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NSF RTG Conference: Materials and Optimization, Program

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Friday, October 16, 2026

Saturday, October 17, 2026

Sunday, October 18, 2026

Abstracts

Ray Adams, Shadow company

Title: TBA

Abstract: TBA

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Nathan Albin, Kansas State University

Title: TBA

Abstract: TBA

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Behman Azadpour, Brigham Young University

Title: Intrinsic Wettability Prediction from Surface Characterization Using Machine Learning

Abstract: Understanding and predicting the wettability of engineering materials is important for applications including coatings, biomedical devices, membranes, additive manufacturing, and liquid – solid interactions. Conventional wettability characterization relies on experimental contact angle measurements, which is time consuming when screening large numbers of materials. Machine learning provides an opportunity to accelerate this process by establishing quantitative relationships between material characterization data and wetting behavior. In this work, we investigate a data - driven framework for predicting the intrinsic wettability of polymeric materials directly from surface characterization measurements. Spectroscopic information obtained from ATR-FTIR is transformed into numerical descriptors that serve as inputs to supervise machine learning models. Multiple feature engineering strategies, dimensionality reduction techniques, and regression algorithms are evaluated to identify representations that maximize predictive performance while maintaining model interpretability. From an optimization perspective, the study formulates wettability prediction as a data-driven optimization problem involving feature selection, model selection, and hyperparameter optimization to minimize prediction error while improving generalization to unseen materials. The resulting workflow reduces reliance on extensive experimental measurements and provides a scalable framework for rapid property prediction. Beyond predicting contact angle, this approach establishes a foundation for integrating machine learning with materials characterization to support accelerated materials discovery and inverse materials design. The methodology is general and can be extended to additional characterization techniques, including Raman spectroscopy, XPS, SEM/EDS, and AFM, enabling broader optimization of structure – property relationships in polymeric and other engineering materials.

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Batuhan Bayir, University of Utah

Title: JKO-Based Framework for a Nonlinear Fokker-Planck Type Model of Grain Growth

Abstract: Polycrystalline materials are crucial for various technological applications. Structurally they consist of a myriad of small monocrystallines called grains which are separated by grain boundaries. As the grain structure characterizes the material’s properties, it is highly important to understand grain growth during microstructure evolution for engineering of new materials. In this talk, we will introduce a nonlinear Fokker-Planck-type model which describes the evolution of grain boundary and triple junction statistics. In this model, the inhomogeneous absolute temperature results in a non-standard entropy-type nonlinearity. We formulate a JKO-based framework for the model, and establish the existence of global weak solutions and their long-time behavior. This is a joint work with my advisors Yekaterina Epshteyn and William M Feldman.

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Kenneth Beard, University of Utah

Title: Double-Incommensurate Twisted Trilayer Graphene: A Momentum Space Tight-Binding Model

Abstract: Numerical algorithms for computing the electronic structure of incommensurate 2D materials are essential for predicting material properties. However, in double-incommensurate systems like generic twisted trilayer graphene (TTG), previous algorithms utilized a continuum approximation and radial truncation that resulted in poor numerical convergence and suppression of physically relevant phenomena. In this talk, we present a momentum space framework for double-incommensurate TTG that directly transforms the tight-binding model into momentum space. By introducing a highly efficient truncation scheme that exploits the energy-momentum confinement of the monolayer Dirac cone structure, we effectively reduce the problem’s computational scaling to two dimensions. For this presentation, we focus primarily on the physical insights and numerical results generated by applying the Kernel Polynomial Method (KPM) to an ab initio tight-binding model under our truncation scheme. This includes a direct comparison of the converged momentum local density of states (LDoS) for both the previous continuum approximation and the tight-binding model. Crucially, we demonstrate qualitative alterations to band behavior near the flat band regime for the tight-binding model that are lost in the continuum approximation.

