The talks will typically take place on Tuesdays at 4:00-5:00pm in Adel Room 164. Please contact Nandor Sieben if you would like to give a talk or have a question about the colloquium.
Short organizational meeting
Speaker: Shannon Guerrero Title: Teacher-authored culturally responsive mathematics curriculum: Lessons from the Diné Institute for Navajo Nation Educators
Abstract: This presentation shares research conducted with a long-term professional development program for teachers in Navajo-serving schools, with a focus on the mathematics curriculum developed by teachers in this program. We address the research question: To what extent and in what ways do teachers in DINÉ math seminars develop curriculum units that evidence culturally responsive principles and mathematics education best practices? We analyze teacher-authored mathematics curriculum from two years of this program and share key lessons learned in supporting teachers from Indigenous-serving schools to engage culturally responsive principles in their math teaching and learning.
Speaker: Jeffrey Covington Title: Curve fitting and Gaussian process regression
Abstract: Gaussian process regression, also known as Kriging, is a powerful curve fitting and statistical regression tool which has grown in popularity over the past few years. I’ve found it to be a powerful tool in my own research in spatial and dynamical modeling. This talk will introduce (kernel-based) Gaussian processes and their applications, relate them to curve fitting through Gaussian process regression, and explore the power and pitfalls of the methods.
Speaker: Michele Torielli Title: Hyperplane arrangements and signed graphs
Abstract: In this talk, we will recall the notion of hyperplane arrangement and discuss when an arrangement is free. We will then discuss their connection with simple graphs and finally, generalize this connection to the notion of signed graphs.
Speaker: Roy St. Laurent Title: Diversions: My Favorite Logic Puzzles from Nikoli
Abstract: This is not a research talk. I will introduce three or four of my favorite Nikoli puzzles, with an opportunity for you to solve examples of them yourself. Paper copies will be provided, just bring a pencil (or pen).
Nikoli is a Japanese publisher that specializes in culture-independent puzzles – especially pencil/paper logic puzzles played on a rectangular grid. I have been hooked on Nikoli puzzles since being introduced to them by now-retired Mathematics professor Dr. Steve Wilson. The English names of some of my favorites are Akari, Fillomino, Hashiwokakero, Heyawake, Hitori, Kakuro, Nurikabe, Slitherlink, Yajilin.
While this isn’t a research talk, a couple of interesting questions come to mind that will be raised during the talk.
Site visit week. No colloquium.
No colloquium.
Speaker: Peter Vadasz Title: Magnetostrophic Flow and Electromagnetic Columns in Magneto-Fluid Dynamics and short updates on my previous presentations of Quantum Mechanics and Newtonian Gravitational Waves
Abstract: An analogy between magneto-fluid dynamics (MFD/MHD) and geostrophic flow in a rotating frame of reference including the existence of electromagnetic columns identical to Taylor-Proudman columns is identified and demonstrated theoretically. The latter occurs in the limit of large values of a dimensionless group representing the magnetic field number. Such conditions are shown to be easily satisfied in reality. Consequently, the electromagnetic fluid flow subject to these conditions is two dimensional and the streamlines are being shown to be identical to the pressure lines in complete analogy to rotating geostrophic flows. An experimental setup is suggested to confirm the theoretical results experimentally.
Speaker: Rachel A Neville Title: A Fractal Dimension for Measures via Persistent Homology
Abstract: A fractal is a geometric object that displays self-similarity on all scales. There are common examples, such as the Sierpinsky Triangle or the Koch snowflake. The “fractal dimension” quantifies the complexity of the fractal. While fractal dimensions are most classically defined for a space, there are a variety of fractal dimension definitions for a measure, including the Hausdorff or packing dimension of a measure. In this talk, I will give a brief introduction to fractal dimension and describe how persistent homology can be used in order to define a family of fractal dimensions. I will end with a discussion of some work done with John Leland on a persistence based distribution test.
Speaker: Sam Harris Title: The Max 3-Cut problem for graphs
Abstract: A famous problem in graph theory is the Max Cut problem: given an undirected graph G, determine whether there is a partition of the vertices of G into two subsets so that every edge of G is “cut” by the partition. While this problem is NP-hard, the non-commutative version is surprisingly solvable in polynomial time, and even can be used to approximate the (classical) maximum cut of a graph. In this talk, we’ll look at some of the history of both problems, and also look at recent work on the Max 3-Cut problem and its noncommutative variants.
