Young diagrams are all possible arrangements of n boxes into rows and columns, with the number of boxes in each subsequent row weakly decreasing. For a partition λ of n, a standard Young tableau S of shape λ is built from the Young diagram of shape λ by filling it with the numbers 1 to […]
Speaker: Jack Wesley, Department of Mathematics, UC Davis
Let x_1,...,x_n be an overdetermined spanning set for the Euclidean space R^k, where n > k. Let L be the integer span of these vectors. Then L is an additive subgroup of R^n. When is it discrete in R^n? Naturally, this depends on the choice of the spanning set, but in which way? We will […]
Let L be a full-rank lattice in R^n and write L+ for the semigroup of all vectors with nonnegative coordinates in L. We call a basis X for L positive if it is contained in L+. There are infinitely many such bases, and each of them spans a conical semigroup S(X) consisting of all nonnegative […]
Title: No-arbitrage Pricing in a Market for Position on a Multilane Freeway Speaker: Henry Schellhorn, Department of Mathematics, Claremont Graduate University Abstract: We introduce a trading mechanism allowing cars to change position in a multilane congested freeway by doing peer-to-peer transactions. For the car initiating the operation, or incoming car, the goal can be to […]
Many knot invariants are defined from features of knot projections such as arcs or crossings. Gauss diagrams provide an alternative combinatorial scheme for representing knots. In this talk we will use Gauss diagrams to enhance the biquandle counting invariant for classical and virual knots using biquandle arrow weights, a new algebraic structure without a clear […]
Title: Building trustworthy data-driven epidemiological models: Application to the COVID-19 outbreak in New York City Speaker: Joan Ponce, Department of Mathematics, Arizona State University Abstract: Epidemiological models can provide the dynamic evolution of a pandemic but they are based on many assumptions and parameters that have to be adjusted over the time the pandemic lasts. […]
There are two different measures of how far a given Euclidean lattice is from being orthogonal -- the orthogonality defect and the average coherence. The first of these comes from the study of sphere packing while the second is motivated by frame theory, but both of them have applications in digital communications, especially in coding […]
Title: The mathematics of neural networks: recent advances, thoughts, and the path forward Speaker: Prof. Mikhail Belkin, Department of Mathematics, University of California San Diego Abstract: The recent remarkable practical achievements of neural networks have far outpaced our theoretical understanding of their properties. Yet, it is hard to imagine that progress can continue indefinitely, without […]
We introduce the notion of linear multifractional stable sheets in the broad sense (LMSS) to include both linear multifractional Brownian sheets and linear multifractional stable sheets. The purpose of the framework is to study the existence and joint continuity of the local times of LMSS, and also the local Holder condition of the local times […]
