Talk_id  Date  Speaker  Title 
29362

Tuesday 5/10 2:00 PM

Fan Yang, Michigan State University

Uniqueness of equilibrium state for Lorenz attractors (cont'd)
 Fan Yang, Michigan State University
 Uniqueness of equilibrium state for Lorenz attractors (cont'd)
 05/10/2022
 2:00 PM  3:00 PM
 C517 Wells Hall
 Huyi Hu (hhu@msu.edu)
In this talk, we will introduce the ClimenhagaThompson criterion for the existence and uniqueness of equilibriums state and use it to prove that every Lorenz attractor supports a unique equilibrium state for (almost) every Holder continuous potential.

29340

Thursday 5/12 2:30 PM

Pablo Groisman, Universidad de Buenos Aires

Learning distances to learn topologies, to learn dynamical systems, to learn from chaos.
 Pablo Groisman, Universidad de Buenos Aires
 Learning distances to learn topologies, to learn dynamical systems, to learn from chaos.
 05/12/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Consider a finite sample of points on a manifold embedded in Euclidean space. We'll address the following issues.
1. How we can infer, from the sample, intrinsic distances that are meaningful to understand the data.
2. How we can use these estimated distances to infer the geometry and topology of the manifold (manifold learning).
3. How we can use this knowledge to validate dynamical systems models for chaotic phenomena.
4. Time permitting, we will show applications of this machinery to understand data from the production of songs in canaries.
We will prove that if the sample is given by iid points with density f supported on the manifold, the metric space defined by the sample endowed with a computable metric known as sample Fermat distance converges in the sense of Gromov–Hausdorff. The limiting object is the manifold itself endowed with the population Fermat distance, an intrinsic metric that accounts for both the geometry of the manifold and the density that produces the sample. Then we'll apply this result to estimate the topology of the manifold by constructing intrinsic persistence diagrams (an estimator of the homology of the manifold), which are less sensitive to the particular embedding of the manifold in the Euclidean space and to outliers. We'll also discuss how to use these tools to validate (or to refute) models for chaotic dynamical systems, with applications to the study of birdsongs.

29363

Tuesday 5/17 2:00 PM

Fan Yang, Michigan State University

Uniqueness of equilibrium state for Lorenz attractors (cont'd)
 Fan Yang, Michigan State University
 Uniqueness of equilibrium state for Lorenz attractors (cont'd)
 05/17/2022
 2:00 PM  3:00 PM
 C304 Wells Hall
 Huyi Hu (hhu@msu.edu)
In this talk, we will introduce the ClimenhagaThompson criterion for the existence and uniqueness of equilibriums state and use it to prove that every Lorenz attractor supports a unique equilibrium state for (almost) every Holder continuous potential.

29364

Tuesday 5/24 2:00 PM

Zhenqi Wang, Michigan State University

Smooth local rigidity for hyperbolic toral automorphisms
 Zhenqi Wang, Michigan State University
 Smooth local rigidity for hyperbolic toral automorphisms
 05/24/2022
 2:00 PM  3:00 PM
 C304 Wells Hall
 Huyi Hu (hhu@msu.edu)
We study the regularity of a conjugacy $H$ between a hyperbolic toral automorphism $A$ and its
smooth perturbation $f$. We show that if $H$ is weakly differentiable then it is $C^{1+\text{Holder}}$ and, if $A$ is also weakly irreducible, then $H$ is $C^\infty$. As a part of the proof, we establish results of independent interest on Holder continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve
regularity of the conjugacy to $C^\infty$ in prior local rigidity results. This is a joint work with B. Kalinin an V. Sadovskaya

29365

Wednesday 5/25 3:00 PM

Angela Wu, Louisiana State

Obstructing Lagrangian concordance
 Angela Wu, Louisiana State
 Obstructing Lagrangian concordance
 05/25/2022
 3:00 PM  4:00 PM
 C304 Wells Hall
(Virtual Meeting Link)
 Honghao Gao (gaohongh@msu.edu)
Two knots are said to be concordant if they jointly form the boundary of a cylinder in fourdimensional Euclidean space. In the symplectic setting, we say they are Lagrangian concordant if the knots are Legendrian and the cylinder is Lagrangian. We can ask: what Legendrian knots can be both concordant to and from the unstabilized Legendrian unknot? In this talk I'll explain a strategy that can be used to obstruct many knots from this double concordance.