Speaker: Dana Ernst Title: Pattern-avoiding Cayley permutations via combinatorial species
Abstract: Any permutation of $n$ may be written in one-line notation as a sequence of entries representing the result of applying the permutation to the identity $12\cdots n$. If $p$ and $q$ are two permutations, then $p$ is said to contain $q$ as a pattern if some subsequence of the entries of $p$ has the same relative order as all of the entries of $q$. If $p$ does not contain a pattern $q$, then $p$ is said to avoid $q$. One of the first notable results in the field of permutation patterns was obtained by MacMahon in 1915 when he proved that the ubiquitous Catalan numbers count the 123-avoiding permutations. The study of permutation patterns began receiving focused attention following Knuth’s introduction of stack-sorting in 1968. Knuth proved that a permutation can be sorted by a stack if and only if it avoids the pattern 231 and that the Catalan numbers also enumerate the stack-sortable permutations. In this talk, we study pattern avoidance in the context of Cayley permutations, which were introduced by Mor and Fraenkel in 1983. A Cayley permutation is a finite sequence of positive integers that include at least one copy of each integer between one and its maximum value. When possible we will take a combinatorial species-first approach to enumerating Cayley permutations that avoid patterns of length two, pairs of patterns of length two, patterns of length three, and pairs of patterns of length three with the goal of providing species, exponential generating series, and counting formulas. We also include several conjectures and open problems.
Speaker: Jim Swift Title: Amazingly Fast Computations of Polydiagonal Subspaces using Constraint Programming
Abstract: Polydiagonal subspaces of $\mathbb{R}^n$ are defined by equations of the form $x_i = \pm x_j$. They are a generalization of the diagonal subspace, which has $x_1 = x_2 = \cdots = x_n$. Given an $n \times n$ matrix $M$, the $M$-invariant polydiagonal subspaces of $\mathbb{R}^n$ describe synchrony or anti-synchrony in a network of $n$ coupled cells. Computing all $M$-invariant polydiagonal subspaces is hard. We use constraint programming to do computations in minutes that took weeks with the previously state-of-the-art algorithm. We show results of the computation where $M$ is the adjacency matrix of the 60-vertex Buckyball graph.
Speaker: Minah Kim Title: The Nature of an Online Work Group of Inquiry-Oriented Linear Algebra Instructors through Their Goals for Instruction
Abstract: Postsecondary instructors interested in inquiry-oriented instruction of linear algebra participated in a sequence of eight one-hour online work group meetings with other inquiry-oriented linear algebra instructors and facilitators. Recordings were analyzed to see how two participants referenced goals for instruction in discussions of implementing a new instructional unit on subspaces. We identified four instructional goals for teaching subspaces and discussed the intersections of several goals that exist due to the tension caused by real-world contexts and abstract mathematical concepts. The instructors presented resolutions to the tension by utilizing varying teaching knowledge. Based on the results, we make suggestions for those who want to transition to inquiry-oriented instructional approaches.
Speaker: Adeolu Taiwo Title: Iterative Regularization Methods for Bi-level Optimization
Abstract: Bi-level optimization problems consist of two optimization problems, called outer and inner problems, where one problem is embedded within another. This class of problems has applications in diverse fields, such as decision sciences, machine learning, regression analysis, and signal processing. In this talk, we investigate iterative regularization methods for solving bi-level optimization problems where the inner and outer functions have a composite structure. We provide novel theoretical results, including the first convergence rate analysis for the Iteratively REgularized Proximal Gradient (IRE-PG) method, a variant of Solodov’s algorithm. These results establish simultaneous convergence rates for the inner and outer functions, highlighting the inherent trade-offs between their respective convergence rates. We extend this analysis to an accelerated version of IRE-PG, proving faster convergence rates under specific settings. Additionally, we propose a new scheme for handling cases where these methods cannot be directly applied to the bi-level problem due to the difficulty of computing the associated proximal operator. This scheme offers surrogate functions to approximate the original problem and a framework to translate convergence rates between the surrogate and original functions. Our results show that the advantage of the accelerated method diminishes under this translation.
Speaker: Annie and Gina Title:
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Speaker: Andrew Schultz (Wellesley College) Title:
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Speaker: Joe Polman (CU Boulder) CSTL STEM Education speaker series Title:
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