The Department of Mathematics is committed to providing students with the foundational training necessary for graduate work as well as careers in education, business, industry, and public service. Our faculty come from all over the world and have a strong commitment to both research and teaching. Stop by Bachelor Hall and ask your professor what a mathematician does!
Speaker/Affiliation:
Khodakhast Bibak, Miami University, Department of Computer Science and Software Engineering
Title: Authentication of variable length messages in quantum key distribution using number-theoretic and combinatorial techniques
Abstract: Authentication plays a critical role in the security of quantum key distribution (QKD) protocols. We propose using Polynomial Hash and its variants for authentication of variable length messages in QKD protocols. Since universal hashing is used not only for authentication in QKD but also in other steps in QKD like error correction and privacy amplification, and also in several other areas of quantum cryptography, Polynomial Hash and its variants as the most efficient universal hash function families can be used in these important steps and areas, as well. We introduce and analyze several efficient variants of Polynomial Hash and, using deep results from number theory, prove that each variant gives an $\varepsilon$-almost-\(\Delta\)-
Date/Time/Location:
Thursday, September 14, 2023 from 3:00-3:50 pm in BAC 219
Speaker/Affiliation:
Todd Kapitula, Calvin University
Title: Viewing spectral problems through the lens of the Krein matrix
Abstract: Determining the stability of nonlinear waves usually requires that the spectrum for the appropriate linearized operator be known. In the case of Hamiltonian systems, the spectrum has a great deal of structure. This structure can be exploited to determine things like the number of (potentially) unstable eigenvalues, or when a destabilizing Hamiltonian-Hopf bifurcation can occur. In my talk I will discuss some of the mathematical tools which allow us to address these questions. Applications will also be given.
Date/Time/Location:
Thursday, September 28, 2023 from 3:00-3:50 pm in BAC 219
Speaker/Affiliation:
Bob Krueger, University of Illinois, Urbana-Champaign
Title: Sparse random analogues of classical combinatorial theorems
Abstract: A successful trend in modern extremal/probabilistic combinatorics is the investigation of how well classical theorems, like those of Ramsey, Turán, and Szemerédi, hold in sparse random contexts. Graph and hypergraph container methods have played a big role in improving our knowledge of these sparse structures. I will present an overview of this area, including some joint work with Jozsef Balogh and Haoran Luo on a random version of the Erdős-Ko-Rado Theorem and Sperner's Theorem. If time permits, I will also talk about some recent work on the typical behavior of graph homomorphisms from expanders, including Lipschitz functions on expanders.
Date/Time/Location:
Thursday, November 9, 2023 from 3:00-3:50 pm in BAC 219
Speaker/Affiliation:
Bryan Van Scoy, Miami University, Department of Electrical and Computer Engineering
Title: Systematic analysis of iterative black-box optimization algorithms using control theory
Abstract: Iterative algorithms are used to solve optimization problems throughout control, robotics, statistics and estimation, signal processing, communication, networks, machine learning, and data science. Recent work from both optimization and control communities has developed a systematic methodology to analyze the worst-case performance of a black-box algorithm over a class of problems. In this talk, we first describe this systematic methodology from a controls perspective and then show how it can be used to analyze and design algorithms in various contexts, such as trading off convergence rate and robustness to gradient noise with noisy first-order oracles, consensus optimization for a multi-agent system, and primal-dual algorithms.
Date/Time/Location:
Thursday, November 16, 2023 from 3:00-3:50 pm in BAC 219
"Mathematical careers outside of academia rarely carry a simple title of 'mathematician.'" According to the Society for Industrial and Applied Mathematics there are many jobs that utilize mathematics in our modern society, from engineering, data analysis, to actuarial and accounting work.
Getting a degree in mathematics shows employers that you are logical and good at solving problems, as well as showing a desire to take on difficult challenges.
Due to the highly specialized nature of mathematics-based jobs, as well as their high demand job stability is much higher than in other fields. Job growth in mathematics-related fields is also growing faster than qualified people are entering the market by almost 10%.
(Data from Forbes, AMA, and the National Math and Science Initiative)
Can you resist a puzzle when you see one? No. Great! If you like solving problems, puzzles, or using logic just for the fun of it Mathematics may be right for you.
Mathematics can teach you new ways to solve puzzles, beat a computer, and succeed at difficult problems. Not to mention, just how far away from practical logic can take you.
Help us prepare the next generation of leaders in the mathematiical fields—and our society as a whole. We have numerous scholarships, grants, and programs accepting contributions from donors like you.