29355

Thursday 5/26 2:30 PM

Selin Aviyente, Michigan State University

Multiview Graph Learning
 Selin Aviyente, Michigan State University
 Multiview Graph Learning
 05/26/2022
 2:30 PM  3:30 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Modern data analysis involves large sets of structured data, where the structure carries critical information about the nature of the data. These relationships between entities, such as features or data samples, are usually described by a graph structure. While many realworld data are intrinsically graphstructured, e.g. social and traffic networks, there is still a large number of applications, where the graph topology is not readily available. For instance, gene regulations in biological applications or neuronal connections in the brain are not known. In these applications, the graphs need to be learned since they reveal the relational structure and may assist in a variety of learning tasks. Graph learning (GL) deals with the inference of a topological structure among entities from a set of observations on these entities, i.e., graph signals. Most of the existing work on graph learning focuses on learning a single graph structure, assuming that the relations between the observed data samples are homogeneous. However, in many realworld applications, there are different forms of interactions between data samples, such as singlecell RNA sequencing (scRNAseq) across multiple cell types. This talk will present a new framework for multiview graph learning in two settings: i) multiple views of the same data and ii) heterogeneous data with unknown cluster information. In the first case, a joint learning approach where both individual graphs and a consensus graph are learned will be developed. In the second case, a unified framework that merges classical spectral clustering with graph signal smoothness will be developed for joint clustering and multiview graph learning.
This is joint work with Abdullah Karaaslanli, Satabdi Saha and Taps Maiti.

29356

Thursday 6/2 4:30 AM

Florian Boßmann, Harbin Institute of Technology

Beyond SVD  two new adaptive models for moving objects
 Florian Boßmann, Harbin Institute of Technology
 Beyond SVD  two new adaptive models for moving objects
 06/02/2022
 4:30 AM  5:30 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Many data processing techniques treat the given data as union of its coefficients. Sparse transformations like Wavelets, Curvelets, Shearlets, etc. transform the data from one coefficient space into another. Inverse transforms used in MRI, CT, inverse scattering, map the measured data back onto a pixel image. Only in a second step, the obtained result is analyzed to extract the desired information. Although the above mentioned methods perform excellent for their designed task, the overall process is still a two step method. Moreover, the intermediate step often seems to arti cially increase the problem size. Do we really need to solve the complete inverse problem, when in the end only a small part contains the information of interest? Exemplary, do we need to reconstruct the full velocity field of seismic waves, when we are only interested in detecting subsurface material boundaries?
We think that instead of viewing data as union of its coefficients, we should see data as union of its information. As the amount of information required is often much smaller than the data size, this already gives implicit sparsity. In many cases the information is directly bounded to an object contained in the data. For example, each car in a video recorded by a traffic camera carries information about the traffic status. A seismic wave in geophysical data carries information about the subsurface conditions. We want to give those physical objects a mathematical model, such that the data can be mapped into the model space where the information can directly be extracted. Some techniques already use this, or a similar approach. For example, a neural network can be trained as classi er to directly extract information out of the data. This technique requires a lot of training data and is not feasible for all applications. Singular value decomposition (SVD) or Principal Component Analysis (PCA) can also been interpreted as such object orientated method. Applying a SVD to video data will return the video background as largest singular vector as long as the camera is not moving. However, the SVD struggles whenever objects in the video are moving. We present two extensions of SVD that are designed to recover moving objects in the data (not only in video data, but also other applications). The first apporach is the so called shifted rank1 model which allows object movement. The second approach  ORKA  extends this model by allowing the objects to also change form and restricting their movement to a smooth path. (joint work with Jianwei Ma)
References:
[1] F. Bo mann, J. Ma, Enhanced image approximation using shifted rank1 reconstruction. Inverse Problems and Imaging, 14 (2), 267290, 2020.
[2] F. Bo mann, J. Ma, ORKA: Object reconstruction using a Kapproximation graph, submitted, available on ArXiv, 2022.

