A three-field formulation and mixed FEM for poroelasticity
Sparse information representation through feature selection
Abstract
North meets South Colloquium
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Computing distinct solutions of differential equations -- Patrick Farrell
Abstract: TBA
Triangles and equations -- Yufei Zhao
Abstract: I will explain how tools in graph theory can be useful for understanding certain problems in additive combinatorics, in particular the existence of arithmetic progressions in sets of integers.
Strongly semistable sheaves and the Mordell-Lang conjecture over function fields
Abstract
We shall describe a new proof of the Mordell-Lang conjecture in positive characteristic, in the situation where the variety under scrutiny is a smooth subvariety of an abelian variety.
Our proof is based on the theory of semistable sheaves in positive characteristic, in particular on Langer's theorem that the Harder-Narasimhan filtration of sheaves becomes strongly semistable after a finite number of iterations of Frobenius pull-backs. Our proof produces a numerical upper-bound for the degree of the finite morphism from an isotrivial variety appearing in the statement of the Mordell-Lang conjecture. This upper-bound is given in terms of the Frobenius-stabilised slopes of the cotangent bundle of the variety.
(Joint Number Theory and Logic) On a modular Fermat equation
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I will describe some diophantine problems and results motivated by the analogy between powers of the modular curve and powers of the multiplicative group in the context of the Zilber-Pink conjecture.
Geometric integrators in optimal control theory
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A GPU Implementation of the Filtered Lanczos Procedure
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This talk describes a graphics processing unit (GPU) implementation of the Filtered Lanczos Procedure for the solution of large, sparse, symmetric eigenvalue problems. The Filtered Lanczos Procedure uses a carefully chosen polynomial spectral transformation to accelerate the convergence of the Lanczos method when computing eigenvalues within a desired interval. This method has proven particularly effective when matrix-vector products can be performed efficiently in parallel. We illustrate, via example, that the Filtered Lanczos Procedure implemented on a GPU can greatly accelerate eigenvalue computations for certain classes of symmetric matrices common in electronic structure calculations and graph theory. Comparisons against previously published CPU results suggest a typical speedup of at least a factor of $10$.
A fast hierarchical direct solver for singular integral equations defined on disjoint boundaries and application to fractal screens
Abstract
Our starting point for specialized linear algebra is an alternative algorithm based on a recursive block LU factorization recently developed by Aminfar, Ambikasaran, and Darve. This algorithm specifically exploits the hierarchically off-diagonal low-rank structure arising from coercive singular integral operators of elliptic partial differential operators. The hierarchical solver involves a pre-computation phase independent of the right-hand side. Once this pre-computation factorizes the operator, the solution of many right-hand sides takes a fraction of the original time. Our fast direct solver allows for the exploration of reduced-basis problems, where the boundary density for any incident plane wave can be represented by a periodic Fourier series whose coefficients are in turn expanded in weighted Chebyshev or ultraspherical bases.