Meetings of the GSS will take place in Carver 401 on Fridays at 1:00 pm.
No meetings will take place during holidays.
2/6/26
Just my Pot Luck!
2/13/26
Khiem Nguyen
Title: Ultrafilters, Ultraproducts and Stone-Čech compactification!
Abstract: This talk is an introduction to several concepts such as ultrafilters, ultraproducts, and Stone-Čech compactification, as well as their connection. This talk will introduce many concepts that will show up in upcoming talks at the Junior Analysis Seminar.
2/20/26
Channing Bentz
Title: Derived Categories
Abstract: When working in a general category, sometimes we would like to say that things "are the same" up to a weak equivalence. How do we do this? Localization! In this talk I will talk about localization of a category on a weak equivalence and then look at it's application to the category of chain complexes over an abelian category. This is what is known as the derived category and it has a lot of fun properties!
2/27/26
Matt Burnham
Title: Spectral theory of K_t-decomposable graphs
Abstract: The q-Laplacian of a graph G is the matrix L^{(q)} = A + qD where A is the adjacency matrix and D the diagonal degree matrix. A graph is called K_t-decomposable if the edges of G can be partitioned into edge-disjoint copies of K_t. The 1-Laplacian A + D is a well-studied matrix called the signless Laplacian. In this talk, we give an overview of well-known results about the spectrum of the signless Laplacian, and then show how these results extend to the 1/(t-1)-Laplacian of K_t-decomposable graphs.
3/6/26
Micah Coats
Title: The Perimetric Inequality, some Hyperbolic Geometry, and Symmetrization of functions on Hyperbolic Space
Abstract: Steiner Symmetrization on a function f:R^n->R is a rearrangement of f such that measures of level sets are unchanged and where the rearrangement f* is radially symmetric and decreasing. It has been used as a tool for some optimization problems and classically was important for proving the isoperimetric inequality. In this talk we discuss a technique used to prove many fascinating properties of symmetrization that also has a hyperbolic analogue. A short discussion of hyperbolic geometry and its transformations is included to explain the technique.
3/13/26
Joanna Held
Title: Micro-macro decomposition scheme for the kinetic Vlasov system.
Abstract: Kinetic theory is a classical description of the thermodynamic behavior of gases. In this model, the movement and collisions of particles govern the large-scale behavior of a system. However, kinetic equations like the Vlasov-Poisson which describes the behavior of an electrostatic plasma are computationally challenging as they exist in a high-dimensional phase space, these problems are multiscale in nature, and dynamics change based on which collisional regime the system is in. There are a variety of ways to handle these challenges, but one is to apply a so-called micro-macro framework to the Vlasov system in order to combine fluid representations while still resolving the kinetic or particle effects. In this talk, I will discuss this framework and show examples applying it to the 1D1V Vlasov-Poisson equation.
3/20/26
Spring Break!
3/27/26
Dajuan Kinney
Title: Where are the balls? A Look Into The Mathematics of Juggling
Abstract: Interest in the mathematics of juggling has grown significantly over the past three decades. This presentation provides a brief overview of several discrete mathematical methods used to describe and analyze juggling patterns. Representations such as \textbf{siteswaps}, \textbf{juggling cards}, and \textbf{state graphs} will be introduced as tools for encoding and studying patterns. The concept of \textbf{multiplex juggling patterns} will be defined, along with methods for counting them. Connections between juggling structures and classical combinatorial objects, including \textbf{Stirling numbers of the second kind} and \textbf{Bell numbers}, will also be explored. If time permits, audience members will have the opportunity to demonstrate their own juggling skills—and the presenter will be juggling as well.
4/3/26
Joe Miller
Title: Certifying the block restricted isometry property for totally symmetric subspaces
Abstract: In compressed sensing, the goal is to solve an underdetermined system Ax = b with the assumption that x is sparse, i.e. has many zeros. There are multiple efficient solvers which only work if A satisfies the restricted isometry property (RIP). It’s well-known that random matrices satisfy RIP with high probability, but it is an NP-hard problem to check if a specific matrix actually does. This led to the problem of constructing matrices which can be verified to satisfy RIP. This open problem has seen little progress in the last 15 years, stuck behind the “Gershgorin bottleneck”: a simple upper bound for our RIP constants. In this talk, we’ll see how representation theory of the symmetric group allows us to construct block matrices which satisfy block RIP and beat the Gershgorin bottleneck.
4/10/26
Billy Duckworth
Title: Generic Properties of "Nice" Functions
Abstract: Much of our undergraduate exposure to functions gives us the illusion that all functions are "nice". When we reach our first analysis class we learn that general functions can be quite pathological, but our collections of "nice" functions are a safe sandbox to carry out most of our work. In this talk we will investigate just how scary generic "nice" functions can really be.
4/17/26
Laura Gamboa Guzman
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4/24/26
Kylie Schnoor
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5/1/26
Micah Coats
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5/8/26
Kean Fallon
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