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Wednesday, April 19th
8:50 AM

The Converse Sharkovskii Theorem and Characterization of Maximal Orbits

Jeff Duan, Illinois Mathematics and Science Academy

8:50 AM - 9:05 AM

The Sharkovsky ordering of the natural numbers is 3 ≻ 5 ≻ 7 ≻ ... ≻ 2·3 ≻ 2·5 ≻ 2·7 ≻ ...... ≻ 22·3 ≻ 22·5 ≻ 22·7 ≻ ... ≻ 23 ≻ 22 ≻ 2 ≻ 1. Sharkovsky proved that if m comes before n in this ordering and a continuous map f: R → R has a ... Read More

9:05 AM

Approximating the Row-Wise Weighted Total Least Squares Regression Solution

Cole Plepel, Illinois Mathematics and Science Academy

9:05 AM - 9:20 AM

Motivated by applications as a kernel of nonlinear regression algorithms, the row-wise weighted total least squares regression problem is examined to find a consistent and accurate estimator. Specifically, the proposed estimator has a time complexity linear in the number of observations and a space complexity constant in the same value, as the number of observations can be quite large in ... Read More

Hypothesis Testing Involving Candidate Topological Spaces To Learn How Topological Noise Arises Through Different Probability Distributions

Akshat Gupta, Illinois Mathematics and Science Academy

9:05 AM - 9:20 AM

Topological data analysis (TDA) combines algebraic topology and other tools from pure mathematics to allow for a rigorous study of the 'shape' inherent to data. The foundational tool is persistent homology, an extension of homology to point cloud data. Persistent homology has been applied to various types of data in computer vision, manufacturing of porous materials, and cell differentiation trajectories.

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9:20 AM

Defined Benefits vs Defined Contribution Plan Defined Benefits Plan; Defined Contribution Plan; Annuitization; Retirement Wealth

Rafael Rotger '23, Illinois Mathematics and Science Academy

9:20 AM - 9:35 AM

For public sector jobs such as university professors, there are two types of available retirement plans for their retirement package: The Defined Contribution (DC) and Defined Benefit (DB) plan. We will discuss the key differences between these plans, including their structure, benefits, and risks. One critical factor to compare these two plans is the Net Present Value (NPV). NPV is ... Read More

11:25 AM

The Isomorphy Classes of the Special Orthogonal Group of Low Dimension in Characteristic 2

Shiqi Cheng '23, Illinois Mathematics and Science Academy

11:25 AM - 11:50 AM

In 1926, Cartan introduced the concept of real symmetric spaces as a class of homogeneous Riemannian manifolds, where a symmetric space is defined as the homogeneous space $G/H$ with $G$ a reductive group and $H=G^{\theta}=\{g\in G|\theta(g)=g\}$, the fixed-point group of an $n$-automorphism. Of special interest are automorphism of order 2, also called involutions. In this project we focused on classifying ... Read More