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Kaushik Bhattacharya, Caltech

Title: Forward and inverse problems in materials characterization

Abstract: This talk concerns two complementary approaches of characterizing the overall properties of materials. The first approach — the forward approach — is based on multiscale modeling where one infers the effective behavior at the scale of applications from known physics at a smaller scale through homogenization. We discuss recent approaches that exploit neural operators. The second approach — the inverse approach — is to infer it from experimental observations. Advances in experimental methods have not been matched by advances in quantitative models due to the difficulties of solving the inverse problem. We discuss emerging approaches to solving this problem, as well as the problem of designing experiments.

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Brandon Burkhardt, Arizona State University

Title: Mechanical Modeling of Graphene

Abstract: A fundamental limitation of modeling bilayer graphene with a Lennard-Jones (LJ) potential, despite its widespread use for its numerical simplicity, is that it does not fully capture the registry dependence or the relative orientation between layers arising from interlayer van der Waals interactions. Instead, this work proposes using the Kolmogorov-Crespi (KC) potential, which provides a more complete description of these registry-dependent interactions. To investigate the KC potential, we simplify each graphene lattice as a one-dimensional chain of carbon atoms. We examine different stacking configurations of these chains and allow the system to relax to its equilibrium state. Our model predicts the relaxed equilibrium configuration of this simplified heterostructure. We compare the relaxed structures obtained using the LJ and KC potentials, highlighting the differences in their predicted equilibrium states. We also compare the full KC model with a simplified version that depends only on the interchain distance and neglects the orientation of the normals associated with the interatomic bonds. This one-dimensional model serves as a foundation for developing a more complete model of bilayer graphene heterostructures.

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Maxence Cassier, Fresnel Institute

Title: Geometric spectral properties of electromagnetic waveguides

Abstract: In this talk, which is based on the article [1], we consider a homogeneous electromagnetic waveguide with a simply connected cross-section embedded in a perfect conductor and study how geometric deformations (bending and twisting) affect its propagating frequencies, or equivalently, the real spectrum of the associated self-adjoint Maxwell operator. We first provide conditions on the geometrical deformation that ensure the preservation of the essential spectrum, which is symmetric, exhibits a spectral gap around the origin, and coincides with the spectrum of a reference unperturbed waveguide with constant twist. To prove such a result, our approach relies on a Birman-Schwinger-type principle (of independent interest), combined with a meromorphic Fredholm theorem.We then focus on purely bent waveguides and derive sufficient conditions, including one involving the geometry of the cross-section, ensuring the existence of discrete eigenvalues within the spectral gap. These eigenvalues correspond to trapped modes. We provide theoretical and numerical results that further investigate our sufficient conditions. Finally, we examine the stability of the sufficient condition involving the geometry of the cross-section under shape deformations, focusing in particular on the case of a waveguide with a rectangular cross-section.

[1] Philippe Briet, Maxence Cassier, Thomas Ourmières-Bonafos, Michele Zaccaron, Geometric spectral properties of electromagnetic waveguides, to appear in the Journal of the London Mathematical Society, available on arxiv at https://arxiv.org/abs/2508.13591.

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Andrej Cherkaev, University of Utah

Title: Some Optimization Problems in Continuum Mechanics

Abstract: This talk provides an overview of three related topics: optimal composites, structural optimization, and the design of resilient structures. The optimization of periodic material layouts is formulated as a nonconvex variational problem with a multiwell Lagrangian, where the wells represent the energies of the constituent materials. The analysis combines dual methods. Structure-independent energy bounds are obtained using the translation method (polyconvex envelope) together with pointwise constraints on the optimizers. The obtained optimal fields guide the search for optimal structures among laminates of infinite rank that realize these fields pointwise. The resulting optimal composites are used to solve several design problems. These include minimizing the energy of a domain, minimizing a continuous functional of the potential—as in the design of an optimal thermal lens—and performing robust optimization when the external load is only partially known. Inverse structural optimization seeks to identify functionals that may have been minimized through millions of years of biological evolution. An example concerns the functional advantages of the spiral grain in the trunk of the ponderosa pine. The other topic is the design of resilient structures capable of withstanding impacts. Such structures absorb impact energy by distributing partial damage and by generating waves that transport energy away from a contact region. Several concepts are investigated, including bistable structures with sacrificial links, inhomogeneous lattices, and nonperiodic Penrose lattices.

