• Speaker: Alberto Takase, MSU
• Title: The Integrated Density of States and the Gap Labeling Theorem via "K-Theory"
• Date: 12/05/2022
• Time: 4:00 PM - 5:30 PM
• Place: C517 Wells Hall
• Contact: Brent Nelson (banelson@msu.edu)

My talk will be about the Integrated Density of States and the Gap Labeling Theorem via "K-Theory". The primary source is Bellissard, Jean; Bovier, Anton; Ghez, Jean-Michel \textit{Gap labelling theorems for one-dimensional discrete Schrödinger operators}. Rev. Math. Phys. 4 (1992), no. 1, 1–37.

• Speaker: Ekaterina Shchetka, University of Michigan
• Title: Semiclassical analysis and spectrum of Harper operator
• Date: 12/06/2022
• Time: 11:00 AM - 12:00 PM
• Place: C304 Wells Hall
• Contact: Ilya Kachkovskiy (ikachkov@msu.edu)

In this talk we’ll discuss semiclassical analysis of difference operators in the complex plane via complex WKB method. As application the method can be used to study the spectrum of Harper operator (a.k.a. almost Mathieu operator, or Hofstadter model).

• Speaker:  Yuping Ruan, University of Michigan
• Title: Boundary rigidity and filling minimality via the barycenter method
• Date: 12/06/2022
• Time: 2:00 PM - 3:00 PM
• Place: A106 Wells Hall
• Contact: Fan Yang (yangfa31@msu.edu)

A compact manifold with a smooth boundary is boundary rigid if its boundary and boundary distance function uniquely determine its interior up to boundary preserving isometries. Under certain natural conditions, the notion of boundary rigidity is closely related to Gromov's filling minimality. In this talk, we will first give a brief overview of Burago-Ivanov's approach to prove filling minimality and boundary rigidity for almost Euclidean and almost real hyperbolic metrics. Then we will explain how we generalize their results to regions in a rank-1 symmetric space equipped with an almost symmetric metric. We will also explain the relations to Besson-Courtois-Gallot's barycenter constructions used in their celebrated volume entropy rigidity theorem.

• Speaker: Cameron Gates Rudd, Max Planck Institute, Bonn
• Title: Untriangulating knots
• Date: 12/06/2022
• Time: 3:00 PM - 4:00 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Vijay B Higgins (higgi231@msu.edu)

Knots are determined by their exteriors and producing a triangulation of the exterior given a knot diagram is computationally simple. Taking a three manifold that is a knot exterior however, and turning it into a knot diagram is not. I will discuss a practical algorithm for finding a diagram of a knot, given a triangulation of its exterior. Our method, when given a little bit of extra data, applies to links as well as knots, and allows us to recover links with hundreds of crossings. This is joint work with Nathan Dunfield and Malik Obeidin.

• Speaker: Jinting Liang, Michigan State University
• Title: Enriched toric $[\vec{D}]$-partitions
• Date: 12/07/2022
• Time: 3:00 PM - 3:50 PM
• Place: Online (virtual meeting) (Virtual Meeting Link)
• Contact: Bruce E Sagan (bsagan@msu.edu)

In this talk I will discuss the theory of enriched toric $[\vec{D}]$-partitions. Whereas Stembridge's enriched $P$-partitions give rises to the peak algebra which is a subring of the ring of quasi-symmetric functions QSym, our enriched toric $[\vec{D}]$-partitions will generate the cyclic peak algebra which is a subring of cyclic quasi-symmetric functions cQSym. In the same manner as the peak set of linear permutations appears when considering enriched $P$-partitions, the cyclic peak set of cyclic permutations plays an important role in our theory.

• Speaker: Hassan Allouba, Kent State University
• Title: Well-posedness for the Kuramoto-Sivashinsky equation until the 6p-th dimension
• Date: 12/07/2022
• Time: 3:00 PM - 3:50 PM
• Place: C405 Wells Hall
• Contact: Dapeng Zhan (zhan@msu.edu)

Lately, I’ve been finalizing a couple of papers on the local and global analysis of the KS PDE in multidimensional space. This includes the well known open problem of the global well-posedness of KS for d ≥ 1. In this talk, I will discuss my Brownian-time (or L-KS kernel) approach to the Burgers incarnation of the KS equation for all dimensions. This yields a new formulation for the KS equation (deterministic or stochastic), even in the better known one dimensional case. I will then focus on my latest results on the uniqueness and local well-posedness of the KS PDE for d ≥ 1. In particular, I’ll show—using careful estimates on the fundamental L-KS kernel—the existence of $L^{2p}$ solution, locally in time, till the 6p-th dimension, as well as the global uniqueness of KS solutions. Since this Brownian-time setting includes time fractional equations, I will briefly mention the corresponding results for time-fractional Burgers equations in multidimensional space—which I’m also finalizing in separate papers. The rest of the global well-posedness results (existence and more) use additional new tools, some of which are inspired in part by my earlier work on Brownian-time processes and L-KS equations; and I plan to discuss this in the near future. This work—both local and global—is at the heart of other work on the delicate path properties of the SPDEs version of the KS and time-fractional Burgers equations, currently under investigation with Yimin Xiao.

• Speaker: Rongjie Lai , Rensselaer Polytechnic Institute
• Title: 1W-MINDS talk (passcode is the first prime number > 100).
• Date: 12/08/2022
• Time: 2:30 PM - 3:30 PM
• Place: Online (virtual meeting)
• Contact: Mark A Iwen ()

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