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Noah Falstein

Title:
Games and AI: A Transformational Future

Abstract:
Since the 1970s, video games have been at the forefront of technological innovation. While the modern gaming industry has faced certain challenges, the future holds immense promise, particularly with the transformative potential of AI. This technology is poised to drive unprecedented growth, initially within the gaming sector and subsequently across broader society. Notably, games that go beyond entertainment to create meaningful change in players' lives are proliferating, revolutionizing educational opportunities, advancing healthcare solutions, and even saving lives.

Dr Christopher Rackauckas

Title:
Symbolic-Numeric Methods: Cheating for Robustness and Speed

Abstract:
Symbolic-numeric methods are a form of algorithms which incorporate symbolic derivations into numerical methods. In this talk we will look into the plethora of ways that symbolic-numeric methods can greatly outperform purely numerical methods. We will showcase how integrating symbolic nonlinear solvers into stiff ODE solving can greatly improve compute times, not just by decreasing the computational cost but also by improving the convergence properties of the implicit systems that need to be solved with Newton methods. We will showcase how symbolic-numerics is essential in many domains such as solving differential-algebraic equations, where many of the equations are simply unsolvable by common numerical solvers without a symbolic transformation. Finally, we will explore how automatic differentiation works as a symbolic-numeric technique at the compiler level, and explore generalizations to automating uncertainty quantification and other mathematical problems using similar transformation-based approaches. All of these algorithms will be demonstrated using the Julia open source tools such as ModelingToolkit.jl which are paving the way for symbolic-numerics to be the standard of next-generation algorithms.

Mathematica Tutorial

Title:
AI and Algorithms in the Wolfram Language

Abstract:
This session explores the Wolfram Language's capabilities for modern AI development, demonstrating seamless integration with large language models (LLMs), automated algorithmic workflows, and machine learning implementation. We'll show how the language's symbolic computation framework enables developers to combine traditional reasoning with neural networks, leveraging built-in functions for natural language processing, computer vision, and predictive modeling. Attendees will learn practical techniques for orchestrating LLM interactions, automating data analysis, and deploying ML models at scale within Wolfram's unified computational environment that bridges exploratory data science and production-ready AI systems.

Prof. Hong Duong

Title:
Evolutionary Game Theory, Evolution of Cooperation and Institutional Incentives

Abstract:
Darwin's theory of evolution by natural selection, also known as “survival of the fittest”, implies that evolution is based on a fierce competition between individuals and should therefore only reward selfish behavior. However, cooperation occurs at all levels of biological organizations, from cellular clusters to bees to humans. Cooperation is in fact needed for evolution to construct new levels of organization. The problem of promoting cooperative behaviour within populations of self-regarding individuals has been intensively investigated across diverse fields of behavioural, social and computational sciences. Evolutionary Game Theory provides a powerful mathematical framework for understanding this key challenge over the last 50 years. Under this framework, several mechanisms for promoting the evolution of cooperation have been identified, including kin selection, direct reciprocity, indirect reciprocity, network reciprocity, group selection and different forms of incentives.

In this talk, I will discuss these topics and present our recent research on promoting cooperation via institutional incentives. We will show how this practical problem can be formulated into mathematically constrained, multi-objective optimization problems, where one wishes to minimize the cost of providing incentives while ensuring a minimum level of cooperation, sustained over time.

Dr Chatchawan Panraksa

Title:
Gröbner Bases: A Swiss Army Knife for Problem-Solving in Mathematics

Abstract:
I will introduce Gröbner bases as a powerful, multi-purpose tool—much like a Swiss Army knife—for tackling challenging problems in mathematics. Gröbner bases provide a systematic way to approach and solve systems of polynomial equations, offering elegant solutions to tasks in fields such as algebraic geometry and automated theorem proving. This talk aims to make the core concepts of Gröbner bases accessible by illustrating how these techniques unify problem-solving across various subdisciplines. By the end, attendees will see why Gröbner bases remain a cornerstone of modern computational algebra and how they may be applied in their own studies and research.

Dr Shahrooz Janbaz

Title:
Coding Theory: From Brain to Quantum

Abstract:
In this talk, we will explore the fascinating journey of coding theory, from its origins in understanding how the brain processes information to its cutting-edge applications in the quantum realm. We will highlight the critical role of error correction in communication and computation, driven by one universal truth: noise. Whether in the noisy neural circuits of the brain or the quantum fluctuations of the universe, noise is an ever-present challenge. By learning how to harness the power of coding theory, we can overcome this challenge and unlock new possibilities in fields ranging from biology to quantum computing and quantum communication. Join us as we uncover the fundamental connection between noise and information, and explore how coding theory is shaping the future of modern technology.