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Grzegorz Dzierzanowski, Warsaw University of Technology

Title: Optimum design of plates under simultaneous membrane and bending loads

Abstract: This talk addresses the question of how to design the stiffest plate subjected to in-plane (membrane) and out-of-plane (bending) forces. Loads act simultaneously, so the answer is more general than that obtained by a typical approach, where loads are considered separately. Formulation of the problem is classical. It calls for the optimal distribution of an isotropic, two-phase material throughout the plate, assuming a fixed volumetric share of each phase. The material is homogeneous in the transverse direction, so the phase layout is optimized only on the mid-surface of the plate.

The existence of a solution to the problem of maximum structural stiffness (equivalently, minimum compliance) is guaranteed if microstructural mixtures of phases are allowed. Consequently, to minimize the compliance of the plate, one must consider all possible microstructural phase layouts. This extreme difficulty is overcome by a generalized translation method, in which the translator is a three-parameter quasiconvex function, similar to that used for solving the pure in-plane and out-of-plane problems. Consequently, a family of lower approximations of the compliance functional is introduced. Members of the family are isotropic functions that take eight arguments: three translation parameters and five invariants of the membrane and bending stress resultants.

As long as the explicit formula for the best lower bound on compliance is unknown in the general, two-phase setting, the problem is analytically tractable only when the weak phase degenerates to a void. Optimal values of translation parameters are found in five regions (regimes) of stress resultants. Moreover, constitutive relations for the maximum-stiffness plate are derived explicitly, thereby facilitating the computational treatment of the problem. The question of identifying microstructures that correspond to optimal stress resultants is also addressed, but the result is limited only to third-rank laminates.

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Likhit Ganedi, University of Utah

Title: Analysis of Bifurcations in Ferromagnetic Elastica subjected to External Forcing

Abstract: We study the stability and bifurcation behavior of ferromagnetic Kirchhoff rods subjected to gravity and external magnetic fields. For spatially uniform fields, we characterize the stability of straight configurations and show that magnetic loading can stabilize rods against gravity. In an appropriate parameter regime, loss of stability from the straight state occurs through a supercritical pitchfork bifurcation. For localized fields generated by spherical permanent magnets, we identify we show the existence of 2D-3D bifurcations and hysteresis in different regimes depending on the strength and placement of the external magnets. These results are confirmed through theory, numerics, and experiments done in collaboration with Raghavendra Venkatraman (Utah), Vivekanand Dabade (IISc), and Mohd Tahseen (IISc).

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Leonid Gibiansky, QuantPharm LLC

Title: Optimal bounds and optimal structures for three-dimensional three-phase composites containing an ideal conductor

Abstract: In collaboratiojn with: Andrej Cherkaev (University of Utah) with the help of Claude Opus 5 (Anthropic)

Problem. We consider the problem of exact bounds on the effective conductivity of an isotropic composite made of two isotropic conductors $k_1 \le k_2$ and an ideal conductor $k_3 = \infty$, taken in prescribed volume fractions $m_1$, $m_2$ and $m_3$. For this problem, the Hashin–Shtrikman (HS) bounds are not attainable in general [1]. In two dimensions (2D), the optimal bounds were found by Nesi [2] and Cherkaev [3], while two families of optimal structures were found by Albin, Cherkaev and Nesi [4] and by Cherkaev [5]. In $d \ge 3$ the problem has remained open.

Method. The 2D bounds were based on the fact that $\det E$ (where E is the matrix of the gradient fields) does not change sign [7]. In 3D this is false for general structures [8], but we assume E to be positive semidefinite for the optimal ones: an optimality condition in the sense proposed in [3]. The resulting bounds improve on HS only well below its attainability range, and are not optimal. We then add a second translator: the cubic quasiaffine invariant $\det E$, which for 3D is independent of the classical quadratic one [9, 10], while in 2D the two coincide up to a factor.

Bounds. The translation method, applied with this extra translator and the pointwise restriction, yields the bounds. The minimax problem has five solution branches, depending on $m_1$. An exact closed form holds in region 1, where material 1 is abundant, and in region 3, where it is very scarce. The intermediate region 2 splits into three subregions: 2A, where the bound has exact closed form, 2B, where the bound is an explicit function of a root r of a cubic equation, and 2C, where r and a second multiplier solve a pair of algebraic equations.

