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September 2018

Michael Weselcouch, NC State, P-partition Generating Functions of Naturally Labeled Posets

September 12, 2018 | 3:00 pm - 4:00 pm EDT

The P-partition generating function of a (naturally labeled) poset P is a quasisymmetric function enumerating order-preserving maps from P to Z^+. Using the Hopf algebra of posets, we give necessary conditions for two posets to have the same generating function.…

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October 2018

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

October 17, 2018 | 3:00 pm - 4:00 pm EDT

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…

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November 2018

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

November 14, 2018 | 3:00 pm - 4:00 pm EST

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…

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January 2019

Zev Woodstock, NC State, The Gospel of Proximal Calculus: Optimization for non-differentiable problems

January 29 | 2:00 pm - 3:00 pm EST

This discussion includes an eclectic mix of convex analysis, subdifferential calculus, and nonlinear analysis. We will introduce modern theoretical tools and algorithms used to solve non-differentiable optimization problems across the sciences. This discussion will focus more on the theory, proofs,…

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February 2019

Dustin Leininger, NC State, Crash Course on Spectral Sequences

February 5 | 2:00 pm - 3:00 pm EST

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…

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

February 12 | 2:00 pm - 3:00 pm EST

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…

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Georgy Scholten, NC State, Hyperplane Arrangements

February 19 | 2:00 pm - 3:00 pm EST

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.…

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March 2019

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

March 5 | 2:00 pm - 3:00 pm EST

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…

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September 2019

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

September 20 | 11:45 am - 12:45 pm EDT

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…

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

September 27 | 11:45 am - 12:45 pm EDT

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…

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October 2019

Ella Pavlechko, Visualizing Curves in the Projective Plane

October 25 | 11:45 am - 12:45 pm EDT

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…

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