Skip to main content

Ben Freedman, NC State, Nonlinear differential equations subject to generalized boundary conditions

In this talk, we analyze nonlinear differential equations subject to generalized boundary conditions. More specifically, I will provide a framework from which we can provide conditions, which are straightforward to check, for the solvability of a large number of nonlinear scalar boundary value problems. I will begin by giving the general strategy which involves a reformulation of our…

Suzanne Crifo, NC State, Some Maximal Dominant Weights and their Multiplicities for Affine Lie Algebra Representations

Affine Lie algebras are infinite dimensional analogs of finite dimensional simple Lie algebras. It is known there are finitely many maximal dominant weights for any integrable highest weight representation of an affine Lie algebra. However, determining these maximal dominant weights is a nontrivial task. So far only the descriptions of these weights are known for…

Dustin Leininger, NC State, Crash Course on Spectral Sequences

SAS 4201

Spectral sequences are an algebraic tool for computing (co)homology of differential graded algebras (DGAs) developed by by Leray in the 1940's and have since found applications in various fields which utilize DGAs to compute useful invariants (e.g. Algebraic Topology, Knot Theory, ect.). This talk will provide a broad overview and attempt to answer some basic…

Owen Coss, NC State, Resolving Singularities by the Blowup Process in R^2

SAS 4201

In this talk I will introduce the ideas of singularities of a polynomial and resolution of those singularities, and then develop the blowup process algorithm. For a polynomial f, a point is singular if f and all its first partials vanish at that point. A resolution of the singularities of f gives a non-singular polynomial…

Georgy Scholten, NC State, Hyperplane Arrangements

SAS 4201

The study of hyperplane arrangements begins at fundamental questions such as: how many pieces can one cut a cake into with n slices? Quickly, hyperplane arrangements generate many intricately interesting mathematical structures and connections to many seemingly unrelated topics appear. I will attempt to show how matroids offer a convenient framework to study hyperplane arrangements…

Benjamin Hollering, NC State, The Monomial Model and Limits of Trees

In this talk I'll introduce a new random tree model that associates a family of probability distributions on binary trees to each binary tree shape. We'll then use this new model, convex geometry, and the combinatorics of multisets and trees to obtain a finite form of a deFinetti-type theorem for rooted binary trees. This talk…

Pratik Misra, NC State, Bounds on the expected size of the maximum agreement subtree

Rooted binary trees are used in evolutionary biology to represent the evolution of a set of species where the leaves denote the existing species and the internal nodes denote the unknown ancestors. Maximum agreement subtree is used as a measure of discrepancy between two trees. In this talk, I will define the notion of "maximum…

Christian Smith, NC State, The Algebra of “up-operators” for Young’s Lattice and Bruhat Order on S_n

Let  be a free associative algebra over  generated by  for  in some indexing set  and let  be a poset.  For  and   we define an action of   on  (the complex vector space with basis )  in a way such that  either annihilates   or sends it to  where  covers  and we extend multiplicatively and linearly.  Let  be the two-sided ideal which annihilates all elements of .  We characterize  when  is Young's Lattice and we discuss the…

Ella Pavlechko, Visualizing Curves in the Projective Plane

The Italian Renaissance painters began to incorporate perspective into their drawings in the 1400’s, but our eyes naturally understand depth from the 2-dimensional image on the back of our eyeball. It’s this projection on the retina that allows mathematicians to represent field of view with the projective plane, and in this talk we’ll investigate what makes it so difficult to…

Aida Maraj, Asymptotic Behaviours of Hierarchical Models

Hierarchical models are statistical log-linear models that record the dependency relations among random variables in statistics. Diaconis and Sturmfels in '98 propose using ideals to study these models. I will start by introducing hierarchical models and their ideals. In this talk we'll show that studying an entire family of ideals simultaneously can lead to greater insight than studying them individually. No…

Jordan Altmeter, NC State, Hypercube Graph Associahedra

Zoom

The associahedron is a well-studied polytope. For n dimensions, its vertices are counted by the n-th Catalan number, a sequence starting 1,1,2,5,14,42,... and which counts many, many, many combinatorial objects, such as Dyck paths, planar binary trees, noncrossing set partitions, and polygonal triangulation. There is a well-known generalization of the associahedron, called the graph associahedron,…

Joseph Cummings, University of Kentucky, Well-Poised Embeddings of Arrangement Varieties

Zoom

An affine variety  is said to be well-poised if  is prime for every . Arrangement varieties are a special class of -varieties built from a hyperplane arrangement decorated by polyhedra. We will show that arrangement varieties always have a well-poised embedding and explore their toric degenerations coming from their tropicalizations. As a class of examples, we realize the Cox…

Erik Mainellis, Factor Systems and the Second Cohomology Group of Leibniz Algebras

Zoom

Factor systems are a tool for working on the extension problem for algebraic structures such as groups, Lie algebras, and associative algebras. We construct the Leibniz algebra analogue to a series of group-theoretic results from W. R. Scott’s Group Theory. Fixing a pair of Leibniz algebras A and B, we develop a correspondence between factor systems…

Jane Coons, Quasi-Independence Models with Rational Maximum Likelihood Estimator

Zoom

Let X and Y be random variables. Quasi-independence models are log-linear models that describe a situation in which some states of X and Y cannot occur together, but X and Y are otherwise independent. We characterize which quasi-independence models have rational maximum likelihood estimator, or MLE, based on combinatorial features of the bipartite graph associated…

Cashous Bortner, NC State, Identifiabiity of Linear Compartmental Tree Models

Zoom

A linear compartmental model is a linear ODE model which can be visualized by a directed graph.  Identifiability is the study of determining whether a model's parameter values can be inferred from the defining "input-output equation" under perfect conditions.  In this talk, I present a novel combinatorial formula for the computation of the coefficients of these…

Cashous Bortner, NC State, “What is an Internship” Panel

Zoom

Are you a math undergrad or grad student and interested in doing an internship related to math?  This event is for you!  The Graduate Training Module for Friday, October 8th is titled, "What is an Internship?" and consists of a panel of current graduate students who have done several different types of internships,  and are ready and…

Jordan Almeter, NC State, P-graph Associahedra

Zoom

Graph associahedra are simple polytopes dual to tubing complexes based on graphs, where a tubing consists of compatible connected subgraphs of a graph G. Graph associahedra can be realized by repeatedly truncating faces of a simplex. We generalize graph associahedra to define P-graph associahedra, which can be realized by repeatedly truncating faces of a simple polyhedron P. When P is…

Joe Johnson, NC State, Birational Labelings of the Rectangle and Trapezoid Posets

Zoom

The rectangle poset and the action of rowmotion on it are two well studied objects in dynamical algebraic combinatorics, but work involving the trapezoid poset has proven more difficult. In 1983 Proctor showed that the number of reverse plane partitions of the rectangle poset and its associated trapezoid are the same. Since then it has…