Michael Grabchak

Stanislav Molchanov, UNC Charlotte

Title: Large scale testing for random number generators

Sébastien Bossu, UNC Charlotte

Title: “Least-squares function approximation and single-pair Gram matrices”

Abstract: Least-squares optimization techniques can be applied to approximate a function f(x) by a line (similar to linear regression in statistics), Fourier cosines, or ReLU functions.  In the first part of this talk, we will review the theory of least-squares function approximation and see how Gram matrices (covariance matrices in statistics) play an important role.  In the second part of this talk, I will present my recent results about the inverse sum of two single-pair matrices corresponding to the Gram matrix of a system of ReLU functions.

The first part of this talk is educational and graduate students are encouraged to attend.

Stanislav Molchanov, UNC Charlotte

Title: On Physical Brownian Motion

Vlad Mărgărint, UNC Charlotte

Title: On the Cramer model of pseudo-primes and related topics

Michael Grabchak, UNC Charlotte

Title: An introduction to Lévy processes

Stanislav Molchanov, UNC Charlotte

Title: Fürstenberg Theorem

Michael Grabchak, UNC Charlotte

Title: Rejection Sampling for Tempered Lévy Processes and Related OU Processes

Stanislav Molchanov, UNC Charlotte

Title: Brownian motion on 2D quantum graph and related topics

Isaac Sonin, UNC Charlotte

Title: Water Puzzle and Marginal Utility Optimization

Abstract. There are two cups of tea on a table, each with a two-unit capacity. Cup 1 has one unit of tea at 80% concentration, and cup 2 has one unit with 25% concentration. You have one unit of hot water in your own cup, which you should distribute between these two cups, say volume  x into cup 1 and the rest, i.e., 1-x, into cup 2. After that, the volume x is returned to you from cup 1, and the volume 1-x from cup 2, i.e., you get back one unit in total. Now you are ready to drink your tea. The question is, what should be the value of x such that your tea is as strong as possible? Is x=1 or x<1? Strangely enough, this simple problem leads to the maximization problem with a transparent socio-economic interpretation, related to so-called marginal utility, one of the fundamental concepts in Economics. Calculus 1 is the only prerequisite for this talk.

Sébastien Bossu, UNC Charlotte

Title: Spanning multi-asset option payoffs with ReLUs: A distributional & a neural network approach