Posted December 5, 2024
Last modified January 22, 2025
Colloquium Questions or comments?
3:30 pm Lockett 232
Ken Ono, University of Virginia
Partitions detect primes
This talk presents “partition theoretic” analogs of the classical work of Matiyasevich that resolved Hilbert’s Tenth Problem in the negative. The Diophantine equations we consider involve equations of MacMahon’s partition functions and their natural generalizations. Here we explicitly construct infinitely many Diophantine equations in partition functions whose solutions are precisely the prime numbers. To this end, we produce explicit additive bases of all graded weights of quasimodular forms, which is of independent interest with many further applications. This is joint work with Will Craig and Jan-Willem van Ittersum.
Posted December 6, 2024
Last modified January 2, 2025
Control and Optimization Seminar Questions or comments?
11:30 am – 12:20 pm Zoom (click here to join)
Harbir Antil, George Mason University
Optimization and Digital Twins
With recent advancements in computing resources and interdisciplinary collaborations, a new research field called Digital Twins (DTs) is starting to emerge. Data from sensors located on a physical system is fed into its DT, the DT in turn help make decisions about the physical system. This cycle then continues for the life-time of the physical system. A typical example is for instance a bridge. In many cases, these problems can be cast as optimization problems with finite or infinite dimensional (partial differential equations) constraints. This talk will provide an introduction to this topic. Special attention will be given to: 1) Optimization algorithms that are adaptive and can handle inexactness, e.g., Trust- Regions and ALESQP; 2) Optimization under uncertainty and tensor train decomposition to overcome the curse of dimensionality; 3) Reduced order modeling for dynamic optimization using randomized compression. Additionally, the DT framework may require coupling mutiphysics / systems / data with very different time scales. Keeping this in mind, a newly introduced notion of barely coupled problems will be discussed. Realistic examples of DTs to identify weakness in structures such as bridges, wind turbines, electric motors, and neuromorphic imaging will be considered.
Posted January 21, 2025
Combinatorics Seminar Questions or comments?
1:30 pm – 2:30 pm Lockett Hall 233
Avin Sunuwar, LSU
Chain theorems on 3-connected graphs
Chain theorems provide a pathway in constructing and analyzing families of graphs. In this seminar, we explore improvements in chain theorems for 3-connected graphs and their subclasses. We discuss an improved version of Tutte’s Wheel Theorem, which enhances algorithmic efficiency by limiting the construction process to extensions of the wheel W4 with restricted operations. Then, we discuss a chain theorem for smoothly 3-connected graphs. Additionally, we present a chain theorem for rooted graphs. These results not only refine classical theorems but also pave the way for further advancements in graph theory and its applications.
Posted January 28, 2025
Colloquium Questions or comments?
3:30 pm – 4:30 pm Lockett 232
Federico Glaudo, Institute for Advanced Study, Princeton
A Journey through PDEs and Geometry
This talk will explore a range of intriguing questions that lie at the crossroads of partial differential equations and geometry. Topics include the stability of near-solutions to PDEs, the isoperimetric inequalities on curved spaces, as well as the random matching problem. The aim is to make the ideas accessible and engaging for a broad mathematical audience.
Posted January 23, 2025
Last modified January 27, 2025
Geometry and Topology Seminar Seminar website
3:30 pm Lockett 233
Matthew Stoffregen, Michigan State University
Pin(2) Floer homology and the Rokhlin invariant
In this talk, we describe a family of homology cobordism invariants that can be extracted from Pin(2)-equivariant monopole Floer homology (using either Manolescu or Lin's definitions), that have some properties in common with both the epsilon and upsilon invariants in knot Floer homology. We'll show a relationship of this family to questions about torsion in the homology cobordism group, and to triangulation of higher-dimensional manifolds. This is joint work in progress with Irving Dai, Jen Hom, and Linh Truong.