• Speaker: Sergey Shadrin, Korteweg-de Vries Instituut
• Title: Non-commucative $M_{0,1+n}$, https://msu.zoom.us/j/94925518997
• Date: 05/14/2020
• Time: 9:30 AM - 10:30 AM
• Place: C204A Wells Hall

There is a huge system of parallels between various geometric and topological properties of the moduli space of curves of genus $0$ with marked points $M_{0,1+n}$ and the so-called brick manifolds $B_n$, defined a few years ago by Laura Escobar. In fact, it appears that all interesting properties relevant for the topological field theory (considered as general phenomena surrounding $M_{0,1+n}$) find their non-commutative analogs in $B_n$: -- stratification, description of cohomology (that implies the WDVV equations), psi-classes, structure of topological operad, cohomological field theories, Givental group action, surrounding topological operads (little disks, framed little discs, gravity), algebraic structures implied by their representations (hypercommutative algebra, also known in the literature as flat F-manifold, BV/Gerstenhaber algebras, etc.), and so on. (To this end, my favourite alternative title for this talk would be "What is a non-commutative hypercommutative algebra?" ) In addition the brick manifolds have very rich geometric structure: they are toric varieties of Loday's realisations of associahedra and have interpretation as wonderful models of De Concini-Procesi. In the talk, we'll try to show some of the properties mentioned above, step-by-step constructing them both on the side of moduli spaces of curves and on the side of brick manifolds. (along the lines of my joint work with Volodya Dotsenko and Bruno Vallette).

• Speaker: Daniel Spielman, Yale
• Title: Balancing covariates in randomized experiments using the Gram–Schmidt walk
• Date: 05/21/2020
• Time: 2:30 PM - 3:30 PM
• Place: 

(Part of the One World MINDS series: https://sites.google.com/view/minds-seminar/home) In randomized experiments, such as a medical trials, we randomly assign the treatment, such as a drug or a placebo, that each experimental subject receives. Randomization can help us accurately estimate the difference in treatment effects with high probability. We also know that we want the two groups to be similar: ideally the two groups would be similar in every statistic we can measure beforehand. Recent advances in algorithmic discrepancy theory allow us to divide subjects into groups with similar statistics. By exploiting the recent Gram-Schmidt Walk algorithm of Bansal, Dadush, Garg, and Lovett, we can obtain random assignments of low discrepancy. These allow us to obtain more accurate estimates of treatment effects when the information we measure about the subjects is predictive, while also bounding the worst-case behavior when it is not. We will explain the experimental design problem we address, the Gram-Schmidt walk algorithm, and the major ideas behind our analyses. This is joint work with Chris Harshaw, Fredrik Sävje, and Peng Zhang. Paper: https://arxiv.org/abs/1911.03071 Code: https://github.com/crharshaw/GSWDesign.jl

• Speaker:  Ronald Coifman, Yale
• Title: The Analytic Geometries of Data; zoom link @ https://sites.google.com/view/minds-seminar/home
• Date: 05/28/2020
• Time: 2:30 PM - 2:30 PM
• Place: 

(Part of the One World MINDS series: https://sites.google.com/view/minds-seminar/home) \[\] We will describe methodologies to build data geometries designed to simultaneously analyze and process data bases. The different geometries or affinity metrics arise naturally as we learn to contextualize and conceptualize. I.e; relate data regions, and data features (which we extend to data tensors). Moreover we generate tensorial multiscale structures. We will indicate connection to analysis by deep nets and describe applications to modeling observations of dynamical systems, from stochastic molecular dynamics to calcium imaging of brain activity.

• Speaker: Ben Adcock, Simon Fraser University
• Title: The troublesome kernel: instabilities in deep learning for inverse problems; zoom link @ https://sites.google.com/view/minds-seminar/home
• Date: 06/04/2020
• Time: 2:30 PM - 3:30 PM
• Place: 

(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home) \[\] Due to their stunning success in traditional machine learning applications such as classification, techniques based on deep learning have recently begun to be actively investigated for problems in computational science and engineering. One of the key areas at the forefront of this trend is inverse problems, and specifically, inverse problems in imaging. The last few years have witnessed the emergence of many neural network-based algorithms for important imaging modalities such as MRI and X-ray CT. These claim to achieve competitive, and sometimes even superior, performance to current state-of-the-art techniques. However, there is a problem. Techniques based on deep learning are typically unstable. For example, small perturbations in the data can lead to a myriad of artefacts in the recovered images. Such artifacts can be hard to dismiss as obviously unphysical, meaning that this phenomenon has potentially serious consequences for the safe deployment of deep learning in practice. In this talk, I will first showcase the instability phenomenon empirically in a range of examples. I will then focus on its mathematical underpinnings, the consequences of these insights when it comes to potential remedies, and the future possibilities for computing genuinely stable neural networks for inverse problems in imaging. This is joint work with Vegard Antun, Nina M. Gottschling, Anders C. Hansen, Clarice Poon, and Francesco Renna Papers: https://www.pnas.org/content/early/2020/05/08/1907377117 https://arxiv.org/abs/2001.01258

• Speaker: Jelani Nelson, UC Berkeley
• Title: Optimal terminal dimensionality reduction in Euclidean space; zoom link @ https://sites.google.com/view/minds-seminar/home
• Date: 06/11/2020
• Time: 2:30 PM - 3:30 PM
• Place: 

(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home) \[ \] The Johnson-Lindenstrauss lemma states that for any X a subset of R^d with |X| = n and for any epsilon, there exists a map f:X-->R^m for m = O(log n / epsilon^2) such that: for all x in X, for all y in X, (1-epsilon)|x - y|_2 <= |f(x) - f(y)|_2 <= (1+epsilon)|x - y|_2. We show that this statement can be strengthened. In particular, the above claim holds true even if "for all y in X" is replaced with "for all y in R^d". Joint work with Shyam Narayanan.

• Speaker: Gitta Kutyniok, TU Berlin
• Title: TBA
• Date: 06/18/2020
• Time: 2:30 PM - 3:30 PM
• Place: 

(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home)

• Speaker: Stephane Mallat, Ecole Normal Superieure
• Title: TBA
• Date: 07/02/2020
• Time: 2:30 PM - 3:30 PM
• Place: 

(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home)

• Speaker: Helmut Bolcskei, ETH Zurich
• Title: TBA
• Date: 07/16/2020
• Time: 2:30 PM - 3:30 PM
• Place: 

(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home)

• Speaker: Mary Wooters, Stanford University
• Title: TBA
• Date: 07/30/2020
• Time: 2:30 PM - 3:30 PM
• Place: 

(Part of One World MINDS seminar: https://sites.google.com/view/minds-seminar/home)