Structures. Every regime has an attaining structure: region 1 (the HS-attainable range [6]) by neutral coated spheres and an enveloped wheel; region 2 by a wheel structure with a core of material 2 and a graded shell of extremal transversely isotropic materials whose transverse conductivity attains the optimal 2D bound [3, 4]; and region 3 by finite-rank laminates. The wheel construction can equivalently be realised as a graded rank-3 matrix laminate.

Claude assistance. AI assistance was used to generate and test hypotheses, and to guide the numerical and then the analytical study of the bounds and the structures. Without this help we would not have obtained these results. On the other hand, the AI could not solve the problem by itself: it needed detailed guidance at every step.

References

[1] G. W. Milton, Phys. Rev. Lett. 46 (1981) 542.

[2] V. Nesi, Proc. R. Soc. Edinburgh 125A (1995) 1219.

[3] A. Cherkaev, Mech. Mater. 41 (2009) 411; see also A. Cherkaev, Variational Methods for Structural Optimization, Springer (2000), §7.

[4] N. Albin, A. Cherkaev and V. Nesi, J. Mech. Phys. Solids 55 (2007) 1513.

[5] A. Cherkaev, arXiv:1105.4302 (2011).

[6] L. P. Liu, Philos. Mag. Lett. 91 (2011) 473.

[7] G. Alessandrini and V. Nesi, Arch. Ration. Mech. Anal. 158 (2001) 155.

[8] M. Briane, G. W. Milton and V. Nesi, Arch. Ration. Mech. Anal. 173 (2004) 133 .

[9] K. A. Lurie and A. V. Cherkaev, Proc. R. Soc. Edinburgh 99A (1984) 71; 104A (1986) 21.

[10] F. Murat and L. Tartar, Calcul des variations et homogénéisation, in Les méthodes de l’homogénéisation, Eyrolles (1985) 319; see also L. Tartar, Estimations fines des coefficients homogénéisés, in Ennio De Giorgi Colloquium, Pitman (1985) 168.

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Christian Kern, University of Utah

Title: Tight bounds on the elastic properties of three-dimensional composites

Abstract: In the theory of composites, bounding the effective elastic moduli is a classical problem to which both honorees, Graeme W. Milton and Andrej Cherkaev, have made transformative and lasting contributions. Particularly challenging is the three-dimensional isotropic case, which I will consider for composites made from two isotropic phases. Perhaps the best-known corresponding bounds are those of Hashin and Shtrikman (in the well-ordered case) and of Hill and Walpole (in the non-well-ordered case). Improvements have been obtained by Milton and Phan-Thien as well as by Berryman and Milton. Tight bounds, however, have remained elusive. In my talk, I will present new bounds that substantially improve on all of these results. These bounds are derived using the translation method, introduced by Lurie and Cherkaev as well as by Murat and Tartar. The problem of finding the tightest bound is cast as a numerical optimization problem. Closed-form expressions of the bounds are then obtained using the numerical results as a guide.

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Tianyu Kong, University of Chicago

Title: Continuum model for twisted bilayer graphene with strain and relaxation

Abstract: We prove the convergence of solutions of a time-dependent tight-binding model for the single-particle electronic dynamics of twisted bilayer graphene (TBG) in the presence of strain and mechanical relaxation to an equivalent multiscale continuum approximation. The tight-binding Hamiltonian with uniform strain and disregistry-dependent displacement fields depends explicitly on a small dimensionless parameter corresponding to the ratio of the atomic lattice constant to the moir'e scale. We justify parameter scaling regimes near TBG’s magic angle at around one degree where electronic tunneling and mechanical relaxation operate on comparable energy scales. Using multiscale asymptotic expansions, we provide a novel derivation of an effective continuum Hamiltonian that explicitly incorporates strain and relaxation effects. We then establish rigorous long-time error estimates for initial wave packets spectrally localized to the monolayer Dirac points.