Dr Amir Hashemi

Title:
Complexity of the Saturation of Zero-Dimensional Ideals

Abstract:
In this talk, we give first a brief review on a hidden algorithm due to Traverso for computing Grobner bases. Specifically, it addresses the process of updating a Grobner basis for a zero-dimensional ideal I to a Grobner basis for I+<f> where f is a new polynomial. This algorithm was formulated in one of Mora's books. Based on this algorithm and by applying linear algebra techniques, we propose two new algorithms for calculating the saturation of a zero-dimensional ideal with respect to a polynomial. Finally, we discuss the arithmetic complexity of these algorithms. This talk is based on a joint work with Fateme Akbari.

Dr Mohsen Rezapour

Title:
Robust dimensionality reduction for heavy-tailed data: challenges and new approaches

Abstract:
Dimensionality reduction is a fundamental challenge in high-dimensional statistical analysis, particularly when dealing with heavy-tailed random variables. Traditional linear reduction methods, such as Principal Component Analysis (PCA), rely on the existence of first and second moments, making them unsuitable for data distributions with infinite variance. This paper ex- plores alternative approaches for dimensionality reduction under heavy-tailed distributions, emphasizing robust estimators and moment-free methodologies. We present theoretical properties of these methods and illustrate their advantages through empirical studies. Our findings contribute to the development of more reliable techniques for high-dimensional data analysis in non-Gaussian settings.

Dr Muhammad Asif Farooq

Title:
PINNs for Artery Disease Detection

Abstract:
High-fidelity CFD simulations provide accurate insights into arterial hemodynamics and play a crucial role in modeling fluid dynamics within complex vascular geometries. However, these simulations are often computationally expensive and time-intensive, particularly when applied to patient-specific anatomies or when conducting extensive parameter sweeps. These challenges are further exacerbated by the requirement for substantial domain expertise to refine meshes, adjust solvers, and interpret results effectively. Physics-Informed Neural Networks (PINNs) have shown strong agreement with CFD results while significantly reducing computational costs, demonstrating their potential for real-time clinical applications. Our findings highlight the critical role of hemodynamic factors in aneurysm progression and rupture risk, offering valuable insights for optimizing diagnostic and therapeutic strategies in vascular diseases.

Dr Ali Kemal Uncu

Title:
Finding New Applications for Algorithms; Computing Normal Cones with Quantifier Elimination

Abstract:
Algorithms are usually constructed as solutions to a particular problem. They are tools that can find new uses. The more general the algorithm is the more uses it finds. In this talk, we will show an example of this. In optimization applications, normal cones play an important role. As the dimensions rise in the problems and at cusp points where the partial derivatives fail to exist, the normal cone calculations become harder. We will shift the problem of calculating normal cones for optimization problems with rational constraints to solving quantifier elimination problems and real satisfiability problems.

This is based on a joint work with Michael Mandlmayr.

Dr Anass Bouchnita

Title:
Leveraging a turn-Based video game player data to inform H. pylori AI-based treatment optimization algorithms

Abstract:
Helicobacter pylori (H. pylori) is a common bacterial infection that causes gastric ulcers and, in some cases, stomach cancer. The increasing prevalence of H. pylori strains resistant to multiple antibiotics presents a significant challenge to effective treatment. In this work, we present AntibioQuest, an educational turn-based 2D video game designed to simulate bacterial dynamics under various treatment regimens. In the game, players assume the role of a clinician who has to select combinations of antibiotics over time to treat a virtual patient, assuming that bacterial populations adapt in response. The simulation incorporates realistic pharmacokinetics, mutation rates, and patient-specific strain characteristics. AntibioQuest was showcased to the public at the El Paso Festival of Science, held in El Paso on April 6–7, 2025. Anonymous data from players, reflecting their treatment strategies, is collected, along with patient-specific parameters in each game. This data is then used to train machine learning algorithms capable of optimizing treatment protocols. We conclude by discussing the benefits of incorporating human input into the training of optimization algorithms, as compared to purely AI-driven approaches.

Dr Abhishek Pal Majumdar

Title:
Monomolecular Reaction networks under stochastic environments

Abstract:
We studied stochastic mono-molecular reaction network models under stochastic environments and their long-time behaviors with applications in gene-regulatory networks (that are applied in synthetic biology). Along with giving a time-dependent distributional representation of the species counts, we explicitly showed their long-time behaviors and conditions of stability using graphical structures. Using a stochastic recursion equation, we give a characterization of the time-limiting distribution. In this talk, we show that this representation holds for the semi-Markovian environment as well (more than just Markovian) and a sampling algorithm is provided from the limiting measure of the species dynamics, with a convergence guarantee.

Dr Josue Tonelli-Cueto

Title:
Condition-based Low-Degree Approximation of Real Polynomial Systems

Abstract:
In this talk, we show how well-conditioned polynomial systems can be approximated locally and in parallel by many low-degree polynomial system. We explore the consequence of this phenomenon: both theoretical and algorithmic. This is joint work with Elias Tsigaridas.

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