Seminar Schedule
The Program of Mathematics often hosts colloquiums and invites a variety of speakers from other universities and companies. Details of past and future colloquiums will be updated and listed here.
Upcoming Colloquiums
Past Colloquiums
Cancer Cachexia: Insights from Modelling and Analysis of the Wasting Condition
Speaker: Dr. Kathleen P. Wilkie; Department of Mathematics; Toronto Metropolitan University, Toronto, Canada
Date: Thursday, February 29, 2024
Time: 12:30 pm - 1:30 pm
Location: Zoom
Abstract: Cancer cachexia is the loss of muscle and adipose tissues that directly correlates with patient mortality rates, and that causes fatigue, weakness, pain, and poor quality of life. Chemotherapy is a standard cancer treatment with notorious side effects, including the unfortunate loss of muscle mass. Cancer presence itself may induce cachexia, leading to a double-barrelled attack on healthy lean mass, and thus patient quality of life. In this talk I will present recent work on modelling and analysis of cancer cachexia. We have developed a framework to describe the response of muscle tissue to cancer-derived signals and to chemotherapy. We model the role of stem cells in tissue maintenance and use the model to examine mechanisms of cancer and chemotherapy induced muscle loss, including disruption of the differentiation pathway. We simulate various treatment regimes to explore the trade off between targeting the tumour and preserving lean mass. Additionally, I will present a network approach to examine gene expression data for cachectic muscle. Using mutual information we inferred a network structure and then applied community detection and clustering techniques to identify regions of the network that may target particular biological processes in the diseased tissue. Our new approach suggests biological activities not identified with the standard statistical approach, and may shed new light on tissue level alterations in cachectic muscle.
Clocks, Parking Garages, and the Solvability of the Quintic: A Friendly Introduction to Monodromy
Speaker: Dr. Edray H. Goins; Department of Mathematics and Statistics; Pomona College, California
Date: Tuesday, January 23, 2024
Time: 12:30 pm - 1:30 pm
Location: Zoom
Abstract: Imagine the hands on a clock. For every complete the minute hand makes, the seconds hand makes 60, while the hour hand only goes one twelfth of the way. We may think of the hour hand as generating a group such that when we “move” twelve times then we get back to where we started. This is the elementary concept of a monodromy group. In this talk, we give a gentle introduction to a historical mathematical concept which relates calculus, linear algebra, differential equations, and group theory into one neat theory called “monodromy”. We explore lots of real world applications, including why it’s so easy to get lost in parking garages, and present some open problems in the field. We end the talk with a discussion of how this is all related to solving polynomial equations, such as Abel’s famous theorem on the insolubility of the quintic by radicals.
Algebraic Methods in Distributed Storage
Speaker: Dr. Daniel Bossaller; Department of Mathematical Sciences; The University of Alabama in Huntsville, Alabama
Date: Tuesday, January 16, 2024
Time: 12:30 pm - 1:30 pm
Location: Zoom
Abstract: With the advent of cloud storage, big data, and social media, it is important to store user files across many computers/drives in such a way that guards against data loss/corruption. However, a greater resilience against data loss requires more storage space on the network, forcing a compromise. Furthermore, if one or many of the computers storing the file is lost, it is crucial to develop efficient algorithms to replace those missing nodes while minimizing, for example, computational complexity of the repair and/or network traffic. In this talk I will survey some of the ways in which algebraic methods, such as algebraic coding theory, may be employed to achieve these goals, with a special focus on regenerating codes and Reed-Solomon codes. If time permits, I will report on my joint work with Hiram Lopez (Virginia Tech) on the exact repair problem for generalizations of Reed Solomon codes and possible applications to other areas of information theory and theoretical computer science.
Analysis of Long Transient Dynamics in Two-Timescale Predator-Prey Models
Speaker: Dr. Susmita Sadhu; Department of Mathematics; Georgia College & State University, Georgia
Date: Thursdasy, November 30, 2023
Time: 12:30 pm - 1:30 pm
Location: Zoom
Abstract: The leading role of long transient dynamics in ecological timescales can be very important in explaining regime shifts, which refer to abrupt large-scale changes in ecosystems. Hence, developing methods to analyze transient dynamics in mathematical models can be useful to understand regime shifts. In this talk, I will discuss some mathematical techniques to analyze long transient dynamics preceding a regime shift in a class of three-dimensional predator-prey models featuring two timescales. I will address the underlying dynamical mechanism leading to the long transients in such systems and use tools from singular perturbation theory to develop methods to analyze them. The methods are then used to devise early warning signals of a large population transition leading to an outbreak or a sudden transition resulting in an extinction of one of the species. Finally, I will end with some preliminary analysis on extending the results to stochastic settings.
