The Mathematics Undergraduate Colloquium is held each Wednesday from 12:55 - 1:45 during the regular academic year in LCB 225. Each week a different speaker will present information on a specific subject area in mathematics. Anyone can come by to listen, socialize, get to know members of the department, and hear some interesting information on the many areas of mathematics.
Spring 2022 Schedule
Introduction to the course
Edge Ideals: one of the beautiful bridges between algebra and combinatorics
Abstract: In this talk, we will learn about three types of monomial ideals (called edge ideals) associated to graphs. We will consider edge ideals of finite simple graphs, vertex weighted graphs, and vertex weighted oriented graphs. The focus of this talk will be on reviewing some of the results on how algebraic structure and invariants of these edge ideals can be studied through the combinatorial structure and invariants of graphs.
Evolution of logical paradoxes
Abstract: A paradox is an argument that derives an absurd conclusion by rigorous deduction from obviously true premises. A group of paradoxes particularly attracting a lot of interests is "logical paradoxes" which are ones derived from self-inference. We will go through numerous examples from the ancient to modern time.
Abstract: You are the owner of Hotel Infinity. It has infinitely many rooms, and it's full. A new guest arrives and insists you give her a room. How do you accommodate her? The next day, a family with infinitely many members arrives, each of whom wants a private room. The Hotel is still full. The next day infinitely many families, each with infinitely many members, arrive. Each member of each family insists on a private room. What do you do? We'll use this puzzle as an introduction to some subtleties of the concept of infinity.
Abstract: Wireless communications has become prevalent in our lives in the United States and across the world. We use our mobile telephones every day but we don’t stop to think of all the mathematics is it built upon. In fact, your mobile telephone is based on many concepts including detection and estimation, statistical analysis number theory, and information theory. L3Harris Technologies in Salt Lake City is a leader in wireless communication systems for ground, air, sea, and space. In this brief talk, we will give an overview and L3Harris and then go into some of the mathematics involved in the transmission and reception of information (voice, video and data).
From the Pythagorean theorem and beyond
Abstract: Many ideas and theories in mathematics have come from simpler ideas and a key question: what if?
Do you have a theorem that works in two dimensions? Then what if the dimension is now 3?
Do you know how to integrate a continuous function over a closed interval? Then what if the function is not continuous?
This question motivates new concepts and theories, and expands the boundaries of our knowledge. The invitation is to see this method in action, by exploring how far we can push one very familiar theorem: the Pythagorean theorem.
Geometry on Surfaces
Abstract: We'll see examples of surfaces exhibiting spherical, Euclidean, and hyperbolic geometries, and we'll discuss the Gauss-Bonnet Theorem which says that a finite surface can be associated with only one of the three geometric options from above.
Mathematics and Machine Learning
Abstract: Machine learning is used everywhere from self driving cars, to detecting spam emails, to Snap Chat filters. Although machine learning can seem quite mysterious, the mathematics behind many examples can be fairly accessible. In this talk we will examine how Calculus and a little bit of matrix multiplication can come together to build surprisingly accurate models.
Models of Astrocytic Glutamate Transporter EAAT2
Abstract: Glutamate is an excitatory neurotransmitter that is widespread throughout mammalian nervous systems and is thought to be linked to various health issues including drug addiction. Modeling glutamate uptake is key in improving our understanding of glutamate’s role within the nervous system and in turn, its role in drug addiction. Current models of the glutamate transporter EAAT2 are time-expensive and costly, spurring the need for simplified models which can accurately capture characteristics of the transporter efficiently. In this paper, we created a simplified model of EAAT2 which captures the voltage-dependence, ion-saturation, and time-varying properties of the current produced by EAAT2 within a single piecewise-equation. We also show that this reduced model is more computationally efficient than the 20-state kinetic model utilized in previous work and provides a lower bound for glutamate clearance in ischemic conditions. Our reduced model demonstrates easier integration of EAAT2 into complex systems and reduces the workload for ODE solvers, effectively reducing computation time and expense for large-scale models of the synaptic cleft.
Newcomb, Benford, Pareto, Heaps, and Zipf
Are arbitrary numbers random?
Abstract: An arbitrary collection of measured numbers from various sources ought, it seems, to be random, but the surprising observation is quite different. The implications of this discovery are astonishingly broad, from mathematical curiosity, to accounting, criminology, demographics, fraud, linguistics, nuclear decay, taxation, terrorism, Web searching, and even the rise of Fascism in the early Twentieth Century, and the Greek debt crisis that began in 2009, and still continues. Come and learn something of this fascinating subject that can broaden your view of what mathematics is good for, and perhaps even turn your planned career in another direction.
Insurance, what is it, how math works for it, and why you should work for WCF insurance?
Abstract: WCF Insurance is a rapidly growing, 105-year-old company headquartered in Sandy, Utah with employees across the country. WCF’s Aryn DeJulis, Director of Product Management and graduate of the University of Utah, and Haris Hadzimujic, Business Intelligence Manager, will discuss the use of mathematics and predictive analytics in the insurance industry along with career opportunities at WCF Insurance. We hope you’ll join us!
Applying to grad school
Homeomorphisms of the biinfinite flute surface
Abstract: At some point, we’ve all found ourselves wondering, “What would happen to a curve on the surface of an infinitely long cylinder with an infinite number of holes if you iteratively applied a composition of functions which continuously deformed the surface while preserving all the topological properties of the cylinder? What if you applied the functions backward?” The answers to these questions will be presented in this topological lecture on homeomorphisms of infinite-type surfaces.
Math 3000 (Receive Credit for Attending)
The Undergraduate Colloquium is open to anyone to attend; however, if students would
like to receive credit, you may register for Math 3000.
This is a 1 credit hour CR/NC course. To receive credit:
- You may not miss more than 2 of the colloquia
- You will need to write a short paper on one of the topics presented during the semester.
|Kevin Wortman||Lisa Penfold|
|Course Instructor||Administrative Coordinator|