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…
Computing Tor with spectral sequences.
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…
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…
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…
Fixed point theory studies the extent to which fixed points of a self map of a space are intrinsic. In many mathematical settings, the existence of a solution can be rephrased in terms of the existence of a fixed point for an appropriate map, leading to applications across mathematics. Variations of fixed point problems have…
“I have traversed this bottomless night, which extinguished all light and joy of my life. I entreat you, leave the science of parallel alone”, wrote a Hungarian mathematician Farkas Bolyai to his son János, horrified at the thought that his son is attracted by the problem of parallels. János was not deterred, however, and discovered,…
Convex optimization problems appear naturally across the sciences in fields such as compressed sensing, statistics, machine learning, image processing, and inverse problems. This talk will discuss the theory, applications, and methods of proximal minimization: a wide-reaching subset of convex optimization. Advantages: you do not need your optimization problem to be differentiable (e.g. minimization problems with l-1…
(Brief Note: In this talk, we utilize Jupyter notebooks to re-create some of our published results in real-time and also build a "computational intuition" for the ideas presented. In this way, we are (mostly) transparent about all the computations involved in our work. I will email these materials to anyone interested after the presentation.) Models are useful for…
A Floer homology is an invariant of a closed, oriented 3-manifold Y that arises as the homology of a chain complex whose generators are either the set of solutions to a differential equation or the intersection points between Lagrangian manifold, and its differential arises as the count of solutions of a differential equation on Y…
We consider nonparametric estimation of probability measures for parameters in problems where only aggregate (population level) data are available. We summarize an existing computational method for the estimation problem which has been developed over the past several decades. Theoretical results are presented which establish the existence and consistency of very general (ordinary, generalized and other)…
In calculus, we study series and learn how to add infinitely many numbers--but how about multiplying infinitely many numbers? In this talk, we'll start with familiar series from calculus, and then move on to study more exotic infinite sums and infinite products and the interactions between them. We'll see some number theory, complex analysis, and…
Time-dependent hyperbolic partial differential equations can be efficiently solved using adaptive mesh refinement, with a hierarchy of finer grid patches in regions where the solution is discontinuous or rapidly varying. These patches can be adjusted every few time steps to follow propagating waves. For many problems the primary interest is in tracking waves that reach…
An important construction for (the information theoretic version of) semantic security is a "Biregular Irreducible Function" (BRI). These can be constructed from a complete biregular graph on $2^k d \times 2^k d$ by by coloring it with $2^k$ colors in such a way that each vertex has degree $d$ in each color. Good BRI's are…
Upcoming meeting: Saturday, March 30, 2019 Location: Wake Forest University in Winston-Salem, NC Lecture Hall: Manchester 16 More information: https://wp.math.ncsu.edu/tlc/ Speakers: James Haglund, University of Pennsylvania Adam Marcus, Princeton University Jennifer Morse, University of Virginia Nathan Reading, North Carolina State University Registration and funding applications: To register and/or apply for funding, please fill out this form. If you have…