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 Events
Vanderbilt
Wed 14 Nov 2018, 2:45pm
Topology and related seminars
ESB 4133 (PIMS Lounge)
Cutting and Pasting in Algebraic K-theory -- AKA Combinatorial K-theory
ESB 4133 (PIMS Lounge)
Wed 14 Nov 2018, 2:45pm-3:45pm

Abstract

 Algebraic K-theory is an invariant defined on categories that records how object in the category are related by exact sequences --- it is a homotopical version of the classical Euler characteristic. However, there are many categories of interest that do not have exact sequences, but instead have cutting and pasting operations. For example, the category of varieties or the category of polytopes. I'll describe how to define a higher algebraic K-theory for categories like this, and show that it's not so different from the case of more algebraic categories. Even better, theorems like Quillen's Devissage and Localization can be proved internal to these structures. Time permitting, I'll describe how the cutting and pasting of polytopes is intimately related to the weight filtration on the algebraic K-theory of fields.
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Department of Botany, UBC
Wed 14 Nov 2018, 3:00pm
Mathematical Biology Seminar
ESB 4127
Mechanisms modulating developmental transitions in plants
ESB 4127
Wed 14 Nov 2018, 3:00pm-4:00pm

Abstract


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University of British Columbia
Wed 14 Nov 2018, 4:00pm
Probability Seminar
ESB 2012
Heat kernel bounds and resistance estimates
ESB 2012
Wed 14 Nov 2018, 4:00pm-5:00pm

Abstract

Sub-Gaussian heat kernel estimates are typical of fractal graphs. We show that sub-Gaussian estimates on graphs follow from a Poincaré inequality, capacity upper bound, and a slow volume growth condition. An important feature of this work is that we do not assume elliptic Harnack inequality, cutoff Sobolev inequality, or exit time bounds.
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Guillermo Dibene
Fri 16 Nov 2018, 12:00pm
Graduate Student Seminar
MATX 1115
Can we escape a ma´ze maze?
MATX 1115
Fri 16 Nov 2018, 12:00pm-1:00pm

Abstract

Question: imagine you are located somewhere inside a maïze maze that extends all over the plane. Could you find an exit towards infinity?

To be (just) a (little) bit more accurate, consider the following model. Suppose maïze grows in the Euclidean plane (denoted R2 from now onwards) forming walls parallel to the axes of R2. The walls have length 1 and they grow between every two neighbouring points of the standard whole numbers lattice (henceforth denoted Z2). The walls are set up in such a way that every point in Z2 is adjacent to a wall (there are no points left alone) and so that, for whatever the closed square K of R2 may be, there always exists a path from whatever point inside A = K - the walls of maïze to the exterior of K and such that you never backtrack (nor cross through a wall). From these conditions, it should be intuitively clear that from whatever point in R2 (not in the walls) there exist paths that never backtrack and that go on forever. How many such paths exist? We shall see that in almost every case, the answer is surprising. To respond this we shall introduce the language of graphs and the uniform spanning tree. The talk will aim at the undergraduate level and exceeding formalities will be avoided.
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MIT
Mon 19 Nov 2018, 4:00pm
Algebraic Geometry Seminar
Math 126
Motivic Hilbert zeta functions of curves
Math 126
Mon 19 Nov 2018, 4:00pm-5:00pm

Abstract

The Grothendieck ring of varieties is the target of a rich invariant associated to any algebraic variety which witnesses the interplay between geometric, topological and arithmetic properties of the variety. The motivic Hilbert zeta function is the generating series for classes in this ring associated to a certain compactification of the unordered configuration space, the Hilbert scheme of points, of a variety. In this talk I will discuss the behavior of the motivic Hilbert zeta function of a reduced curve with arbitrary singularities. For planar singularities, there is a large body of work detailing beautiful connections with enumerative geometry, representation theory and topology. I will discuss some conjectural extensions of this picture to non-planar curves.
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University of Southern California
Mon 19 Nov 2018, 4:00pm
Institute of Applied Mathematics
LSK 460
IAM Lecture Series on Quantum Computing: The impact of quantum computing
LSK 460
Mon 19 Nov 2018, 4:00pm-5:00pm

Abstract

 Quantum information processing holds great promise, yet large-scale, general purpose, universal quantum computers capable of solving hard problems are not yet available, despite 20+ years of immense worldwide effort and large investments. However, special-purpose quantum information processors, such as the quantum simulators originally envisioned by Feynman, now appear to be within reach. Another type of currently operational special-purpose quantum information processor is a "quantum annealer," designed to speed up the solution to classical optimization problems. “Quantum supremacy” has meanwhile been identified as an intermediate target, allowing the current generation of quantum computers to demonstrate superiority against classical computers. After a brief introduction to “what is quantum computing,” this talk will review these developments and their broader impacts, with an eye toward the long-term prospects of quantum computers.

Bio. Daniel Lidar is the Viterbi Professor of Engineering at USC, and a professor of Electrical Engineering, Chemistry, and Physics. He holds a Ph.D. in physics from the Hebrew University of
Jerusalem. He did his postdoctoral work at UC Berkeley. Prior to joining USC in 2005 he was a faculty member at the University of Toronto. His main research interest is quantum information processing, where he works on quantum control, quantum error correction, the theory of open quantum systems, quantum algorithms, and theoretical as well as experimental adiabatic quantum computation. He is the Director of the USC Center for Quantum Information Science and Technology, and is the co-Director (Scientific Director) of the USC-Lockheed Martin Center for Quantum Computing. Lidar is a recipient of a Sloan Research Fellowship, a Guggenheim Fellowship and is a Fellow of the AAAS, APS, and IEEE.

The IAM Lecture Series on Quantum Computing is generously sponsored by 1QBit, DWave, and PIMS.

Note for Attendees

Please join us for refreshments immediately preceding Daniel's talk, 3:30-4p in LSK 306.
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Robert Bridson
Autodesk
Tue 20 Nov 2018, 12:30pm
Scientific Computation and Applied & Industrial Mathematics
ESB 4133 (PIMS Lounge)
Preconditioning with Semi-Assembled Matrices
ESB 4133 (PIMS Lounge)
Tue 20 Nov 2018, 12:30pm-1:30pm

Abstract

For my work supporting Bifrost, a programming environment built for visual effects artists, I am seeking a good “default” preconditioner for solving linear systems or accelerating nonlinear solvers in problems arising in physics simulation and geometric problems. Narrowing the focus, I’m looking particularly at large, sparse, symmetric-positive definite matrices with either an explicit or implied sum-of-squares structure, most notably finite element stiffness matrices for elliptic problems. On the other hand, I do not want to make further assumptions such as the signs of off-diagonal nonzeros, whether the vector of all ones plays a special role, etc. which may break down in the face of situations such as biharmonic-like shell problems and matrix rescalings to avoid unnecessary ill-conditioning. In this talk I’ll discuss my current experiments with preconditioners inspired by Shklarski and Toledo’s "fretsaw extension”, itself based on ideas from support graph preconditioning. Rather than viewing this as a way to approximate the graph of the original matrix with a tree plus a few extra edges (which implies an efficient exact Cholesky factorization), I introduce two new ideas:

1) sparsification viewed as partial assembly of the stiffness matrix, guided by exactly what an efficient Cholesky factorization needs, and

2) adding constraints to the semi-assembled system to keep it equivalent to the original problem, rather than just an approximation.

While the constrained semi-assembled system cannot be efficiently factored in its entirety, it opens up more avenues for how to approach preconditioning, which hopefully will lead to the desired solver characteristics.
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