29366

Tuesday 6/7 2:00 PM

Zhenqi Wang, Michigan State University

Smooth local rigidity for hyperbolic toral automorphisms
 Zhenqi Wang, Michigan State University
 Smooth local rigidity for hyperbolic toral automorphisms
 06/07/2022
 2:00 PM  3:00 PM
 C304 Wells Hall
 Huyi Hu (hhu@msu.edu)
We study the regularity of a conjugacy $H$ between a hyperbolic toral automorphism $A$ and its
smooth perturbation $f$. We show that if $H$ is weakly differentiable then it is $C^{1+\text{Holder}}$ and, if $A$ is also weakly irreducible, then $H$ is $C^\infty$. As a part of the proof, we establish results of independent interest on Holder continuity of a measurable conjugacy between linear cocycles over a hyperbolic system. As a corollary, we improve
regularity of the conjugacy to $C^\infty$ in prior local rigidity results. This is a joint work with B. Kalinin an V. Sadovskaya.

29357

Thursday 6/9 4:30 AM

Fanny Yang, ETH Zurich

Fast rates for noisy interpolation require rethinking the effects of inductive bias
 Fanny Yang, ETH Zurich
 Fast rates for noisy interpolation require rethinking the effects of inductive bias
 06/09/2022
 4:30 AM  4:30 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova (turanova@msu.edu)
Modern machine learning has uncovered an interesting observation: large over parameterized models can achieve good generalization performance despite interpolating noisy training data. In this talk, we study highdimensional linear models and show how interpolators can achieve fast statistical rates when their structural bias is moderate. More concretely, while minimuml2norm interpolators cannot recover the signal in high dimensions, minimuml1interpolators with strong sparsity bias are much more sensitive to noise. In fact, we show that even though they are asymptotically consistent, minimuml1norm interpolators converge with a logarithmic rate much slower than the O(1/n) rate of regularized estimators. In contrast, minimumlpnorm interpolators with 1<p<2 can trade off these two competing trends to yield polynomial rates close to O(1/n).

29367

Tuesday 6/14 2:00 PM

Huyi Hu, Michigan State University

The SRB measures for pointwise hyperbolic systems on open regions
 Huyi Hu, Michigan State University
 The SRB measures for pointwise hyperbolic systems on open regions
 06/14/2022
 2:00 PM  3:00 PM
 C304 Wells Hall
 Huyi Hu (hhu@msu.edu)
A pointwise partially hyperbolic diffeomorphism is different from a partially hyperbolic one if the expansion and contraction depend on points. If the system is defined on an open set, then the hyperbolicity may not be uniform. We show that under certain conditions such a suystem has unstable and stable manifolds, and admits a finite or an infinite uGibbs measure. If the system is pointwise hyperbolic, then the uGibbs measure $\mu$ is an SinaiRuelleBowen (SRB) measure
or an infinite SRB measure. As applications, we show that some almost Anosov diffeomorphisms and gentle perturbations of Katok's map have the properties.

29368

Wednesday 7/6 2:00 PM

Huyi Hu, Michigan State University

The SRB measures for pointwise hyperbolic systems on open regions
 Huyi Hu, Michigan State University
 The SRB measures for pointwise hyperbolic systems on open regions
 07/06/2022
 2:00 PM  3:00 PM
 C304 Wells Hall
 Huyi Hu (hhu@msu.edu)
A pointwise partially hyperbolic diffeomorphism is different from a partially hyperbolic one if the expansion and contraction depend on points. If the system is defined on an open set, then the hyperbolicity may not be uniform. We show that under certain conditions such a suystem has unstable and stable manifolds, and admits a finite or an infinite uGibbs measure. If the system is pointwise hyperbolic, then the uGibbs measure
μ
is an SinaiRuelleBowen (SRB) measure or an infinite SRB measure. As applications, we show that some almost Anosov diffeomorphisms and gentle perturbations of Katok's map have the properties.

29369

Tuesday 7/12 2:00 PM

Fan Yang, Michigan State University

A dichotomy for generic star flows
 Fan Yang, Michigan State University
 A dichotomy for generic star flows
 07/12/2022
 2:00 PM  3:00 PM
 C304 Wells Hall
 Huyi Hu (hhu@msu.edu)
In this talk we will present some recent progress on the topological structure of the socalled star flows (flows whose critical elements, i.e., singularities and periodic orbits, are hyperbolic in a robust way). In particular, we will prove that for $C^1$ generic star flows, every chain recurrent class with positive topological entropy must be isolated. On the other hand, zero entropy chain recurrent classes only support trivial ergodic measures.

