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Pages
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Posts
Building a queue in Mojo
Published:
The Mojo programming language is officially open source, so what better opportunity to dig around and see what it can do? I decided on a simple graph search problem, Advent of Code Day 12, 2022.
Advent of Code 2023 or: Things I don’t like about Julia
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What began as a quick recap of my experience doing Advent of Code 2023 (my solutions) quickly devolved into a screed about what I dislike about Julia. But first, some math.
Benchmarking Mojo, Julia, and Python + NumPy
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Image: the Julia set for $f(z) = z^4 + 0.6 + 0.55i$, which the author could not elegantly work into this post.
Comparing Go and Rust performance for a high-throughput HTTP server
Published:
Let’s begin with the results, because that’s why you’re here. Go was faster than Rust in this test. I do not know why. When Go outperforms Rust, it means you’ve done something wrong in Rust. I can’t tell what. All the code is in this repo.
AI Interpretations of Jane Eyre’s Paintings
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In chapter XIII of Jane Eyre, Mr. Rochester asks to see Jane’s painting portfolio. In an act of 19th century negging, Mr. Rochester identifies three of her paintings as most worthy:
Ranking Kate Bush Songs With Svelte (and ChatGPT)
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Kate Bush has (roughly) 29 singles that charted in the U.K. The count is a little foggy because it’s not clear what should and shouldn’t be called a single. For example, Running Up That Hill charted three times: once in 1985, supporting the Hounds of Love Album; again in 2012 as a remixed version played for the 2012 London Olympic Games; and once again in 2022 after it was used in a Stranger Things episode. So I made some executive decisions and ended up with a list of 29.
Advent of Code 2022 Days 11-15 in Rust and Haskell
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I’ve given up following the narrative. There’s some kind of receiver and some beacons and maybe still some monkeys? I don’t know. The puzzles have gotten more challenging, more interesting, and more time-consuming.
Advent of Code 2022 Days 6-10 in Rust and Haskell
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The elves are on their expedition. They’re building tree houses and tossing people into rivers. A computer was involved somehow. We approached this with both Rust and Haskell.
Advent of Code 2022 Days 1-5 in Rust and Haskell
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The elves are preparing for their expedition and we’re using coding to help them do it. I’m using this year’s Advent of Code to acquire/sharpen skills in Rust and Haskell programming and the purpose of this post is to summarize my thoughts on the first five days.
Optimal but terrible answers to common coding interview questions
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Today we have set ourselves the task of providing technically correct but actually appalling answers to some common coding exercises. The exercises under consideration are
Creating a CTA bus tracker with go
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The source code for this post is available on my github.
Analyzing a broken GPS watch with pandas
Published:
The GPS watch I bought last November was broken. Industry standard GPS watches make a recording once every second and log it to a .gpx file, but mine wasn’t doing that. Sometimes it was logging every second, sometimes it wasn’t. In this post, I explore and visualize the data logged by my failing GPS device.
portfolio
Portfolio item number 1
Short description of portfolio item number 1
Portfolio item number 2
Short description of portfolio item number 2
publications
Effective cycles on blow-ups of Grassmannians
Published in Journal of Pure and Applied Algebra, 2018
In this paper we study the pseudoeffective cones of blow-ups of Grassmannians at sets of points. For small numbers of points, the cones are often spanned by proper transforms of Schubert classes. In some special cases, we provide sharp bounds for when the Schubert classes fail to span and we describe the resulting geometry.
Recommended citation: J. Kopper. Effective cycles on blow-ups of Grassmannians. Journal of Pure and Applied Algebra, 222 no. 4 (2018), 846--86769.
The nef cone of the Hilbert scheme of points on rational elliptic surfaces and the cone conjecture
Published in Canadian Mathematical Bulletin, 2020
We compute the nef cone of the Hilbert scheme of points on a general rational elliptic surface. As a consequence of our computation, we show that the Morrison-Kawamata cone conjecture holds for these nef cones.
Recommended citation: J. Kopper. The nef cone of the Hilbert scheme of points on rational elliptic surfaces and the cone conjecture. Canadian Mathematical Bulletin 64 no. 1 (2020), 216--227.
Stability conditions for restrictions of vector bundles on projective surfaces
Published in Michigan Mathematical Journal, 2020
Using Bridgeland stability conditions, we give sufficient criteria for a stable vector bundle on a smooth complex projective surface to remain stable when restricted to a curve. We give a stronger criterion when the vector bundle is a general vector bundle on the plane. As an application, we compute the cohomology of such bundles for curves that lie in the plane or on Hirzebruch surfaces.
Recommended citation: J. Kopper. Stability conditions for restrictions of vector bundles on projective surfaces. Michigan Mathematical Journal 69 no. 4 (2020), 711--732..
The cohomology of general tensor products on the plane
Published in Selecta Mathematica, 2021
We compute the cohomology of general tensor products of stable bundles on the projective plane.
Recommended citation: I. Coskun, J. Huizenga, and J. Kopper. The cohomology of general tensor products on the plane. Selecta Mathematica 27 no. 5 (2021), article number 94.
Ample stable vector bundles on rational surfaces
Published in Communications in Algebra, 2022
We study sufficient and necessary conditions for stable vector bundles on the plane to be ample. Joint work with Jack Huizenga.
Recommended citation: J. Huizenga, and J. Kopper. Ample stable vector bundles on rational surfaces. Communications in Algebra (2022), to appear.
Non–globally generated bundles on curves
Published in International Mathematics Research Notices, 2022
We study the locus of stable vector bundles on smooth curves that fail to be globally generated. We compute the dimension of this locus and study its irreducibility. Joint work with Sayanta Mandal.
Recommended citation: J. Kopper and S. Mandal. Non-globally generated bundles on curves. International Mathematics Research Notices (2022), to appear.
Disconnected moduli spaces of stable bundles on surfaces
Published in Bulletin of the London Mathematical Society, 2022
We construct moduli spaces of stable bundles on surfaces with arbitrarily many connected components. Joint work with Izzet Coskun and Jack Huizenga.
Recommended citation: I. Coskun, J. Huizenga, and J. Kopper. Disconnected moduli spaces of stable bundles on surfaces. Bull. Lond. Math. Soc. (2022), to appear.
talks
Talk 1 on Relevant Topic in Your Field
Published:
This is a description of your talk, which is a markdown files that can be all markdown-ified like any other post. Yay markdown!
Conference Proceeding talk 3 on Relevant Topic in Your Field
Published:
This is a description of your conference proceedings talk, note the different field in type. You can put anything in this field.
teaching
Teaching experience 1
Undergraduate course, University 1, Department, 2014
This is a description of a teaching experience. You can use markdown like any other post.
Teaching experience 2
Workshop, University 1, Department, 2015
This is a description of a teaching experience. You can use markdown like any other post.