Exploring Quantum Simulations: Generalized Lie-Trotter Formulas and Enhanced Error Estimations
Speaker: Dr. Zhenhua Wang; Department of Physics, Chemistry, and Mathematics; Alabama A&M University, Alabama
Date: Tuesday, November 28, 2023
Time: 12:30 pm - 1:30 pm
Location: Zoom
Abstract: Quantum simulations have emerged as powerful tools for understanding complex physical systems. At the heart of these simulations lies the formulation of Trotter product formulas - a practical and efficient approach for modeling the dynamics of quantum systems. The reliability of quantum simulations crucially depends on accurate error estimation, providing a nuanced understanding of the deviations between approximate and exact solutions. In this talk, we introduce some generalized Lie-Trotter product formulas by utilizing Jordan product. Additionally, we present enhanced error estimations, offering explicit formulas. Our generalizations of Trotter product formulas, as well as their relative precision scalings, not only extend their applicability to broader classes of quantum systems, but also have implications in both mathematical and some physical settings.Quantum simulations have emerged as powerful tools for understanding complex physical systems. At the heart of these simulations lies the formulation of Trotter product formulas - a practical and efficient approach for modeling the dynamics of quantum systems. The reliability of quantum simulations crucially depends on accurate error estimation, providing a nuanced understanding of the deviations between approximate and exact solutions. In this talk, we introduce some generalized Lie-Trotter product formulas by utilizing Jordan product. Additionally, we present enhanced error estimations, offering explicit formulas. Our generalizations of Trotter product formulas, as well as their relative precision scalings, not only extend their applicability to broader classes of quantum systems, but also have implications in both mathematical and some physical settings.
Towards a Unified Pandemic Response System
Speaker: Dr. Satyaki Roy; Department of Mathematical Sciences; The University of Alabama in Huntsville, Alabama
Date: Tuesday, November 14, 2023
Time: 3:30 pm - 4:30 pm
Location: Zoom
Abstract: The pandemic, instigated by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2), left a profound impact on the economy, healthcare, and the social fabric. The emergence of new viral strains compounded the complexities of management, necessitating epidemiological, clinical, and physiological data for decisions concerning containment. Recent strides in the Internet of Things (IoT) and edge computing have ushered in solutions for pandemic management through the systematic collection of data and computational processes. However, they fall short of encapsulating the interplay amongst statistical and computational models, communication infrastructure, and the data that underpins them. We conceptualize a unified pandemic management architecture, one that harnesses the overarching paradigms of IoT and edge computing to impart automation to critical facets of pandemic response. These facets encompass but are not limited to, the automation of recommendations about vaccine distribution, dynamic lockdown strategies, mobility scheduling, and the prognostication of pandemic trends. It explores the dynamics of data flow across the stratified layers of this architecture, delineated as the cloud, edge, and end device layers. We end with a deliberation of the inherent limitations of such an architecture and chart avenues for future research endeavors aimed at bolstering its pragmatic viability.
Btor2MLIR: A Format and Toolchain for Hardware Verification
Speaker: Dr. Joseph Tafese; Department of Electrical and Computer Engineering; University of Waterloo, Canada
Date: Thursday, October 19, 2023
Time: 12:30 pm - 1:10 pm
Location: Zoom
Abstract: Hardware Verification has been one of the biggest drivers of formal verification research, with a history that spans many breakthroughs. Insights derived from hardware verification often serve as the foundation for more complex verification research. Therefore, it is extremely important to have formats, for representing and manipulating verification problems, that can support our ecosystem of tools, developers and practitioners. A good format allows representing many different types of problems, has a strong toolchain for manipulating and translating problems, and can grow with the community. In the world of hardware verification, and, specifically, the Hardware Model Checking Competition (HWMCC), the Btor2 format has emerged as the dominating format. It is supported by Btor2Tools, verification tools, and Verilog design tools like Yosys. We present an alternative format and toolchain, called Btor2MLIR, based on the recent MLIR framework. The advantage of Btor2MLIR is in reusing existing components from a mature compiler infrastructure, including parsers, text and binary formats, converters to a variety of intermediate representations, and executable semantics of LLVM. We hope that our format and toolchain will lead to rapid prototyping of verification and related tools for hardware verification.
