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…
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)…
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…
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…
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…
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…