• Speaker: Cullen Haselby, MSU
• Title: Efficient Modewise Measurements for Compressive Sensing or Recovery of Tensor Data
• Date: 10/10/2022
• Time: 1:00 PM - 2:00 PM
• Place: C117 Wells Hall (Virtual Meeting Link)
• Contact: Craig Gross (grosscra@msu.edu)

Recovery of sparse vectors and low-rank matrices from a small number of linear measurements is well-known to be possible under various model assumptions on the measurements. The key requirement on the measurement matrices is typically the restricted isometry property, that is, approximate orthonormality when acting on the subspace to be recovered. Among the most widely used random matrix measurement models are (a) independent subgaussian models and (b) randomized Fourier-based models, allowing for the efficient computation of the measurements. $\\$ For the now ubiquitous tensor data, direct application of the known recovery algorithms to the vectorized or matricized tensor is memory-heavy because of the huge measurement matrices to be constructed and stored. In this talk, we will discuss two different modewise measurement schemes and related recovery algorithms. These modewise operators act on the pairs or other small subsets of the tensor modes separately. They require significantly less memory than the measurements working on the vectorized tensor, and experimentally can recover the tensor data from fewer measurements and do not require impractical storage. $\\$ This will be a hybrid seminar and take place in C117 Wells Hall and via Zoom at https://msu.zoom.us/j/99426648081?pwd=ZEljM3BPUXg2MjVUMVM5TnlzK2NQZz09 .

• Speaker: Vijay Higgins, Michigan State University
• Title: Sp(4) stated skein algebras
• Date: 10/10/2022
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall
• Contact: Linhui Shen (shenlin1@msu.edu)

Skein algebras are spanned by webs or links in a thickened surface subject to skein relations. When the skein relations are the Kauffman bracket relations associated to SL(2), they provide a diagrammatic way to encode cluster algebras, as shown by Muller, and also quantum groups, as shown by Costantino and Le. In this talk, we will explore a construction of a basis for the stated skein algebra for Sp(4) which is built from Kuperberg's web relations along with extra skein relations along the boundary of the surface. We will use the basis to obtain results about the structure of the skein algebra, relating it to the quantum group associated to Sp(4). We will also recover Kuperberg's result about the Sp(4) web category.

• Speaker: Pavel Čoupek, MSU
• Title: Ramification bounds for mod p étale cohomology via prismatic cohomology
• Date: 10/10/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall
• Contact: Preston Wake (wakepres@msu.edu)

Let $K/\bf{Q}_p$ be a local number field of absolute ramification index $e$, and let $X$ be a proper smooth $O_K$-scheme. I will discuss how one can obtain bounds on ramification of the mod $p$ Galois representations arising as the étale cohomology of (the geometric generic fiber of) $X$ in terms of $e$, the given prime $p>2$ and the cohomological degree $i$. The key tools for achieving this are the Breuil-Kisin and $A_{\rm inf}$-cohomology theories of Bhatt, Morrow and Scholze, and a series of conditions based on a criterion of Gee and Liu regarding crystallinity of the representation attached to a free Breuil-Kisin-Fargues $G_K$-module.

• Speaker: Lucas Hall, MSU
• Title: Graph algebras: universality, uniqueness, and ideal structure
• Date: 10/10/2022
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

We illustrate various aspects of graph algebras introduced last week, including usage of the universal property, aspects of their representation theory, and ideals, pointing to relationships with the structure of the underlying graph.

• Speaker: Jacob Gloe, MSU
• Title: Diffusion for a Quantum Particle in a Lindbladian Environment with a Periodic Hamiltonian
• Date: 10/11/2022
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall
• Contact: Jeffrey Hudson Schenker (schenke6@msu.edu)

A quantum particle restricted to a lattice of points has been well studied in many different contexts. In the absence of disorder or environmental interaction, the particle simply undergoes ballistic transport for many suitable Hamiltonian operators. Recently, progress has been made on introducing a Lindbladian interaction term to the model, which drastically changes the dynamics in the large time limit. We prove that indeed diffusion is present in this context for an arbitrary periodic Hamiltonian. Additionally, we show that the diffusion constant is inversely proportional to the particles' coupling strength with its environment.

• Speaker: Daniel Douglas, Yale
• Title: Dimers, webs, and local systems
• Date: 10/11/2022
• Time: 3:00 PM - 4:00 PM
• Place: C304 Wells Hall (Virtual Meeting Link)
• Contact: Vijay B Higgins (higgi231@msu.edu)

For a planar bipartite graph G equipped with a SLn-local system, we show that the determinant of the associated Kasteleyn matrix counts “n-multiwebs” (generalizations of n-webs) in G, weighted by their web-traces. We use this fact to study random n-multiwebs in graphs on some simple surfaces. Time permitting, we will discuss some relations to Fock-Goncharov theory. This is joint work with Rick Kenyon and Haolin Shi.

• Speaker: Stan Halstead
• Title: Cycles and the Chow Ring
• Date: 10/11/2022
• Time: 4:30 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: Ivan So ()

Intersections between varieties and subschemes can result in structures with many varying dimensions, which naturally leads us to consider something like a homology structure. The non-Hausdorff nature of the Zariski topology limits our ability to utilize algebraic topology, so we must first define cycles, the formal sum of subvarieties, to get something we can work with.

• Speaker: Dustin Mixon, Ohio State University
• Title: 1W-MINDS talk (passcode is the first prime number > 100).
• Date: 10/13/2022
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Mark A Iwen (iwenmark@msu.edu)

See https://sites.google.com/view/minds-seminar/home

• Speaker: Patricia Hersh, University of Oregon
• Title: Generalized recursive atom ordering and equivalence to CL-shellability
• Date: 10/13/2022
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

When Björner and Wachs introduced one of the main forms of lexicographic shellability, namely CL-shellability, they also introduced the notion of recursive atom ordering, and they proved that a finite bounded poset is CL-shellable if and only if it admits a recursive atom ordering. We generalize the notion of recursive atom ordering, and we prove that any such generalized recursive atom ordering may be transformed via a reordering process into a recursive atom ordering. We also prove that a finite bounded poset admits a generalized recursive atom ordering if and only if it is ``CC-shellable'' by way of a CC-labeling which is self-consistent in a certain sense. This allows us to conclude that CL-shellability is equivalent to self-consistent CC-shellability. As an application, we prove that the uncrossing orders, namely the face posets for stratified spaces of planar electrical networks, are dual CL-shellable. During this talk, we will review plenty of background on poset topology and specifically regarding the technique of lexicographic shellability. This is joint work with Grace Stadnyk

• Speaker: Sgallova Ester , MSU
• Title: Eigenalgebra
• Date: 10/13/2022
• Time: 3:00 PM - 4:00 PM
• Place: C204A Wells Hall
• Contact: Peikai Qi (qipeikai@msu.edu)

Eigenalgebra is a construction attaching to a family of commuting operators acting on some space or module that parameterizes the system of eigenvalue for some operators.