Topos Institute Positions

6 January, 2023

The Topos Institute is doing some remarkable work in applying category theory to real-world problems. And they’re growing!

They want to hire a Finance and Operations Manager and a Research Software Engineer. For more information, go here.

And if you’re a grad student working on category theory, you definitely want to check out their summer research positions! For more information on those, go here. Applications for these are due February 15th, 2023.

Topos Institute

Topos Institute Research Associates

5 March, 2022

Come spend the summer at the Topos Institute! For early-career researchers, we’re excited to open up applications for our summer research associate (RA) program.

Summer RAs are an important part of life at Topos — they help explore new directions relevant to Topos projects, and they bring new ideas, energy, and expertise to our research groups. This year we’ll welcome a new cohort of RAs to our offices in Berkeley, CA, with the program running from June to August.

RAs will be responsible for performing an in-depth research or teaching project, mentored by a Topos faculty mentor or advisor. This year possible mentors may include Conal Elliott, Valeria de Paiva, Evan Patterson, Dana Scott, David Spivak, and others. RAs will work closely with their mentor to define and pursue a research project.

Along the way, RAs will also participate in our weekly lunches and seminars, blog about their time here, and produce papers, books, software, or policy, according to the parameters of their project.

Applications are now open. The position is full-time (~40 hours per week) and paid hourly starting at $30/hour. Unfortunately, Topos is not able to sponsor US work visas for participants.

Please apply by Sunday March 27th. Offers of positions will be made in early April.

For some more information, and to apply, go here.

Topos Institute Postdoc

19 October, 2021

The Topos Institute is trying to hire a postdoc to work on polynomial functors! Here is the ad, written by David Spivak.

Dear all,

I’m happy to announce that Topos Institute is hiring a postdoctoral research fellow to study polynomial functors and their applications. A mathjobs listing is here:

and information on the precise project can be found here:

Applicants should be strong in mathematics or computer science and know category theory. Strong programming experience or strong math research experience is required, and a combination of the two is preferred. The position is for 1 year, but a renewal may be possible, depending on funding.

Topos is committed to building a team with diverse perspectives and life experiences, so those with underrepresented personal or professional backgrounds are highly encouraged to apply. Unfortunately, Topos is unable to sponsor visas for international candidates at this time.

We are looking to hire as soon as possible. Please feel free to contact me if you have any questions.

Best regards,


Postdocs in Categories and Chemistry

24 February, 2020

The University of Southern Denmark wants to hire several postdocs who will use category theory to design enzymes. This sounds like a wonderful job for people who like programming, chemistry and categories—and especially double pushout rewriting. The application deadline is 20 March 2020. The project is described here and the official job announcement is here.

I’ve seen Christoph Flamm, Daniel Merkle, Peter Sadler give talks on this project in Luxembourg, and it’s really fascinating. They’re using double pushout rewriting (as shown in the picture above) and other categorical techniques to design sequences of chemical reactions that accomplish desired tasks.

Let me quote a bit from the job announcement:

Several two-year postdoc positions starting 1 July 2020 are available at the University of Southern Denmark (SDU) for research on an exciting project in algorithmic cheminformatics supported by the Novo Nordisk Foundation: “From Category Theory to Enzyme Design – Unleashing the Potential of Computational Systems Chemistry”. We are seeking highly motivated individuals with a PhD in computer science, computational chemistry/biochemistry, or related areas. The ideal candidate has familiarity with several of the following areas: concurrency theory, graph transformation, algorithmics, algorithm engineering, systems chemistry, systems biology, metabolic engineering, or enzyme design. Solid competences in programming and ease with formal thinking are prerequisites.

The project is based on the novel application of formalisms, algorithms, and computational methods from computer science to questions in systems biology and systems chemistry. We aim to expand these methods and their formal foundations, create efficient algorithms and implementations of them, and use these implementations for research in understanding the catalytic chemistry of enzymes.

The Algorithmic Cheminformatics group at the Department of Mathematics and Computer Science at SDU offers a dynamic research environment, comprising two full professors, an assistant professor, and several students. The project includes partnerships with Harvard Medical School (Department of Systems Biology) and the University of Vienna (Institute for Theoretical Chemistry), who will host the postdoctoral researcher for extended visits.

The research group is located at the main campus of SDU, which is located in Odense, the third largest town in Denmark, 1:20 hours by train west of Copenhagen. Denmark is known for its high standards of living, free health care, and competitive salaries. Applicants from outside Denmark are eligible for substantial tax reductions.

For further information contact Professor Daniel Merkle (e-mail:, phone: +45 6550 2322).

