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Past Events › Graduate Student Algebra Seminar

February 2017

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

February 8, 2017 | 3:00 pm - 4:00 pm EST

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…

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Faye Pasley, “Determinantal representations of hyperbolic plane curves with dihedral invariance”

February 15, 2017 | 3:00 pm - 4:00 pm EST

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…

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March 2017

McKay Sullivan, “Supersymmetric bilinear forms and oscillator algebras”

March 22, 2017 | 3:00 pm - 4:00 pm EDT

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…

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Zach Hough, “Degree-optimal moving frames for rational curves”

March 29, 2017 | 3:00 pm - 4:00 pm EDT

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…

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April 2017

Michael Ruddy, “Signature map on algebraic varieties”

April 5, 2017 | 3:00 pm - 4:00 pm EDT

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?…

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August 2017

Organizational Meeting

August 24, 2017 | 3:00 pm - 4:00 pm EDT
September 2017

What Is?

September 7, 2017 | 3:00 pm - 4:00 pm EDT

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…

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Shira Viel, NC State

September 14, 2017 | 3:00 pm - 4:00 pm EDT

What Is?

September 21, 2017 | 3:00 pm - 4:00 pm EDT
|Recurring Event (See all)

An event every week that begins at 3:00pm on Thursday, repeating until December 7, 2017

Kristen Boyle, NC State, On derivations of Leibniz algebras

September 28, 2017 | 3:00 pm - 4:00 pm EDT

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…

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October 2017

Jane Coons, NC State

October 12, 2017 | 3:00 pm - 4:00 pm EDT

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…

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Faye Pasley, NC State, Invariance and and the Numerical Range

October 19, 2017 | 3:00 pm - 4:00 pm EDT

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.

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November 2017

Ben Hollering, NC State, Longest increasing subsequences of ordered set partitions

November 15, 2017 | 3:00 pm - 4:00 pm EST

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…

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Michael Ruddy, NC State

November 30, 2017 | 3:00 pm - 4:00 pm EST
January 2018

Talk Sign Up

January 11 | 3:00 pm - 4:00 pm EST

We will meet briefly to sign up for talks.

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March 2018

Daniel Bernstein, NC State, Unimodular hierarchical models

March 1 | 3:00 pm - 4:00 pm EST

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…

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Jane Coons, NC State, Geometry and Combinatorics of the Cavander-Farris-Neyman Model with a Molecular Clock

March 15 | 3:00 pm - 4:00 pm EDT

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…

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April 2018

Chetak Hossain, NC State, Enumerative and Algebraic Combinatorics of OEIS A071356

April 12 | 3:00 pm - 4:00 pm EDT

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…

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Caprice Stanley, Suzanne Crifo, NC State

April 23 | 3:00 pm - 4:00 pm EDT

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,…

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Faye Pasley, Molly Lynch, NC State

April 26 | 3:00 pm - 4:00 pm EDT

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…

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