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Andy Manion, NC State, Higher tensor products and Heegaard Floer homology

SAS 4201

I will discuss some algebraic aspects of recent work with Raphael Rouquier on a tensor product operation for categorified representations of U_q(gl(1|1)^+) and its connections to Heegaard Floer homology. Speaker’s webpage: https://sites.google.com/usc.edu/manion/home Jointly in person and virtually on Zoom. SAS 4201 for in-person participation. The Zoom link is sent out to the Algebra and Combinatorics…

John Darges, Extreme learning machines for variance-based global sensitivity analysis

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Variance-based global sensitivity analysis (GSA) provides useful measures, Sobol' indices, of how important individual input variables are to the output of a mathematical model. Traditional estimation of Sobol' indices by Monte Carlo methods can be unfeasible for models which are computationally expensive to evaluate. An appealing approach is to instead use a surrogate whose Sobol'…

Tim Reid, Examining Sensitivity Large Computational Problems on Early Termination of CG with Probabilistic Numerics

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Many large computational problems depend on solutions to systems of linear equations. One widely used method of solving systems of linear equations is the Conjugate Gradient method (CG). Terminating CG after only a few iterations can save computational resources but can also cause an error in the solution to the system of linear equations, and…

David Keyes, King Abdullah University of Science and Technology, Nonlinear Preconditioning for Implicit Solution of Discretized PDEs

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 Nonlinear preconditioning refers to transforming a nonlinear algebraic system to a form for which Newton-type algorithms have improved success through quicker advance to the domain of quadratic convergence. We place these methods, which go back at least as far as the Additive Schwarz Preconditioned Inexact Newton (ASPIN, 2002) in the context of a proliferation distinguished…

Larry Gu, University of Southern California, Decategorification of HFK_n(L)

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Using a definition of Euler characteristic for fractionally-graded complexes based on roots of unity, we show that the Euler characteristics of Dowlin’s “sl(n)-like” Heegaard Floer knot invariants HFK_n recover both Alexander polynomial evaluations and sl(n) polynomial evaluations at certain roots of unity for links in S^3. We show that the equality of these evaluations can…

Kailash Misra, NC State, Affine Lie Algebras and Crystals

SAS 1102

Affine Lie algebras, also sometimes called current algebras, are infinite-dimensional analogs of finite-dimensional semisimple Lie algebras. The representation theory of affine Lie algebras has applications in many areas of mathematics (number theory, combinatorics, group theory, geometry, topology, etc.) and physics (conformal field theory, integrable systems, statistical mechanics, etc.). To study the combinatorial properties of affine Lie algebra…

Longfei Li, University of Louisiana at Lafayette, Numerical methods for fourth-order PDEs on overlapping grids with application to Kirchhoff-Love plates

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We propose novel numerical methods for solving a class of high-order hyperbolic PDEs on general geometries, which involve 2nd-order derivatives in time and up-to 4th-order derivatives in space. These PDEs are widely used in modeling thin-walled elastic structures such as beams, plates and shells, etc. High-order spatial derivatives together with general geometries bring a number…

Pengtao Sun, University of Nevada, Las Vegas

SAS 4201

The zoom link and passcode for all talks is below: https://ncsu.zoom.us/j/97638681103?pwd=dDJrRkE3d3NQZEhrRlhOMDc4T0pRUT09 passcode: NAseminar

Dan Lucas, Keele University

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The zoom link and passcode for all talks is below: https://ncsu.zoom.us/j/97638681103?pwd=dDJrRkE3d3NQZEhrRlhOMDc4T0pRUT09 passcode: NAseminar

Daniel Massatt, University of Chicago, Electronics of Relaxed Bilayer 2D Heterostructures in Momentum Space

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Incommensurate stacked 2D materials have gained significant attention after the recent discovery of a new mechanism of superconductivity in systems with small twist angles. Theoretically, the electronics of such systems are studied through tight-binding models. These models can be studied in several different spaces, though momentum space is often the leading favorite for physicists because…