Title: Linear independence, counting, and Hilbert's syzygy theorem Speaker: Youngsu Kim, Department of Mathematics, Cal State San Bernardino Abstract: Linear independence is an essential concept in mathematics and one of the most fundamental notions in linear algebra. Linear algebra studies the solutions of linear equations. Algebraic geometry studies the solutions of polynomial equations (of arbitrary degree). […]
Title: Data science and applications in dynamic topic modeling Abstract: The shockwaves of the big data boom have thrown into sharp relief the critical need for domain-driven, large-scale data analytic […]
As $\lambda$ runs through all integer partitions, the set of Schur functions $\{s_{\lambda}\}_\lambda$ forms a basis in the ring of symmetric functions. Hence the rule $$s_{\lambda}s_{\mu}=\sum c_{\lambda,\mu}^{\gamma} s_{\gamma}$$ makes sense and the coefficients $c_{\lambda,\mu}^{\gamma}$ are called \textit{Littlewood-Richardson (LR) coefficients}. The calculations of Littlewood-Richardson coefficients has been an important problem from the first time they were […]
Title: Contact topology and geometry in high dimensions Speaker: Bahar Acu, Department of Mathematics, Pitzer College Abstract: A very useful strategy in studying topological manifolds is to factor them into ``smaller" pieces. An open book decomposition of an n-manifold (the open book) is a special map (fibration) that helps us study our manifold in terms of its (n-1)-dimensional […]
Title: What is the best shape? Geometric problems arising in aggregation models Abstract: How do pair interactions shape the large-scale behaviour of a cloud of particles (animals, social agents ...) […]
Suppose you are given a data set that can be viewed as a nonnegative integer-valued function defined on a finite set. A natural question to ask is whether the data can be viewed as a sample from the uniform distribution on the set, in which case you might want to apply some sort of test […]
The non-orientable 4-genus of a knot K is the smallest first Betti number of any non-orientable surface in the 4-ball spanning the knot. It is defined to be zero if the knot is slice. In joint work with Patrick Shanahan and Cornelia Van Cott, we attempt to determine the value of this invariant for double […]
An elliptic curve $ E: y^2 + a_1 \, x \, y + a_3 \, y = x^3 + a_2 \, x^2 + a_1 \, x + a_6 $ is a cubic equation which has two curious properties: (1) the curve is nonsingular, so that we can draw tangent lines to every point $ P […]
CLAREMONT CENTER for the MATHEMATICAL SCIENCES Fall 2022 Poster Session Title Speaker(s) A New Basis for k-Local Class Functions Hannah Friedman A Quantile Deffuant-Weisbuch Model of Opinion Dynamics Julianna […]
The theory of compact linear operators between Banach spaces has a classical core and is familiar to many. Perhaps lesser known is the factorization of compact maps through a closed […]
The existence of a set $A\subset \N_0$ of positive upper Banach density such that $A-A:=\{m-n:m, n\in A, m>n\}$ does not contain a set of the form $S-S$ with $S$ a piecewise syndetic is in essence the content of a popular result due to K\v r\'{i}\v z in 1987. Since then at least four different proofs […]
Title: Continuity Versus Uniform Continuity Speaker: Gerald Beer, Department of Mathematics, California State University Abstract: In this talk we discuss the class of metric spaces - called the UC-spaces - whose members have […]
