Join us for the first talk in the joint seminar with CCMS Applied Math and the Universidad Nacional de Colombia Title Serre Conjecture. Geometric interpretation of the Quillen-Suslin Theorem. Abstract: The Quillen-Suslin theorem asserts that over the polynomial ring with coefficients in a field K, every projective module is free. Despite the algebraic nature of […]
A projective algebraic variety X is the zero locus of a collection of homogeneous polynomials, in projective space. When the polynomials have integer coefficients, we can think of the k-valued points X(k) of the variety, for any field k. Now suppose we have two different fields k and k'. How does the behavior of X(k) […]
We welcome all undergraduates and graduate students to attend topology seminar! Speaker: Puttipong Pongtanapaisan (Arizona State University) Title: Building Knotted Objects Efficiently Abstract: Knotted objects can be constructed by gluing together standard pieces called handles. Understanding the minimum number of handles required for construction and their sequential attachment provides valuable insights into the complexity of entanglement. […]
Title: Evolution of an Intriguing Recreational Math Problem Speaker: Shawn McMurran, California State University San Bernardino Abstract: Besides being popular and entertaining, recreational mathematics problems are often of historical interest. In this presentation we will highlight the origin and evolution of one such simply stated yet deep problem. The problem emerged during the eighteenth century […]
The 14th Symposium for Women and Gender Minorities in Mathematics in Southern California WiMSoCal returns to SoCal after a four-year-hiatus due to pandemic. The symposium will provide an opportunity for women and gender-nonconforming individuals in mathematics in the Southern California area to get to know each other on a personal as well as professional level. […]
This is the continuation of the semester's joint seminar with the Universidad Nacional de Colombia-Manizales. Title: Enumerating linearity regions of max-pooling layers in convolutional neural networks Abstract: Convolutional neural networks (CNN's) are central tools in the application of machine learning to text, audio and image processing. Their success stems from the ability of these networks to […]
For a finite field F_q, a subset of F_q^N is a Kakeya set if it contains a line in every direction (i.e., a coset of every one-dimensional linear subspace). The finite field Kakeya problem is to determine the minimal size K(N,q) of a Kakeya set in F_q^N. This problem was posed by Wolff in 1999 as […]
No Seminar
Title: A Group-Theoretic Ax-Katz Theorem Speaker: Pete L. Clark, University of Georgia Abstract: The Chevalley-Warning Theorem is a result from 1935 asserting that the number of solutions to a low degree polynomial system over a finite field is divisible by the characteristic of the field. It is an important result -- it includes a conjecture […]
Title: Graphical Anomaly Detection for High Dimensional and Object Data Abstract: Anomaly detection is an important task in data analysis, though an agreed upon definition of what constitutes an outlier does not exist. Accordingly, a graphical tool that can highlight interesting observations in a data set that the scientist can then investigate with domain specific […]
Though mirror symmetry requires much technical background, it gained traction in the mathematical community when physicists Candelas-de la Ossa-Green-Parkes discovered enumerative invariants counting the number of rational degree d curves inside of certain space called a ``quintic threefold." This answered longstanding problems in enumerative geometry from antiquity. In particular, the number of rational degree d=1 […]
