Fall 2020 Colloquium, Wednesdays

Beginning immediately, until at least April 30, all seminars will take place virtually, through Zoom. 

The 2020-2021 Colloquium will take place every Wednesday from 9:00 to 10:00am ET virtually, using zoom. Please email the seminar organizers to obtain a link. This year’s colloquium will be organized by Wei Gu and Sergiy Verstyuk. The schedule below will be updated as speakers are confirmed.

To learn how to attend, please fill out this form.

Information on previous colloquia can be found here.

9/23/2020David Kazhdan (Hebrew University)Title: On Applications of Algebraic Combinatorics to Algebraic Geometry 

Abstract: I present a derivation of a number of  results on morphisms of a high Schmidt’s rank from a result in Algebraic Combinatorics. In particular will explain the flatness of such morphisms and show their fibers have rational singularities.

Mariangela Lisanti (Princeton University)

Title: Mapping the Milky Way’s Dark Matter Halo with Gaia 

Abstract: The Gaia mission is in the process of mapping nearly 1% of the Milky Way’s stars—-nearly a billion in total.  This data set is unprecedented and provides a unique view into the formation history of our Galaxy and its associated dark matter halo.  I will review results based on the most recent Gaia data release, demonstrating how the evolution of the Galaxy can be deciphered from the stellar remnants of massive satellite galaxies that merged with the Milky Way early on.  This analysis is an inherently “big data” problem, and I will discuss how we are leveraging machine learning techniques to advance our understanding of the Galaxy’s evolution.  Our results indicate that the local dark matter is not in equilibrium, as typically assumed, and instead exhibits distinctive dynamics tied to the disruption of satellite galaxies.  The updated dark matter map built from the Gaia data has ramifications for direct detection experiments, which search for the interactions of these particles in terrestrial targets.
10/14/2020Gil Kalai (Hebrew University and IDC Herzliya)

Title: Statistical, mathematical, and computational aspects of noisy intermediate-scale quantum computers 

Abstract: Noisy intermediate-scale quantum (NISQ) Computers hold the key for important theoretical and experimental questions regarding quantum computers. In the lecture I will describe some questions about mathematics, statistics and computational complexity which arose in my study of NISQ systems and are related to
a) My general argument “against” quantum computers,
b) My analysis (with Yosi Rinott and Tomer Shoham) of the Google 2019 “quantum supremacy” experiment.
Relevant papers:
Yosef Rinott, Tomer Shoham and Gil Kalai, Statistical aspects of the quantum supremacy demonstration, https://gilkalai.files.

Gil Kalai, The Argument against Quantum Computers, the Quantum Laws of Nature, and Google’s Supremacy Claims, https://gilkalai.files.

Gil Kalai, Three puzzles on mathematics, computations, and games, https://gilkalai.files.

10/21/2020Marta Lewicka (University of Pittsburgh)Title: Quantitative immersability of Riemann metrics and the infinite hierarchy of prestrained shell models

Abstract: We propose results that relate the following two contexts:
(i) Given a Riemann metric G on a thin plate, we study the question of what is its closest isometric immersion, with respect to the distance measured by energies E^h which are modifications of the classical nonlinear three-dimensional elasticity.
(ii) We perform the full scaling analysis of E^h, in the context of dimension reduction as the plate’s thickness h goes to 0, and derive the Gamma-limits of h^{-2n}E^h for all n. We show the energy quantization, in the sense that the even powers 2n of h are the only possible ones (all of them are also attained).
For each n, we identify conditions for the validity of the corresponding scaling, in terms of the vanishing of Riemann curvatures of G up to appropriate orders, and in terms of the matched isometry expansions. Problems that we discuss arise from the description of elastic materials displaying heterogeneous incompatibilities of strains that may be associated with growth, swelling, shrinkage, plasticity, etc. Our results display the interaction of calculus of variations,
geometry and mechanics of materials in the prediction of patterns and shape formation.

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