29370

Tuesday 7/19 2:00 PM

Jing Zhou, Penn State University

Uniqueness of equilibrium state for Lorenz attractors
 Jing Zhou, Penn State University
 Uniqueness of equilibrium state for Lorenz attractors
 07/19/2022
 2:00 PM  3:00 PM
 C304 Wells Hall
 Huyi Hu (hhu@msu.edu)
In this talk we show the existence of an infinite measure set of exponentially escaping orbits for a resonant Fermi accelerator, which is realized as a square billiard with a periodically oscillating platform. We use normal forms to describe the energy change in a period and employ techniques from the theory of hyperbolic systems with singularities to show the exponential drift given by these normal forms on a divided timeenergy phase.

29371

Monday 7/25 2:00 PM

Yun Yang, Virginia Tech

Entropy rigidity for 3D Anosov flows
 Yun Yang, Virginia Tech
 Entropy rigidity for 3D Anosov flows
 07/25/2022
 2:00 PM  3:00 PM
 C304 Wells Hall
 Huyi Hu (hhu@msu.edu)
Anosov systems are among the most wellunderstood dynamical systems.
Special among them are the {\bf algebraic systems}.
In the diffeomorphism case,
these are automorphisms of tori and nilmanifolds. In the
flow case, the algebraic
models are suspensions of such diffeomorphisms and geodesic flows on negatively
curved rank one symmetric spaces. In this talk, we will show that given an integer
$k \ge 5$, and a $C^k$ Anosov flow $\Phi$ on some compact connected $3$manifold preserving
a smooth volume, the measure of maximal entropy is the volume measure if and
only if $\Phi$ is $C^{k\varepsilon}$conjugate to an algebraic
flow for $\varepsilon > 0$ arbitrarily small. This
is a joint work with Jacopo De Simoi, Martin Leguil and Kurt Vinhage.

29372

Monday 7/25 3:30 PM

Wenbo Sun, Virginia Tech

Equidistribution for nilsequences along spheres
 Wenbo Sun, Virginia Tech
 Equidistribution for nilsequences along spheres
 07/25/2022
 3:30 PM  4:30 PM
 C304 Wells Hall
 Huyi Hu (hhu@msu.edu)
The nilsequence is a generalization for exponential sums which has a wide range of applications in analysis and combinatorics. A well know result of Green and Tao in 2010 states that the equidistribution property of a nilsequence is determined by its projection on the horizontal torus.

29373

Friday 7/29 10:30 AM

Ross Akhmechet, University of Virginia

Lattice cohomology and qseries invariants of 3manifolds
 Ross Akhmechet, University of Virginia
 Lattice cohomology and qseries invariants of 3manifolds
 07/29/2022
 10:30 AM  11:30 AM
 C304 Wells Hall
 Teena Meredith Gerhardt (gerhar18@msu.edu)
I will discuss an invariant of negative definite plumbed 3manifolds which unifies and extends two theories with quite different origins and structures. The first is lattice cohomology, due to Némethi, which is motivated by normal surface singularities and is isomorphic to Heegaard Floer homology for a large class of plumbings. The second theory is the $\widehat{Z}$ series of GukovPeiPutrovVafa, a power series which conjecturally recovers SU(2) quantum invariants at roots of unity and satisfies remarkable modularity properties. I will explain lattice cohomology, $\widehat{Z}$, and our unification of these theories. I will also discuss some key features of our new invariant: it leads to a 2variable refinement of $\widehat{Z}$, and, unlike both lattice cohomology and $\widehat{Z}$, it is sensitive to $spinc^c$conjugation. This is joint work with Peter Johnson and Slava Krushkal.

29374

Friday 7/29 1:00 PM

Michael Willis, Stanford University

Annular Khovanov stable homotopy and sl_2
 Michael Willis, Stanford University
 Annular Khovanov stable homotopy and sl_2
 07/29/2022
 1:00 PM  2:00 PM
 C304 Wells Hall
 Teena Meredith Gerhardt (gerhar18@msu.edu)
The Khovanov complex of a link $L$ in a thickened annulus carries a filtration; the associated graded complex gives rise to the annular Khovanov homology of $L$. GrigsbyLicataWehrli show that this annular homology admits an action by the Lie algebra $\mathfrak{sl}_2$. Using the techniques of LipshitzSarkar, one can define a stable homotopy lift of the annular Khovanov homology of $L$. In this talk I will describe (in part) how to lift the $\mathfrak{sl}_2$action to the stable homotopy category as well, illustrating some features of how one might hope to lift signed maps with cancellations via framed flow categories. This is joint work with Ross Akhmechet and Slava Krushkal.
