The talks will typically take place on Tuesdays at 4:00-5:00pm in Adel Room 164. Please contact Ye Chen if you would like to give a talk or have a question about the colloquium.
Date: Tuesday 1/20 at 4:00-4:50
Speakers: Jaechoul Lee, Associate Professor, NAU
Abstract: The “curse of dimensionality” presents a formidable barrier in modern data applications: as the complexity of a system grows, the cost of acquiring, monitoring, and processing data often scales prohibitively. However, we can frequently overcome this challenge by exploiting the “intrinsic low-dimensional geometry” of the data, i.e., the observation that high-dimensional signals often reside on compact manifolds characterized by sparsity or low-rank dependencies.
This talk is an invitation to explore the rich mathematical landscape underlying critical engineering challenges, such as efficient signal acquisition, network monitoring, and distributed learning. We will begin by revisiting the classical framework of sparse recovery and group testing, examining how we can identify active components in a signal using a minimal number of measurements. I will discuss our results on order-optimal algorithms that achieve reconstruction with sample complexity linear in the sparsity level and sub-linear decoding time.
From these geometric foundations, we will pivot to the domain of distributed learning. Specifically, our recent result on federated learning using zero-order optimization will illustrate how tools like the Johnson-Lindenstrauss (JL) transform allow us to estimate high-dimensional gradients from compressed queries while preserving geometric structure and robustness. We will also look at emerging frontiers, such as the application of low-rank structure in network traffic analysis and LLM fine-tuning, offering a glimpse into the future of scalable, efficient, and trustworthy systems.
Date: Tuesday 1/27 at 4:00-4:50
Speakers: Nandor Sieben, Professor, NAU
Abstract: In theory the winning strategy of a combinatorial game can be found by a simple process analyzing the digraph of positions. In practice this is often impossible because the game digraph is too large. Folding the game digraph identifies positions that are essentially the same. Folding constructs a quotient game that is easier to analyze since it has fewer positions. The theory allows for the four isomorphism theorems known from Universal Algebra. Clever foldings make it possible to analyze many interesting games like “Totative” and “Sliding Coins”. Joint work with Baltushkin and Ernst.
Date: Tuesday 2/3 at 4:00-4:50
Speakers: TBA
Abstract: TBA
Date: Wednesday 2/11 at 4:00-4:50
Speakers: Mayank Bakshi, Assistant Professor, NAU
Abstract: The “curse of dimensionality” presents a formidable barrier in modern data applications: as the complexity of a system grows, the cost of acquiring, monitoring, and processing data often scales prohibitively. However, we can frequently overcome this challenge by exploiting the “intrinsic low-dimensional geometry” of the data, i.e., the observation that high-dimensional signals often reside on compact manifolds characterized by sparsity or low-rank dependencies.
This talk is an invitation to explore the rich mathematical landscape underlying critical engineering challenges, such as efficient signal acquisition, network monitoring, and distributed learning. We will begin by revisiting the classical framework of sparse recovery and group testing, examining how we can identify active components in a signal using a minimal number of measurements. I will discuss our results on order-optimal algorithms that achieve reconstruction with sample complexity linear in the sparsity level and sub-linear decoding time.
From these geometric foundations, we will pivot to the domain of distributed learning. Specifically, our recent result on federated learning using zero-order optimization will illustrate how tools like the Johnson-Lindenstrauss (JL) transform allow us to estimate high-dimensional gradients from compressed queries while preserving geometric structure and robustness. We will also look at emerging frontiers, such as the application of low-rank structure in network traffic analysis and LLM fine-tuning, offering a glimpse into the future of scalable, efficient, and trustworthy systems.
Date: Tuesday 2/17 at 4:00-4:50
Speakers: Sam Harris, Assistant Professor, NAU
Abstract: Entanglement is a crucial resource in quantum information science and is required for many tasks involving quantum computers. In 2003, van Dam and Hayden devised an approximate method for two parties (Alice and Bob), which takes a certain entangled state and uses it to produce a new entangled state “alongside” the first one, while nearly preserving the first state. Such a process has come to be known as embezzlement of entanglement. In the setting where this process is exact (and not approximate), it is known that such protocols can only occur in infinite-dimensional, “commuting operator” frameworks. In this talk, we exhibit something stronger: Alice and Bob’s operations needed to perform embezzlement are unique in a certain sense, and generate unique observable algebras. We explore this “self-testing” phenomenon and describe what observable algebras one obtains.
Date: Tuesday 2/24 at 4:00-4:50
Speakers: Sabrina Zarza, Michigan State
Abstract: This talk explores how Chicana feminist methodologies offer innovative ways of understanding students’ experiences with mathematics across secondary and postsecondary contexts. Drawing on two interconnected studies, one examining high school students’ sense of belonging in mathematics classrooms and a dissertation study using walking pláticas with Latiné mathematics majors who attended both Hispanic-Serving and Predominantly White Institutions, I illustrate how relational and place-based approaches generate new insights into the structural conditions that shape participation in mathematics. Together, these studies center students’ narratives and embodied experiences as a foundation for theory building about belonging and engagement in mathematics. By foregrounding these perspectives, this work complements existing approaches to studying student experience and extends how researchers and educators understand the sociopolitical context of mathematics learning. The talk concludes by considering implications for mathematics educators, teacher preparation programs, and researchers interested in designing studies that more fully account for students’ lived experiences with mathematics.
Date: Tuesday 3/3 at 4:00-4:50
Speakers: TBA
Abstract: TBA
Date: Tuesday 3/10 at 4:00-4:50
Speakers: TBA
Abstract: TBA
Date: Tuesday 3/17 at 4:00-4:50
Speakers: Lan Zhang, Assistant Professor, NAU
Abstract: TBA
Date: Tuesday 3/24 at 4:00-4:50
Speakers: Nellie Gopaul
Abstract: TBA
Date: Tuesday 3/31 at 4:00-4:50
Speakers: Anders Claesson, Professor, University of Iceland
Abstract: Montmort’s classical hat-check problem asks for the probability that a random permutation has no fixed points; the answer, famously, tends to 1/e. The same limit holds, by an elementary argument, for endofunctions. Cayley permutations sit between these two families and present a harder challenge. A Cayley permutation is a function on {1,…,n} whose image contains every positive integer up to its maximum value; via their fibers, Cayley permutations are in bijection with ballots (ordered set partitions).
In this talk, we use two-sort species to study the functional digraphs of Cayley permutations. We derive differential equations for the generating series of R-recurrent Cayley permutations, a class that includes derangements as a special case. From these equations, we obtain an explicit counting formula for fixed-point-free Cayley permutations involving subfactorials and differences of r-Stirling numbers. We then use this formula to prove that the proportion of Cayley derangements again tends to 1/e, just as for permutations and endofunctions.
This is joint work with Giulio Cerbai (University of Iceland).
Date: Tuesday 4/7 at 4:00-4:50
Speakers: Kayode Oshinubi, Postdoc, NAU
Abstract: TBA
Date: Tuesday 4/14 at 4:00-4:50
Speakers: Maddy Cox
Abstract: TBA
Date: Tuesday 4/21 at 4:00-4:50
Speakers: TBA
Abstract: TBA
Date: Tuesday 4/28 at 4:00-4:50
Speakers: TBA
Abstract: TBA