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Xuenan Li, Purdue University

Title: Pseudo-magnetism in a strained discrete honeycomb lattice

Abstract: Slowly varying nonuniform strains of non-magnetic wave propagating media with honeycomb symmetry induce an effective- or pseudo-magnetic field, a phenomenon observed first in graphene, and later in photonic crystals and other physical settings. Starting with a discrete nearest-neighbor tight-binding model of a non-uniformly strained honeycomb medium, we derive the continuum effective magnetic Dirac Hamiltonian governing the envelope dynamics of wave packets, which are spectrally localized near a Dirac point (conical band degeneracy) of the unperturbed honeycomb. For unidirectional deformations of bounded gradient, which preserve translation invariance along the ‘‘armchair’’ direction, we prove the existence of time-harmonic states which are plane-wave like (pseudo-periodic) along the armchair direction and exponentially localized transverse to it. We also obtain the leading order multi-scale structure of such modes for small deformation gradients. Their transverse localization are determined by the eigenstates of a one dimensional effective Dirac Hamiltonian. Our rigorous results apply to deformations which induce an approximate perpendicular constant pseudo-magnetic field (Landau gauge), and yield states with nearly flat band (Landau level) spectrum and hence very high density of states. In contrast, the analogous deformation which preserves translations in the zigzag direction induces no such localization. Corroborating numerical simulations for the different deformation types are presented.

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Robert Lipton, Louisiana State University

Title: Fracture as an initial boundary value problem

Abstract: A field theory is presented for predicting damage and fracture in quasi brittle materials. It is an expression of Newton’s second law for an elastic-plactic continuum. It is based on displacement dependent constitutive laws that are nonlocal in space and time. It is found that material degradation consistent with plastic dissipation can be described by two-point history-dependent phase fields. The theory satisfies power balance, with positive energy dissipation rate in accordance with the laws of thermodynamics. The fracture energy necessary to create flat cracks is recovered directly from the evolution equation via integration by parts and is independent of the length scale of non-locality. The formulation delivers a mesh free method for predicting crack patterns in quasi-brittle media and simulations show quantitative and qualitative agreement with experiments, including hysteresis and damage associated with three-point bending tests on concrete and size effects for quasi-brittle materials. We conduct numerical experiments exhibiting the competition between plastic yield strength and Griffith strength on fracture nucleation.

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Ornella Mattei, San Francisco State University

Title: Developable Surfaces and Wave Propagation in Space–Time Materials: A Geometric Correspondence

Abstract: The isometric bending of developable surfaces, as in curved-crease origami, and the propagation of waves through materials modulated in both space and time appear to have nothing in common, yet they share a single geometric skeleton. Building on the analogue-gravity picture, in which a one-dimensional space–time material is described by an effective Lorentzian metric, this talk shows that the equations governing the two problems coincide in a precise sense: the developability condition of a surface is the wave equation of the medium, and the structures that organize a folded surface reappear as the characteristics of wave propagation. The central object is a single geometric invariant, built from the material’s wave speed and impedance, that decides when a space–time material behaves like a developable surface — one that can be unrolled without distortion. This invariant is, quite literally, a curvature, and its vanishing selects a distinguished family of space–time microstructures: rectangular checkerboards with matched impedance.

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Asher Merrill, University of Utah

Title: Data-Conditioned PINNs for Inverse Modeling of Sea Ice

Abstract: Polar sea ice is a thin but influential component of the earth system, reflecting coupled thermodynamics and elastic viscoplastic mechanics across many spatial scales. In this talk, I investigate an inverse problem for the dynamics of sea ice concentration modeled by a forced advection-diffusion equation, applying a data-conditioned physics-informed neural network (PINN) to determine effective coefficient fields for the polar regions. In contrast to standard coordinate-based PINNs, this model incorporates local observational context directly through learned convolutional features built from NOAA/NSIDC passive-microwave concentration data. The method reconstructs observed concentration fields accurately with small mean absolute error, but thus far has been challenged to yield physically meaningful parameters in the sea ice concentration model equation, resulting from the ill-posedness of the problem. These results demonstrate that data-conditioned PINNs may be a promising architecture for data-rich problems but emphasize the need to constrain the problem to determine meaningful parameterization. Physically or empirically motivating these constraints remains a chief area of investigation for the polar inverse modeling and forecasting problems and will serve to enable the application of data-conditioned PINNs to this domain.

