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Colloquium. Academic Year 22-23
Colloquium Chair (2022-2023): Denis Osin
Sep. 29: Jesus Oliver (California State University, East Bay)
Title: A community of practice model for infusing active learning in the classroom
Abstract: This work outlines a model for creating momentum for active learning at the departmental level through a Mathematics Community of Practice (CoP) model. Our approach focuses on empowering members of our CoP by providing easy access to active learning tasks, course pacing guide, and teaching tips via a Dynamic Calendar. Potential approaches for active learning implementation are discussed and shared in monthly CoP meetings at our math department. The instructors at these meetings provide feedback on course materials, check in on their pacing, and share insights. Our instructors report that they feel heard, respected, and supported as a result of being part of the CoP. Data relevant to student success and equity at CSUEB Calculus 1 courses will be shared in this talk.
Host: Marcelo Disconzi
Oct. 6: Bei Hu (University of Notre Dame)
Title: A free boundary problem for modeling plaques in the artery
Abstract: Atherosclerosis is a leading cause of death worldwide; it originates from a plaque which builds up in the artery. We considered a simplified model of plaque growth involving LDL and HDL cholesterols, macrophages and foam cells, which satisfy a coupled system of PDEs with a free boundary, the interface between the plaque and the blood flow. In an earlier work (with Avner Friedman and Wenrui Hao) of an extremely simplified model, we proved that there exist small radially symmetric stationary plaques and established a sharp condition that ensures their stability. In our recent work (with Evelyn Zhao), we look for the existence of non-radially symmetric stationary solutions. The absent of an explicit radially symmetric stationary solution presents a big challenge to verify the Crandall-Rabinowitz theorem; through asymptotic expansion, we extend the analysis to establish a finite branch of symmetry-breaking stationary solutions which bifurcate from the radially symmetric solutions. Since plaque is unlikely to be strictly radially symmetric, our result would be useful to explain the asymmetric shapes of plaque. Our recent work (with Yaodan Huang, Xiaohong Zhang, Zhengce Zhang) extends to other possible shapes as well as more realistic modeling efforts.
Host: Glenn Webb & Xinyue Zhao
Oct. 20: Vladimir Shpilrain (CUNY)
Title: Yao’s millionaires’ problem and public-key encryption
Abstract: Yao’s millionaires’ problem is: Alice has a private number a and Bob has a private number b, and the goal of the two parties is to figure out which number is larger without revealing any information about a or b. We will discuss relations between this fun problem and serious problems like the possibility of secure public-key encryption and the P=NP? problem.
Host: A. Olshanskii
October 27: Christopher Bishop (Stony Brook University)
Title: Weil-Petersson curves, traveling salesman theorems and minimal surfaces
Abstract: Weil-Petersson curves are a class of rectifiable closed curves in the plane, defined as the closure of the smooth curves with respect to the Weil-Petersson metric defined by Takhtajan and Teo in 2009. Their work solved a problem from string theory by making the space of closed loops into a Hilbert manifold, but the same class of curves also arises naturally in complex analysis, geometric measure theory, probability theory, knot theory, computer vision, and other areas. No geometric description of Weil-Petersson curves was known until 2019, but there are now more than twenty equivalent conditions. One involves inscribed polygons and can be explained to a calculus student. Another is a strengthening of Peter Jones’s traveling salesman condition characterizing rectifiable curves. A third says a curve is Weil-Petersson iff it bounds a minimal surface in hyperbolic 3-space that has finite total curvature. I will discuss these and several other characterizations and sketch why they are all equivalent to each other. The lecture will contain many pictures, several definitions, but not too many proofs or technical details.
Host: Dechao Zheng
November 3: Ionut Chifan (University of Iowa)
November 10: Dmitriy Bilyk (University of Minnesota)
November 17: Dan Margalit (Georgia Tech)