The UIS Mathematics Colloquium aims to create a diverse platform where research scholars, faculty, students, and industrial experts can share and exchange ideas. We hope to provide an opportunity for attendees to discover new interests, encourage faculty and student research activities, enrich students’ educational experiences, and bring together our students and faculty community through our common interests in mathematics.
Our department has strong online mathematics programs. Because of our unique student composition with on-campus and online students, all colloquium talks will either be held virtually through Zoom, or have a Zoom component. We welcome contributed talks from all scholars, experts, and students. If you are interested in sharing a topic related to any aspect of mathematics, please contact Professor Yifei Li (firstname.lastname@example.org) for further information. (All talks will be held through via Zoom.)
- Title: Matroids and high energy physics: What happens when subatomic particles understand geometry
Speaker: Dr. Susama Agarwala (Associate Research Director, Trustworthy AI)
When: 1pm CT, Feb. 9th, 2024
Abstract: In this talk, we introduce two mathematical objects: matroids, a generalization of matrices, and Feynman diagrams, a way to understand interactions between the smallest and fastest particles known to science. Then we show a surprising relationships between these fundamentally geometric and physical objects. Dr. Susama Agarwala is an Associate Research Director for Trustworthy AI. So much of what is known as algorithmic bias comes from a mismatch between how a model is going to be used and the underlying mathematical hypotheses of the model. Her work involves building machine learning tools that respect the the mathematical underpinnings of the models involved. She completed her Ph.D. from Johns Hopkins University, and has 9 years of post-PhD mathematics faculty experience at Caltech, the University of Nottingham, and the United States Naval Academy and has held research positions in the mathematics and physics departments at Oxford and the University of Hamburg. She continues to publish in mathematical journals.
- Title: Words as Vectors
Speaker: Dr. Hei-Chi Chan (Chair of Department of Mathematical Sciences and Philosophy, UIS)
When: 1pm CT, January 26th, 2024
Abstract: Large language models (LLMs) such as GPT-3 and GPT-4 have demonstrated remarkable capabilities in natural language processing. This talk will provide a beginner-friendly "under the hood" exploration of the mathematical and the conceptual frameworks that underlie LLMs, particularly focusing on transformer-based models.
- Title: Data Science from a Math Perspective
Speaker: Dr. Yao Xie (Co-Founder & CEO of Premier Strategy Consulting)
Video Recording: Data Science from a Math Perspective
When: 1pm-2pm central time, November 10th, 2023
Abstract: Being in the data science industry for many years, what I found missing the most in data scientists is not coding, not machine learning algorithms, not communication, but the foundation - math. In this talk I'd like to introduce a mathematics perspective that looks at 3 core technical foundations of data science -statistics, machine learning and optimization, through comparison of math concepts and data science concepts, and through examples across multiple industries.
Dr. Yao received his PhD in mathematics from Washington University in St. Louis in 2014. He is now co-founder and CEO of Premier Strategy Consulting LLC. He has worked in the financial, retail, biotech, and healthcare sector where he has spearheaded several initiatives to fruition. With an experience of 90% deployed machine learning/statistical models and project completion, he founded Premier Strategy Consulting LLC with the intent of helping industry get maximum return on investment (ROI) from their data. Prior to embarking on this journey, he was Director of Data Science at Mastercard and a regional retailer Schnucks. His work has resulted in 8 industrial patents which is unique from homebase of the Midwest. In his downtime, he enjoys strategizing and spending time with his family and friends.
- Title: 2D Laplace Equations with Line Fracture: from Qualitative to Quantitative Analysis
Speaker: Xiang Wan (Assistant professor, Loyola University Chicago)
Video Recording: 2D Laplace Equations with Line Fracture
When: 1:00 pm CT, Friday, October 13th, 2023
Abstract: In this talk, we investigate a partial differential equation (PDE), more specifically, the 2D Laplace equation with the forcing term being a Dirac delta function on a line segment, modeling a singular line fracture. Numerically, such a fracture imposes additional treatment of the meshing while constructing the triangular Finite Element space. Inspired by the 1D case, we can see that a graded meshing is naturally called for, where the level of grading depends on the distance to the fracture.
To tune the numerical analysis of this system with the 'best' level of grading to get the optimal convergence rate, one has to look closer into the regularity of the solution in weighted Sobolev spaces - in contrast to the regularity results in standard Sobolev spaces from the classic Elliptic theory of PDEs. Such examination reveals deeper connections between the qualitative regularity and quantitative behavior of the system. Last but not least, we will present how the characteristics, and lack thereof, of different geometries of domains plays a role via numerical demonstrations.
- Title: The Triple and Quadruple Soap Bubbles
Speaker: Frank Morgan (Atwell Professor of Mathematics, Emeritus, Williams College)
Video Recording: The Triple and Quadruple Soap Bubbles
When: 1:00 pm, Friday, September 15th.
Abstract: In 1884 Schwarz proved that a single round soap bubble is least-perimeter way to enclose a given volume. In 2000, we proved that the familiar double soap bubble that forms when two bubbles come together is the least-perimeter way to enclose and separate two given volumes. Last year Milman and Neeman announced an amazing proof that the familiar triple and quadruple soap bubbles are the least-perimeter way to enclose and separate three or four given volumes in R^3 or R^4 and above. Many open questions remain, including even the planar quadruple soap bubble, with some new results by a high school student.
Professor Frank Morgan is a well accomplished mathematician with around 200 publications. He served as Vice-President for both American Mathematical Society (2009-2012) and Mathematical Association of America (2000-2002), the two largest math organizations in the US. He also co-founded one of the largest and best-known mathematics REU programs in the U.S. and mentored over 100 undergraduate students for mathematical research projects. For more about Dr. Morgan visit his Williams profile. For You can check out bubble images on UIUC's Math Images page (see "Double bubbles" and "Other Bubble Clusters.")
- Title: Entropy, Mutual Information & Prediction
Speaker: Doug Hamilton (Head of AI Research at Nasdaq)
Video Recording: Entropy, Mutual Information & Prediction
When: 10:00 am, Thursday, April 13, 2023
Where: UHB 3081 and Zoom (see the link above)
Abstract: Exploring the connection of entropy, information, and prediction (e.g., involving trading strategies). Doug Hamilton was a math major at UIS (class of 2012). He went on to MIT for an MS in Engineering & Management. He is now Associate Vice President, Managing Director, and Head of AI Research, Nasdaq.
- Title: An Invitation to Enumerative Geometric Combinatorics
Speaker: Andrés R. Vindas Meléndez(University of California, Berkeley)
Video Recording: An Invitation To Enumerative Geometric Combinatorics
When: 1:00 pm, Friday, March 10, 2023
Where: Zoom (see the link above)
Abstract: Enumerative geometric combinatorics is an area of mathematics concerned with counting properties of geometric objects described by a finite set of building blocks. Lattice polytopes are geometric objects that can be formed by taking the convex hull of finitely many integral points. In this talk I will present background on polytopes, lattice-point enumeration, and share some results on a special family of polytopes that can be further studied. Throughout the talk I will present questions and open problems. (No prior knowledge will be assumed, and I will attempt to explain all concepts.)