Skip to main content

Upcoming Seminars

Memorial Union on sunny day

Join us for an upcoming seminar featuring mathematics faculty and invited speakers on one of our seven research topics. You may also see upcoming seminars by topic:

String Diagrams in Representation Theory

Weniger Hall 201
Algebra and Number Theory Seminar

Speaker: Nicholas Davidson

Many important objects in algebra can be encoded using simply defined “string diagrams”. These diagrams often simplify presentations and illuminate connections with other areas of mathematics. In this talk, I’ll give a few examples, including the symmetric group and web diagrams. I’ll also illustrate the important perspective these diagrams provide in representation theory, including the classical theorem now called Schur-Weyl duality. After reviewing some classical results, I’ll discuss recent work with Kujawa, Muth, and Zhu to “deform” these diagrams using superalgebra. Read more.

Inferring Long-term Dynamics of Ecological Communities Using Combinatorics

Dynamical Systems Seminar

Speaker: William Cuello

Traditional fine-scale mathematical models, such as ordinary differential equations (ODEs), have given valuable insights into the long-term behaviors of interacting species. However, they can be difficult to analyze. The higher the number of species and nonlinear interactions, the more challenging it is to find all the qualitative solutions to, say, a system of ODEs modeling a community. More species and interactions often introduce more unknown parameters into the model, where two choices of parameter values may lead to entirely different qualitative dynamics. Thus, increasing interactions and species often produces a community that is infeasible to rigorously and numerically explore.To bypass this mathematical hurdle, I will take a step back from fine-scale dynamics and introduce a new mathematical framework: Widespread Ecological Networks and their Dynamical Signatures (WENDyS). I will show how WENDyS takes a system of species and their relative strengths of interactions and… Read more.

Wave propagation and its failure in lattice equations

STAG 113
Applied Mathematics and Computation Seminar

Speaker: Brian Moore

ABSTRACT: Lattice equations are used to model physical processes or to approximate solutions for continuous models. Various techniques, including Fourier transforms, Jacobi operator theory, and backward error analysis, provide means to construct and study the behavior of traveling-wave-like solutions for discrete reaction-diffusion equations and discrete semi-linear wave equations. The results supply waves speed estimates and necessary and sufficient conditions for fronts and pulses to fail to propagate due to inhomogeneities in the medium, as well as confirmation that certain discretizations reproduce the qualitative solution behavior of the corresponding partial differential equations.BIO: After completing an M.S. degree in mathematical and computer sciences at Colorado School of Mines, Brian Moore earned his Ph.D. in mathematics at the University of Surrey in the United Kingdom in 2003. He held a postdoctoral research position at McGill University in Quebec, followed by a visiting… Read more.

The local-global conjecture for Apollonian circle packings is false

on line
Algebra and Number Theory Seminar

Speaker: Katherine Stange

Primitive integral Apollonian circle packings are fractal arrangements of tangent circles with integer curvatures. The curvatures form an orbit of a 'thin group,' a subgroup of an algebraic group having infinite index in its Zariski closure. The curvatures that appear must fall into one of six or eight residue classes modulo 24. The twenty-year old local-global conjecture states that every sufficiently large integer in one of these residue classes will appear as a curvature in the packing. We prove that this conjecture is false for many packings, by proving that certain quadratic and quartic families are missed. The new obstructions are a property of the thin Apollonian group (and not its Zariski closure), and are a result of quadratic and quartic reciprocity, reminiscent of a Brauer-Manin obstruction. Based on computational evidence, we formulate a new conjecture. This is joint work with Summer Haag, Clyde Kertzer, and James Rickards. Time permitting, I will discuss some new results… Read more.

Improving the accuracy of coupled physics packages in Earth system models

STAG 112
Applied Mathematics and Computation Seminar

Speaker: Sean Santos

ABSTRACT: Earth system models solve exceedingly complicated multiphysics problems by breaking down the Earth system hierarchically into smaller sub-models (e.g. atmosphere, ocean, land, and sea ice), which are composed of smaller components themselves. This decomposition of an Earth system model (which may require millions of lines of code in its software implementation) into many small modules is a vital part of model development. However, naïve coupling of modular physics packages using first-order methods can significantly reduce model accuracy, or even produce numerical instability. This talk covers two examples from the Energy Exascale Earth System Model (E3SM). First, we will see that “sequential” (Lie-Trotter) splitting is a major source of error for E3SM’s cloud and precipitation physics. We will discuss our evaluation of several proposed alternatives, including Strang splitting and multirate methods. Second, we will see that E3SM is prone to spurious “oscillations” in winds… Read more.