The Shattering of SAT

If condensed matter theorists have the Ising model, gravitational physicists have the Schwarzschild solution, and quantum foundation theorists have the Bell inequalities, then theoretical computer scientists have satisfiability, or SAT. In the world of computer science (and particularly computational complexity), many discussions inevitably circle back to SAT. In fact, SAT isn’t just something that theoretical computer scientists study. Satisfiability has a rich history with statistical physics, a field which wields powerful tools to probe the…

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Let’s hear more from the women who leave academia (Part 2)

After the publication of my previous post, I received an email from Dr Sian Grigg, who decided to leave academia following the completion of her PhD. Read on below to hear her story. Dear Kaitlin Thanks for thinking of us who did not continue! I have often thought about this question and still wonder, after 15 years, whether I should have tried harder to pursue a career in academia. And whether I might now try…

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Let’s hear more from the women who leave academia.

“On International Women’s Day”, I wrote on 8 March, “why don’t we instead highlight women who left the workforce due to structural barriers? The current approach is a bit “let’s celebrate the women who navigated this broken system to distract from the fact that it’s broken”.” So far, I have been one of the women who is “celebrated” on days like this, with social media campaigns showcasing the work of women in science. I am…

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Absorbers and Explorers

To be a scientist means to explore. You need to start from what is known and jump out into the void, investigating new ideas. In this regard, the scientist is an explorer, a person searching for new truths in a world without a map. To be more precise, a scientist uncovers the new map as they learn. When we talk about science, we like to emphasize the new discoveries. Whether that’s the discovery of gravitational…

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Virtual CNWW

If you want to learn a topic today, the resources are much more plentiful than even a few decades ago. The internet has given us wonderful resources to learn from, including some which leverage internet technologies to provide animations and teach topics in a much more interactive way. This is particularly true for mathematics and physics, which have been entrenched in dry textbooks that are a chore to read1 for much too long. The tools…

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Pick a State, Any State

Hilbert space is big. No, not big like the how the Earth is big compared to you. Rather, Hilbert space is astronomically big. Actually, that’s not quite right either. It’s bigger than that. I guess the best adverb I can use is that it’s mathematically big. In a Hilbert space, you tend to have a lot of room to maneuver. (To read more about that, check out my essay, “The Curse of Dimensionality”.) In the…

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All in the Corners

As a quantum theorist, I spend a lot of time thinking about high-dimensional spaces. These are the playgrounds for quantum many-body systems, and they are vast. The technical name is a Hilbert space, and it’s the space of complex vectors with the additional structure of a way to put vectors together (called an inner product). Hilbert space is big (see “The Curse of Dimensionality”), but the usable area for quantum theory is often much smaller.…

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Jeremy Côté 2020-11-22 09:42:29

How to pick a random unit vector. As a quantum theorist, I spend a lot of time thinking about high-dimensional spaces. These are the playgrounds for quantum many-body systems, and they are vast. The technical name is a Hilbert space, and it’s the space of complex vectors with the additional structure of a way to put vectors together (called an inner product). Hilbert space is big (see “The Curse of Dimensionality”), but the usable area…

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The Curse of Dimensionality

From combinatorics to many-body quantum systems. If there’s one field of mathematics that everyone encounters in their daily life, I would argue that it’s combinatorics (with perhaps geometry being the other one). The rules of combinatorics cast a shadow over our lives. They affect how we make decisions and form the scaffolding for how options in our lives are displayed to us. In this essay, I want to explore the idea which is known as…

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Physics On A Cube

One of my favourite mathematical pieces of writing is Flatland, by Edwin Abbott Abbott (the book is in the public domain, so you can download it from Wikipedia). Published over a century ago, it’s a story1 involving residents (Flatlanders) who live in a two-dimensional world. Without giving too much of the story away (because you should seriously read it!), the inhabitants find themselves shocked when a strange shape dips into their world. That other “shape”…

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