## Past Events › Graduate Student Algebra Seminar

## Christopher Durden, “Geometry and polynomial invariants of a phylogenetic model”

We will discuss whether it is possible to reconstruct a phylogenetic tree from sequence data, given a specific model of evolution. To answer this question for a coalescent-based model, we study ideals associated to the model. By observing some facts about…

Find out more »## Faye Pasley, “Determinantal representations of hyperbolic plane curves with dihedral invariance”

Given a determinantal representation by means of a cyclic weighted shift matrix, one can show the resulting polynomial is hyperbolic and invariant under the action of the dihedral group. Chien and Nakazato (2015) asked the converse question. By properly modifying…

Find out more »## McKay Sullivan, “Supersymmetric bilinear forms and oscillator algebras”

Many important Lie (super)algebras can be constructed using bosonic and fermionic oscillators. We introduce inhomogeneous supersymmetric bilinear forms on a complex superspace and show that they lead to oscillator-like superalgebras. We classify such forms for superspaces up to dimension 7…

Find out more »## Zach Hough, “Degree-optimal moving frames for rational curves”

I will present an algorithm that, for a given vector of n relatively prime polynomials in one variable over an arbitrary field, outputs an invertible matrix with polynomial entries such that it forms a degree-optimal moving frame for the rational…

Find out more »## Michael Ruddy, “Signature map on algebraic varieties”

Let G be a Lie group acting smoothly on the plane. Then two smooth curves C and C' are G-equivalent if there exists some g in G such that gCC'. Can we answer the question, when are two curves G-equivalent?…

Find out more »## What Is?

Lie Algebras, manifolds, varieties. We have all heard terms like these, but may not know quite what they mean. This week we will have introductory "What Is?" talks. These talks are intended to build your vocabulary/intuition for future talks. This…

Find out more »## Kristen Boyle, NC State, On derivations of Leibniz algebras

Leibniz algebras are a generalization of Lie algebras. In this talk I will discuss some results on characteristic ideals, which are analogs of known results from Lie algebra. I will use these results to prove that the radical of a…

Find out more »## Jane Coons, NC State

Algebraic geometry and combinatorics play an important role in the analysis of phylogenetic models. I will give a brief overview of toric geometry. Then I will introduce a particular phylogenetic model, called the Cavander-Farris-Neyman model with a molecular clock, and…

Find out more »## Faye Pasley, NC State, Invariance and and the Numerical Range

The numerical range has been studied extensively in linear algebra and analysis. We will define and discuss properties of the numerical range, then show every numerical range invariant under rotation is associated with a matrix with nice structure.

Find out more »## Ben Hollering, NC State, Longest increasing subsequences of ordered set partitions

The size of a maximum agreement subtree of two phylogenetic trees is a statistic that is often used to test the null hypothesis that no cospeciation occurred between two families of species of interest. The size of the maximum agreement…

Find out more »## Talk Sign Up

We will meet briefly to sign up for talks.

Find out more »## Daniel Bernstein, NC State, Unimodular hierarchical models

The Zariski closure of a discrete log-linear statistical model is a toric variety. In the last twenty years, this fact has lead not only to the development of useful algorithms for working with data, but developments in algebraic geometry and…

Find out more »## Jane Coons, NC State, Geometry and Combinatorics of the Cavander-Farris-Neyman Model with a Molecular Clock

We prove results about the polytope associated to the toric ideal of invariants of the Cavender-Farris-Neyman model with a molecular clock on a rooted phylogenetic tree. For instance, the number of vertices of this polytope is a Fibonacci number and…

Find out more »## Chetak Hossain, NC State, Enumerative and Algebraic Combinatorics of OEIS A071356

We will talk about bijections between various families of combinatorial objects counted by OEIS A071356. These include certain underdiagonal lattice paths, pattern avoiding permutations, pattern avoiding inversion sequences, and posets. Connections will be made to combinatorial Hopf algebras using some…

Find out more »## Caprice Stanley, Suzanne Crifo, NC State

Speaker 1: Caprice Stanley Title: Markov Chain Mixing Time Abstract: Informally a Markov chain is a memoryless stochastic process and its mixing time is the time required for the chain to be near its stationary distribution. Depending on the context,…

Find out more »## Faye Pasley, Molly Lynch, NC State

Speaker 1: Faye Pasley Title: Determinantal Representations, the Numerical Range, and Invariance We study hyperbolic polynomials with symmetry and express them as the determinant of a Hermitian matrix with special structure. By properly modifying a construction of Dixon (1902), we show for…

Find out more »