Calendar

Posted January 12, 2026
Last modified March 15, 2026

Applied Analysis Seminar Questions or comments?

Daniel Massatt, New Jersey Institute of Technology
Momentum Space Algorithm for Electronic Structure of Double-Incommensurate Trilayer Graphene

Moiré 2D materials are highly tunable through variables including twist angle, species of layers, and number of layers. Various configurations lead to useful physical phenomena and possible applications, including many-body physics such as correlated insulators and superconductivity. To understand many-body models, a careful single-particle model must first be constructed. For example in twisted bilayer graphene, the Bistritzer-MacDonald model is frequently used to capture magic-angle physics in twisted bilayer graphene. More complex geometries including double-incommensurate trilayers however become difficult to accurately quantify even in the single-particle regime. Here we present a momentum space algorithm for computing observables for double-incommensurate trilayers with rigorous error analysis compared to the real space tight-binding model. We include the closest equivalent observable to band structure that this structure seems to admits called the momentum local density of states, revealing the spectral features not captured by rougher models.

Event contact: Stephen Shipman

Posted November 15, 2025
Last modified January 21, 2026

Algebra and Number Theory Seminar Questions or comments?

Kiran Kedlaya, University of California San Diego
TBA

Event contact: Gene Kopp

Posted March 5, 2026
Last modified March 9, 2026

Informal Analysis Seminar Questions or comments?

Long Teng, LSU
Doubling Inequalities for Schrodinger operators with power growth potentials

TBD

Posted January 15, 2026

Informal Geometry and Topology Seminar Questions or comments?

Sayani Mukherjee, Louisiana State University
TBD

TBD

Posted December 1, 2025
Last modified March 5, 2026

Control and Optimization Seminar Questions or comments?

Khai Nguyen, North Carolina State University
On the Structure of Viscosity Solutions to Hamilton–Jacobi Equations

This talk presents regularity results for viscosity solutions to a class of Hamilton-Jacobi equations arising from optimal exit-time problems in nonlinear control systems under a weak controllability condition. A representation formula for proximal supergradients, based on transported normals, is derived, with applications to optimality conditions, the propagation of singularities, and the Hausdorff measure of the singular set.

Posted January 11, 2026
Last modified March 6, 2026

Applied Analysis Seminar Questions or comments?

Zhiyuan Geng, Purdue University
Asymptotics for 2D vector-valued Allen-Cahn minimizers

For the scalar two-phase (elliptic) Allen–Cahn equation, there is a rich literature on the celebrated De Giorgi conjecture, which reveals deep connections between diffuse interfaces and minimal surfaces. On the other hand, for three or more equally preferred phases, a vector-valued order parameter is required, and the resulting diffuse interfaces are expected to resemble weighted minimal partitions. In this talk, I will present recent results on minimizers of a two-dimensional Allen–Cahn system with a multi-well potential. We describe the asymptotic behavior near the junction of three phases by analyzing the blow-up limit, which is a global minimizing solution converging at infinity to a Y-shaped minimal cone. A key ingredient in our approach is the derivation of sharp upper and lower energy bounds via a slicing argument, which allows us to localize the diffuse interface within a small neighborhood of the sharp interface. As a consequence, we obtain a complete classification of global two-dimensional minimizers in terms of their blow-down limits at infinity. This is joint work with Nicholas Alikakos.