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Topological Data Analysis
 Facundo Memoli, The Ohio State University
 Some rigidity results for metric spaces via persistent homology
 05/03/2021
 2:00 PM  3:00 PM
 Online (virtual meeting)
 Shelley Kandola (kandola2@msu.edu)
Persistence barcodes provide computable signatures for datasets. These signatures absorb both geometric and topological information in a stable manner. One question that has not yet received too much attention is: how strong are these signatures? A related question is that of ascertaining their relationship to other more classical invariants such as curvature. In this talk I will describe some results about characterizing metric spaces via persistence barcodes arising from VietorisRips filtrations. Of particular interest is a relationship which we established linking persistence barcodes to Gromov's filling radius.

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Conversations among Colleagues
 Amanda Glazer, UC Berkeley
 National Mathematics Survey: Addressing the Gender Gap in Undergraduate Mathematics
 05/04/2021
 10:00 AM  11:00 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Tsvetanka Sendova (tsendova@msu.edu)
In Spring of 2016 the National Mathematics Survey was sent out to five institutions (Harvard, MIT, Princeton, Yale and Brown) to investigate undergraduate climate issues in math departments, in particular with regards to gender. The survey covered a wide range of topics including college academics, advising/research, study habits, mathematics department community, family background, and mentorship. The quantitative data from the survey indicated that the barrier to entry is much higher for women than men who intend to study mathematics, and the qualitative data illustrated a number of issues including gender stereotypes, pressure to represent and disrespect for intelligence. In this talk, I will present the main results from this survey as well as discuss recommendations and changes made in the Harvard mathematics department to address some of these issues.
Geometry and Topology
 Yury Belousov, Higher School of Economics (HSE)
 On the question of genericity of hyperbolic knots
 05/04/2021
 2:50 PM  3:40 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Matthew Edward Hedden (heddenma@msu.edu)
(based on a joint work with A. Malyutin)
Thurston’s famous classification theorem, of 1978, states that a nontoric nonsatellite knot is hyperbolic, that is, its complement admits a complete hyperbolic metric of finite volume. Until recently there was the conjecture (known as Adams conjecture) saying that the percentage of hyperbolic knots amongst all the prime knots of n or fewer crossings approaches 100 as n approaches infinity. In 2017 Malyutin showed that this statement contradicts several other plausible conjectures. Finally, in 2019 Adams conjecture was found to be false. In this talk we are going to discuss the key ingredients of its disproof

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Analysis and PDE
 Rami Fakhry, MSU
 Canceled due to health issue of the speaker
 05/05/2021
 4:10 PM  5:00 PM
 Online (virtual meeting)
(Virtual Meeting Link)
 Dapeng Zhan (zhan@msu.edu)
For a Chordal SLE$_\kappa$ ($\kappa \in (0,8)$) curve in a simply connected domain $D$ with smooth boundary, the $n$point boundary Green's function valued at distinct points $z_1, ..., z_n\in \partial{D}$ is defined by}
\[ G(z_1,...,z_n)= \lim_{r_1,...,r_n \to 0+} \prod_{j=1}^{n} {r_j}^ { \alpha} \mathbb{P} \left[ dist(\gamma, z_k) \leqq r_k, 1 \leqq k \leqq n \right] ,\]where $ \alpha = \frac{8}{\kappa}  1 $ is the boundary exponent of SLE$_\kappa$, provided that the limit converges. In this talk, we will show that such Green's function exists for any finite number of points. Along the way we provide the rate of convergence and modulus of continuity for Green's functions as well. Finally, we give uptoconstant bounds for them.
We use the same zoom link and passcode as before.

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Applied Mathematics
 Michael KwokPo Ng, University of Hong Kong
 Low Rank Tensor Completion with Poisson Observations
 05/06/2021
 4:30 AM  5:30 AM
 Online (virtual meeting)
(Virtual Meeting Link)
 Olga Turanova ()
Poisson observations for videos are important models in video processing and computer vision. In this talk, we study the thirdorder tensor completion problem with Poisson observations. The main aim is to recover a tensor based on a small number of its Poisson observation entries. An existing matrixbased method may be applied to this problem via the matricized version of the tensor. However, this method does not leverage on the global lowrankness of a tensor and may be substantially suboptimal. We employ a transformed tensor nuclear norm ball constraint and a bounded constraint of each entry, where the transformed tensor nuclear norm is used to get a lower transformed multirank tensor with suitable unitary transformation matrices. We show that the upper bound of the error of the estimator of the proposed model is less than that of the existing matrixbased method. Numerical experiments on synthetic data and realworld datasets are presented to demonstrate the effectiveness of our proposed model compared with existing tensor completion methods.

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