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Owen Miller, Yale University

Title: Optimal near-field antennas: Quasistatic bounds and the advantage of a third material

Abstract: Near-field antennas amplify the radiation of nearby emitters (Purcell enhancement) and, reciprocally, concentrate free-space waves into deeply subwavelength volumes, underpinning applications from single-molecule spectroscopy to quantum optics. The central design question is how the achievable enhancement scales with the antenna’s minimum feature size d. For perfect conductors, the Shockley–Ramo theorem implies $1/d^2$ scaling; for real dielectric and polaritonic materials, little has been known. This problem is, at its heart, quasistatic: an equivalence-principle argument reduces the full-Maxwell design problem to maximizing the induced dipole moment of a quasistatic scatterer. In this setting, we derive upper bounds by adapting modern computational-bound frameworks, semidefinite relaxations of the quasistatic scattering problem. Their solutions turn out to be rank-one, are achieved by radially anisotropic “relaxed” designs, and reveal analytical scaling laws: all two-material dielectric designs, including optimized bowtie antennas, are limited to exponents well below two, even for “high-contrast” materials. We also propose a way to circumvent them: three-material “dual-polarizability” designs, combining positive- and negative-contrast materials, which can recover near-ideal $1/d^2$ scaling. The results echo themes central to the work of Graeme Milton and Andrej Cherkaev: the reach of quasistatic bounds, the novelties of beyond-two-phase materials, and the importance of “spiky-wheel”-like optimal designs.

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Graeme Milton, University of Utah

Title: A mathematical journey

Abstract: In this lecture I’ll talk about the high points, so far, of my mathematical research, with many wonderful collaborators. Also, I’ll make some amusing remarks along the way. So the lecture is intended to be interesting as well as informative.

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Ole Sigmund, Denmark Technical University

Title: TBA

Abstract: TBA

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Natasha Smith, University of Utah

Title: Computational Topology and Geometry of Arctic Melt Ponds

Abstract: Melt ponds on the surface of Arctic sea ice form a critical component of the polar marine environment. Understanding their evolution is essential for modeling and predicting ice pack dynamics. We use topological data analysis to characterize the geometric and connectivity properties of melt pond networks. By looking at the relationship between fractal dimension and area fraction, scaling laws that mirror those found in three-dimensional, millimeter-scale brine inclusions are detected, suggesting a common geometric framework across scales. Using skeletonization to compute the Euler characteristic curve, we further quantify topological phase changes and provide insight into melt pond evolution. Persistent homology is used as another tool to study the fractal dimension and intrinsic topological features of evolving melt ponds. The similarities in topological and geometric descriptors across different types of sea ice structures suggest that they capture fundamental characteristics of sea ice morphology.

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Knut Solna, University of California Irvine

Title: Scattering by a rough surface and source imaging.

Abstract: We consider a situation with imaging of a source hidden behind a complex medium section. It is a classic observation that the resolution then depends on the position of the section. This is the so called ‘shower curtain effect’ and the problem has been analyzed in the context of bulk scattering before. Here we present recent results when we model with a rough interface.

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Kerrek Stinson, University of Utah

Title: Crack propagation for linear elastic materials with non-interpenetration

Abstract: Non-interpenetration prevents two materials from occupying the same space at the same time. In the context of fracture, non-interpenetration accounts for the dramatically different behavior of material under compression or tension, where only the latter should lead to material failure. Despite the ubiquity of such constraints in practice, there are limited analytical results justifying variational models incorporating non-interpenetration. In this talk, we discuss a recent work providing existence of solutions for models of crack growth with non-interpenetration.

