In their celebrated 1993 paper, Brink and Howlett proved that all finitely generated Coxeter groups are automatic. In particular, they constructed a finite state automaton recognising the language of reduced words in a Coxeter group. This automaton is not minimal in general, and recently Christophe Hohlweg, Philippe Nadeau and Nathan Williams stated a conjectural criteria…
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…
Nicolette Price from Mathematics IT will be leading an interactive seminar on today's best features of file sharing using cloud services. You'll have the opportunity to go hands on with her as she walks you through multiple platforms and different ways to get your files where they need to be, and to who needs access to…
During this talk I will present a queuing model for database locking systems, where jobs represent user requests for simultaneous access to a set of files in a large database. While files are in use, their content can change, so to preserve consistency throughout the database files currently in use are locked, creating blocking and…
This talk will address deterministic mean field games for which agents are restricted in a closed domain of R^n with smooth boundary. In this case, the existence and uniqueness of Nash equilibria cannot be deduced as for unrestricted state space because, for a large set of initial conditions, the uniqueness of solutions to the minimization…
Computing Tor with spectral sequences.
Given a positive-definite even lattice Q, one can construct a lattice vertex algebra V. An important problem in vertex algebra theory and conformal field theory is to classify the representations of the subalgebra of fixed points, known as an orbifold, corresponding to an isometry of the underlying lattice. Once the representations are known, one can calculate their characters to further…
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…
In recent years, the study of evolution equations featuring a fractional Laplacian has received much attention due to the fact that they have been successfully applied into the modelling of a wide variety of phenomena, ranging from biology, physics to finance. The stochastic process behind fractional operators is linked, in the whole space, to an…
Knot homology theories
The remarkable Ramanujan’s congruences for the partition function p(n) will be presented. Here is Ramanujan’s own account: “I have proved a number of arithmetic properties of p(n)...in particular that p(5n+4)≡0 (mod 5), p(7n+5)≡0 (mod 7). ... I have since found another method which enables me to prove all of theses properties and a variety of…
How much is an idea really worth? What defines success for a product? How can we quantify "better" or “worse”? At Microsoft we have tens of thousands of engineers and data scientists trying to improve products that touch over a billion people worldwide. The data scale is enormous, and we're trying to learn from that…
When a hurricane threatens North Carolina, researchers use computational models to predict how the ocean waters will rise, and what areas will be flooded. Emergency managers rely on fast and accurate storm surge predictions from these models to make decisions and estimate damages during storm events. These models use unstructured, finite-element meshes to describe the…
The the 14th Annual NC State University Graduate Student Research Symposium will be held in the Jane S. McKimmon Center on Wednesday, March 20, 2019. The poster session will be from 1:30pm to 4:00pm. This year, there will be over 200 poster presentations representing research being conducted in 70 graduate programs from all colleges. …
In the first part of this work, we consider the strategy of realizing the solution of the three-dimensional linear wave equation with radial Cauchy data as a limit of radial exterior solutions satisfying vanishing Neumann and Dirichlet conditions, on the exterior of vanishing balls centered at the origin. We insist on robust arguments based on energy methods and strong convergence. Our findings show that while one…