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Applied Mathematics
- Zhaoran Wang, Northwestern University
- 1W-MINDS talk (passcode is the first prime number > 100).
- 12/01/2022
- 2:30 PM - 3:30 PM
- Online (virtual meeting)
- Mark A Iwen ()
See https://sites.google.com/view/minds-seminar/home
Student Number Theory
- Peikai Qi, MSU
- Classic modular symbol over complex field
- 12/01/2022
- 3:00 PM - 4:00 PM
- C204A Wells Hall
- Peikai Qi (qipeikai@msu.edu)
We will move from the classic modular symbol form to modular symbol over complex field. And we will use a lot of theorem from previous chapter as black box.
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Special Colloquium
- Our undergraduate research teams!
- Exchange Program REU Final Presentations
- 12/02/2022
- 6:30 PM - 9:45 PM
- C304 Wells Hall
(Virtual Meeting Link)
- Jeanne Wald (wald@msu.edu)
Linked Abstract
Exchange Program REU Final Presentations
Speakers: Our undergraduate research teams!
Title: See the program, which includes descriptions of the research projects
Date: Friday December 2, 2022
Time: 6:30 p.m. – 9:45 p.m.
https://msu.zoom.us/j/92801969144
Meeting ID: 928 0196 9144
Passcode: 112358
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Operator Algebras Reading
- Alberto Takase, MSU
- The Integrated Density of States and the Gap Labeling Theorem via "K-Theory"
- 12/05/2022
- 4:00 PM - 5:30 PM
- C517 Wells Hall
- 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.
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Mathematical Physics and Operator Algebras
- Ekaterina Shchetka, University of Michigan
- Semiclassical analysis and spectrum of Harper operator
- 12/06/2022
- 11:00 AM - 12:00 PM
- C304 Wells Hall
- 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).
Dynamical Systems
- Yuping Ruan, University of Michigan
- Boundary rigidity and filling minimality via the barycenter method
- 12/06/2022
- 2:00 PM - 3:00 PM
- A106 Wells Hall
- 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.
Geometry and Topology
- Cameron Gates Rudd, Max Planck Institute, Bonn
- Untriangulating knots
- 12/06/2022
- 3:00 PM - 4:00 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- 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.
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Combinatorics and Graph Theory
- Jinting Liang, Michigan State University
- Enriched toric $[\vec{D}]$-partitions
- 12/07/2022
- 3:00 PM - 3:50 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- 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.
Probability
- Hassan Allouba, Kent State University
- Well-posedness for the Kuramoto-Sivashinsky equation until the 6p-th dimension
- 12/07/2022
- 3:00 PM - 3:50 PM
- C405 Wells Hall
- 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.
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Applied Mathematics
- Rongjie Lai , Rensselaer Polytechnic Institute
- 1W-MINDS talk (passcode is the first prime number > 100).
- 12/08/2022
- 2:30 PM - 3:30 PM
- Online (virtual meeting)
- Mark A Iwen ()
See https://sites.google.com/view/minds-seminar/home
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Mathematical Physics and Operator Algebras
- Renaud Requipas, NYU
- Estimation of entropy production on the one-sided shift
- 12/12/2022
- 11:00 AM - 12:00 PM
- C304 Wells Hall
- Jeffrey Hudson Schenker (schenke6@msu.edu)
Using repeated quantum measurements as a guiding physical example, I will introduce the notion of entropy production for invariant measures on the one-sided shift. Then, I will present recent results on a related estimation problem. Informally, this is an attempt at answering the following question: does a typical sequence of outcomes carry a signature of the irreversibility of the stochastic process generating those outcomes?
This is based on joint works (some still in progress) with G. Cristadoro, N. Cunéo, M. Degli Esposti and V. Jaksic.
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Probability
- Adrián Hinojosa-Calleja, University of Barcelona
- Hitting probabilities and exact modulus of continuity for q-isotropic Gaussian random fields
- 12/14/2022
- 3:00 PM - 3:50 PM
- Online (virtual meeting)
(Virtual Meeting Link)
- Dapeng Zhan (zhan@msu.edu)
A Gaussian random field is q-isotropic if its associated canonical metric is equivalent to a gauge function q. We develop criteria for hitting probabilities and the existence of a global exact modulus of continuity for such processes. We explore the applications of the criteria to two toy examples: The q-Brownian sheet, and the solution to the linear stochastic Poisson equation driven by white noise. This is joint work with Marta Sanz-Solé.
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Dynamical Systems
- Jing Zhou, Penn State University
- Application of KAM Theory in the Fermi-Ulam Models
- 12/16/2022
- 2:00 PM - 3:00 PM
- C304 Wells Hall
- Huyi Hu (hhu@msu.edu)
In this talk I’ll brief introduce the Fermi acceleration problem and some existing results on the subject. In particular, I’ll discuss how KAM theory has been applied in several variants of the Fermi-Ulam models. I’ll also discuss some open problems in this direction.
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