 = 0$ must be a combination of the polynomial equations in the system. In this talk, I will discuss a version of this theorem that holds when complex numbers are replaced with tropical numbers. This is joint work with Rob Easton.

### October 20:

Jonny Comes, College of Idaho
The Heisenberg category: diagram calculus for induction and restriction functors
In 2010 Khovanov introduced the so-called Heisenberg category H. Among other things, H provides a diagrammatic setting for calculations involving induction and restriction functors for the symmetric groups. This talk will be an introduction to the Heisenberg category following Brundan’s more recent treatment. I will start with an introduction to induction and restriction for the symmetric groups. In particular, I will describe a combinatorial interpretation of induction and restriction in terms of arrays of boxes known as Young diagrams. This will lead us to the so-called “Mackey decomposition” for the symmetric group. I will then explain Brundan’s definition of H and its connection to induction and restriction. If time permits, I will discuss Khovanov’s motivation or describe one of my current projects related to this stuff.

### October 27:

Topology Seminar
Kayla Neal, Boise State University

### November 3:

Cassandra Peterson, Boise State University
Statistics and climate change
Several recent developments in statistics are directly related to and used to evaluate climate change.

### November 10:

Topology Seminar
Michelle Pyles, Boise State University
An Introduction to the Cap Set Problem: the game SET and Tic-Tac-Toe

### November 17:

No seminar meeting

### November 24:

No seminar meeting (Thanksgiving holiday)

### December 1:

Marion Scheepers, Boise State University
Permutation sorting and abstract mathematics
In this talk we feature two basic permutation sorting operations that are hypothesized to act in the genome maintenance program of certain organisms. It turns out that these sorting operations are manifestations of more general mathematical structures in graph theory, linear algebra and topology. We briefly survey these connections.

TBA