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…

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…

We show that the category of vector bundles over the vertices of a locally finite \tilde{A}_{n-1} building \Delta, Vec(\Delta), has the structure of a Tilt(SL_{2k+1}) module category. This module category is the q-analogue of the Tilt(SL_{2k+1}) action on vector bundles over the sl_n weight lattice. Our construction of the Tilt(SL_{2k+1}) action on Vec(\Delta) extends to…

For any metric space, the metric gives deep insight into the space such as geometry and topology of the space. Rather than directly studying a specific space, one may wish to study a sequence of spaces with nice properties and then show that desired properties hold in the limit. To study such a sequence of…

The group of permutations is the canonical example of a finite Coxeter group, and each permutation can be represented visually by a noncrossing arc diagram. Each diagram encodes the canonical join representation of its permutation, and diagrams can be used to understand lattice congruences on the weak order of type A, equivalence relations that respect the…

For some nice subclass of braided monoidal categories, the associator and braiding data are described by an Abelian 3-cocycle . Eilenberg and MacLane demonstrated a surprisingly simple isomorphism between the groups of Abelian 3-cocycles with coefficients in  and quadratic forms with coefficients in , the trace map  by . Like many category theoretical results, this was proven at the level of…

Ed Witten's papers in 1988 drew out the connection between Jones Polynomials of Knots and Chern-Simons theory of 3-dimensional TQFT. Following his work, Reshetikhin and Turaev formulated invariants of 3-manifolds via colored framed knots leading to new TQFTs. In this talk, I will introduce Dehn Surgery on knots, framed knots colored with representations of Hopf…

In this talk, we begin by introducing the audience to some fundamentals of differential geometry of surfaces in ℝ3, focusing on curvature and the adequately named first and second fundamental forms. We will discuss what special parameterizations and properties give rise to isothermic surfaces. Equipped with these tools, we will look at the fundamental theorem for surfaces,…

Marginal independence models have been commonly studied in the context of graphical models, where we use a graph to convey the different marginal independence relations between random variables. However, there are marginal independence relations that cannot be expressed with a graph, which is why we provide a more general framework in which we can define…

Room: SAS 2235   Zoom Meeting link:  https://ncsu.zoom.us/j/95923219557?pwd=T3MzUEZRazRaY2tBdjl1dFVJOG50QT09

Even though the field with one element, , is a meaningless concept, shadows of it have been apparent in multiple categorical analogies. More immediately, one can generalize multiple constructions from algebraic geometry over  to general commutative monoids, which behave like rings over this elusive . In this talk we define, via this analogy, schemes over , and consider zeta…

Of course, anybody can deform a surface in whatever way they want. However, is there a way to deform a surface of revolution into a helicoid while preserving an isometry? How many ways are there? All these questions and more will be answered on Monday, February 13. Zoom Meeting link:  https://ncsu.zoom.us/j/92762214990?pwd=MnA1TnNVQUpzUlo3cTM5RmlNWVF4Zz09      Password: noodle

In Riemannian geometry, given a Riemannian manifold (M,g) one can use geodesics associated with (M,g) to determine information about the shortest distance between points, curvature, triangles on a manifold and Euler characteristic of the space of M in special cases. Thankfully, given a metric on a manifold, we can always determine geodesics on said manifold.…

Real symmetric matrices appear in a wide range of disciplines. One geometric problem that can be asked of two real symmetric matrices is: how are their eigenvalues arranged on the real line? Can we characterize all matrices whose eigenvalues realize a certain arrangement? In this talk, we will use principles from basic algebraic geometry and…

Determining the fusion coefficients for an abstract fusion category is very difficult, and generalizes the problem of plethysm for group representations. As is the case in finite groups, restricting the class of objects we consider can help us to obtain better general results. When one has a group acting on a modular category, it is possible to…

 When studying Tensor Categories we want to understand what algebra objects can be found in those categories. After finding such objects it's natural to consider their A -modules and more importantly the category of A (bi)-modules. This talk will attempt to explain this concept and enlighten listeners with motivating examples. Zoom Meeting link:  https://ncsu.zoom.us/j/92762214990?pwd=MnA1TnNVQUpzUlo3cTM5RmlNWVF4Zz09      Password:…

One common problem in machine learning is to train a computer to correctly classify some data set when the potential set of features is known. However, the problem of classification becomes even more tricky if an adversary gains access to the input data set and can modify the features. In this talk, I will first…

 Classically, the primary objects one was concerned with in algebraic geometry were the zero sets of systems of polynomial functions, which we call varieties. Since the work of Grothendieck, the main objects of study in modern algebraic geometry are schemes. In this talk, I will introduce the concept of an affine scheme, a key part…

Hypertoric varieties are quaternionic analogs of toric varieties, important for their interaction with the combinatorics of matroids as well as for their prominent place in the rapidly expanding field of algebraic symplectic and hyperkahler geometry.  In the last decade, hypertoric varieties have appeared prominently in investigations of symplectic duality, a mathematical incarnation of 3d mirror…

Symmetric functions are very interesting combinatorial objects. After decomposing certain symmetric functions in terms of different bases, we can often combinatorially interpret the resulting coefficients. This is made particularly easy if those coefficients are positive (or controllably negative). The chromatic symmetric function is one such symmetric function, and its decomposition has been of interest for…