Abstract: We study the optimization of Steklov eigenvalues with respect to a boundary density function ρ on a bounded Lipschitz domain. We investigate the minimization and maximization of a Steklov eigenvalue over admissible densities satisfying pointwise bounds and a fixed integral constraint. We establish the existence of optimal solutions and provide structural characterizations: minimizers are […]
Inspired by the categorification program for a numerical invariant of three-manifolds, series invariants for closed manifolds and for knot complements were introduced. This in turn motivated an extension of the series invariant of the former case to Lie superalgebras. It was recently generalized to knot complements. In this talk, we review the original series invariants […]
CCMS Colloquium invites you to a talk by Ryan Moruzzi (CSU Northridge) Title: Exploring Leaky Forcing Through Hopi Rectangle graphs Abstract: Leaky forcing, introduced in 2019, is a graph-coloring process motivated by questions of network monitoring, in which the loss of information can hinder propagation through a graph. As a variant of standard zero forcing, […]
Abstract: Turbulence influences our lives in a multitude of ways, ranging from the mundane (when we stir milk into our coffee) to the spectacular (the formation of galaxies). It is a great achievement of the human intellect that we are able to locate fundamental mechanisms shared by phenomenon with such a dramatic difference in scale […]
Diophantine avoidance has been studied by several authors in recent years. This refers to effective results on existence of points of bounded size in a given algebraic set avoiding some specified subsets. The famous primitive element theorem states that every number field K is of the form Q(a) for some element a in K. From the proof of […]
CCMS Colloquium invites you to a talk by Manuel Reyes (UCI) Title: When XY is not equal to YX Abstract: The commutative property of algebra states that the order of multiplication makes no difference: XY = YX. This property is so ingrained in our experience that it becomes difficult to imagine how algebra would function without it! If the commutative property fails, […]
Abstract: I will introduce In-Context Operator Networks (ICON), a framework in which a single neural network learns solution operators for differential equations directly from a few prompted input-output examples at inference time, without any weight updates. ICON acts as a few-shot learner across forward and inverse problems for ODEs, PDEs, and mean-field control. I will […]
One of the key objects used in Ngo's proof of the fundamental lemma is the group scheme of universal centralizers associated to a split reductive group G. In this talk, we'll discuss forthcoming work, joint with Victor Ginzburg, which describes the coordinate ring of the group scheme of universal centralizers in terms of the root datum of G using Demazure (or divided […]
CCMS Colloquium invites you to a talk by Andrew Fiss (Michigan Technological University) Title: “Singing American Math: College Traditions from Book Burnings to Observatory Parties, 1880s-1920s" Abstract: “Singing Math” is a practice that linked American colleges of the late nineteenth and early twentieth centuries. A part of broader college singing traditions, it stood apart because of its […]
Abstract: Consider n independent, biased coins, each with a known probability of heads. Presented with an ordering of these coins, flip (i.e., toss) each coin once, in that order, until we have observed both a head and a tail, or flipped all coins. The Unanimous Vote problem asks us to find the ordering that minimizes […]
Many aggregation problems ask us to turn individual judgments into a single collective outcome. In this talk, we model each voter’s input as a relation on a set of alternatives, allowing pairwise comparisons to include strict preferences, ties, or incomparability. This perspective gives a common framework for median procedures and scoring methods, including several familiar […]
Topology, akin to geometry, delves into the study of the shapes and structures of mathematical spaces, ranging from simple surfaces to intricate collections of functions and objects. In recent years, these foundational concepts have extended beyond pure mathematics to address practical problems in data science, influencing diverse areas such as chemistry, neuroscience, and robotics. This […]
