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 […]
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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 […]
We welcome all undergraduates and graduate students to attend topology seminar! Speaker: Adam Yassine (Pomona College) Title: A Structural Approach to Classical Mechanics Abstract: A structural approach to the study of classical mechanics clarifies the physical heuristics that physicists use in constructing mathematical models of classical mechanical systems. The focus of our current program is to develop […]
Title: Teaching Equity-minded Active Mathematics: A model for Instructional Change Speaker: Amelia Stone-Johnstone, Department of Mathematics, California State University, Fullerton Abstract: Active learning has been championed as a mechanism for greater student learning and participation in STEM. However, recent studies have demonstrated how active learning without an explicit equity focus may harm students from historically […]
There is a rich connection between homogeneous dynamics and number theory. Often in such applications it is desirable for dynamical results to be effective (i.e. the rates of convergence for dynamical phenomena are known). In the first part of this talk, I will provide the necessary background and relevant history to state an effective equidistribution […]
This talk has been cancelled. We welcome all undergraduates and graduate students to attend topology seminar! Speaker: Iris Yoon (Wesleyan College) Title: A generalized Dowker complex for multi-way Relations Abstract: Given a relation between two sets X and Y, one can construct two simplicial complexes, one having X as its vertex set and the other […]
Title: Can a function tell us how immune cells kill? Speaker: Prof. Ami Radunskaya (Pomona College, Claremont CA) Abstract: The immune system is able to fight cancer by mustering and training an army of effector “killer” cells. Mathematical models of tumor-immune interactions must describe the proliferation, recruiting and killing rates of immune cells. Earlier work surprisingly showed that […]