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Zhaosen (Tim) Su, University of Utah

Title: Boundary integral formulation for electromagnetic homogenization problems in composites

Abstract: The interaction of electromagnetic waves with composite materials is a fundamental problem that arises in many areas of application. Understanding how waves propagate in such media is crucial for characterizing microstructures and determining their key transport properties. In this talk, we focus on the effective complex permittivity of two-phase composites. We will briefly review the classical Stieltjes integral representation for the effective permittivity and rigorously demonstrate its connection to the Neumann-Poincaré operator in potential theory. Based on this connection, we introduce a fast, accurate method using integral equations to compute the spectrum of the linear operator at the heart of the Stieltjes representation for the effective permittivity function. We provide an analytical formula for the branch-cut intervals of this function for media whose inclusions are bounded by general curvilinear polygons in 2D.

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Holly VanLooy, University of Utah

Title: Active Exterior Cloaking of Microswimmers in Stokes Flow

Abstract: At low Reynolds number, microswimmers generate long-range hydrodynamic disturbances which can be used for active cloaking, i.e. concealing other swimmers via the constructive and destructive interference of their velocity fields. We investigate numerically the design of swimmer formations that minimize the resulting far-field flow while simultaneously maintaining a given flocking configuration. This is done by solving an optimization problem for the strengths and orientations that minimize the disturbing velocity. We examine the tradeoff between hydrodynamic cloaking performance and the geometric requirements of maintaining a flocking formation, demonstrating how swimmer placement and orientation influence the achievable level of cloaking.

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Robert Viator, Denison University

Title: High Frequency Analysis of Electromagnetic Metamaterials

Abstract: We investigate the Bloch spectrum for transverse electric (TE) modes in a 2D high-contrast dielectric metamaterial. Our analysis focuses on the high-frequency regime where the propagating wavelength is commensurate with the microstructural period $d$, and the permittivity within the inclusions scales as $d^{-2}$. Using operator factorization and Sobolev space decomposition, we demonstrate that Bloch eigenvalues $\omega^2$ can be analytically continued and represented as a power series in $d^2$. We establish a rigorous upper bound on the microstructural length scale $d$, defined by the inclusion geometry, under which this expansion remains valid. Furthermore, we provide a definitive proof for the opening of band gaps in the frequency spectrum for all periods below a critical length scale. The threshold is explicitly characterized as a geometric function determined by the interaction between Dirichlet eigenvalues and the spectrum of the associated Neumann-Poincaré operator.

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Laurel Weber, University of Utah

Title: Randomized Kaczmarz for Reduced-Channel Neonatal EEG Analysis

Abstract: Neonatal seizures are the most common neurological emergency in newborns and frequently present without visible convulsions. Thus continuous electroencephalogram (EEG) is the only reliable detection method. Due to the small size of the neonatal skull, clinicians must use few as nine electrodes, producing more unknown source dipoles than the number of sensor measurements. Therefore, localizing seizures in neonates is a severely underdetermined inverse problem. To address this, I exploit two neonatal, neurobiological phenomena: (1) the dramatic channel reduction relative to research-grade EEG, and (2) the exclusively focal character of neonatal ictal activity. We use a joint Multiple Measurement Vector (MMV) encoding, and Sparse Randomized Kaczmarz (SRK) to recover the support. The former encodes the seizure focus, and the latter iteratively recovers this support via randomized row projections paired with a hard-thresholding step. This achieves exponential convergence in expectation with no matrix inversions required. Further, this algorithm is ideal as the streaming structure is compatible with online NICU monitoring via warm-started window-to-window estimation. To evaluate this algorithm, we implement MMV-SRK on continuous EEG recordings from 31 neonates at the University of Utah Pediatric Neurology Department, subsampled to four, eight, and thirteen channels. Each neonate carries a clinical outcome label, enabling assessment of whether recovered source features discriminate good from poor outcomes. Preliminary results suggest clinically meaningful signal is recoverable from as few as eight channels, and that this recovered support could be used downstream in machine-learning based prediction models.

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Michael I. Weinstein, Columbia University

Title: Waves and spectral degeneracy

Abstract: Degeneracies in the spectra of operators are associated with many novel wave phenomena. I’ll discuss this for some continuum and discrete models of quantum materials and meta-materials.

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Aaron Welters, Florida Tech

Title: TBA

Abstract: TBA

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