Here’s a bit from the project description. (There’s much more here.)

The proposed project builds on a new and powerful methodology that strikes a balance between chemical detail and computational efficiency. The approach lies at the intersection of classical chemistry, present-day systems chemistry and biology, computer science, and category theory. It adapts techniques from the analysis of actual (mechanistic) causality in concurrency theory to the chemical and biological setting. Because of this blend of intellectual and technical influences, we name the approach computational systems chemistry (CSC). The term “computational” emphasizes both the deployment of computational tools in the service of practical applications and of theoretical concepts at the foundation of computation in support of reasoning and understanding. The goal of this exploratory project is to provide a proof-of-concept toward the long-term goal of tackling many significant questions in large and combinatorially complex CRNs that could not be addressed by other means. In particular, CSC shows promise for generating new technological ideas through theoretical rigor. This exploratory project is to be considered as initial steps towards establishing this highly promising area through the following specific objectives:

• Integrate and unify algorithmic ideas and best practices from two existing platforms. One platform was conceived, designed, and implemented for organic chemistry by the lead PI and his group in Denmark as well as the chemistry partner from University of Vienna. The other platform draws on the theory of concurrency and was designed and implemented for protein- protein interaction networks supporting cellular signaling and decision-making processes by the partner from Harvard Medical School and his collaborators. The combination is ripe with potential synergies as both platforms are formally rooted in category theory.

• Demonstrate a proof-of-concept (PoC) using a biochemical driving project. The goal of this exploratory project is the analysis and design of enzymes whose catalytic site is viewed as a small (catalytic) reaction network in its own right. Such enzymes can then be used in the design of reaction networks.

• Train the next generation of scientists for CSC: This will enable the transition towards a large-scale implementation of our approaches to tackle key societal challenges, such as the development of personalized medicine, the monitoring of pollution, and the achievement of a more environmentally friendly and sustainable network of industrial synthesis.

We argue that CSC is in a position today similar to where bioinformatics and computational biology were a few decades ago and that it has similarly huge potential. The long-term vision is to unleash that potential.

Postdoc in Applied Category Theory

8 September, 2017

guest post by Spencer Breiner

One Year Postdoc Position at Carnegie Mellon/NIST

We are seeking an early-career researcher with a background in category theory, functional programming and/or electrical engineering for a one-year post-doctoral position supported by an Early-concept Grant (EAGER) from the NSF’s Systems Science program. The position will be managed through Carnegie Mellon University (PI: Eswaran Subrahmanian), but the position itself will be located at the US National Institute for Standards and Technology (NIST), located in Gaithersburg, Maryland outside of Washington, DC.

The project aims to develop a compositional semantics for electrical networks which is suitable for system prediction, analysis and control. This work will extend existing methods for linear circuits (featured on this blog!) to include (i) probabilistic estimates of future consumption and (ii) top-down incentives for load management. We will model a multi-layered system of such “distributed energy resources” including loads and generators (e.g., solar array vs. power plant), different types of resource aggregation (e.g., apartment to apartment building), and across several time scales. We hope to demonstrate that such a system can balance local load and generation in order to minimize expected instability at higher levels of the electrical grid.

This post is available full-time (40 hours/5 days per week) for 12 months, and can begin as early as October 1st.

For more information on this position, please contact Dr. Eswaran Subrahmanian ( or Dr. Spencer Breiner (

Jobs at U.C. Riverside

30 March, 2017

The Mathematics Department of the University of California at Riverside is trying to hire some visiting assistant professors. We plan to make decisions quite soon!

The positions are open to applicants who have PhD or will have a PhD by the beginning of the term from all research areas in mathematics. The teaching load is six courses per year (i.e. 2 per quarter). In addition to teaching, the applicants will be responsible for attending advanced seminars and working on research projects.

This is initially a one-year appointment, and with successful annual teaching review, it is renewable for up to a third year term.

For more details, including how to apply, go here:

Tipping Points in Climate Systems

4 March, 2013

If you’ve just recently gotten a PhD, you can get paid to spend a week this summer studying tipping points in climate systems!

They’re having a program on this at ICERM: the Institute for Computational and Experimental Research in Mathematics, in Providence, Rhode Island. It’s happening from July 15th to 19th, 2013. But you have to apply soon, by the 15th of March!

For details, see below. But first, a word about tipping points… in case you haven’t thought about them much.

Tipping Points

A tipping point occurs when adjusting some parameter of a system causes it to transition abruptly to a new state. The term refers to a well-known example: as you push more and more on a glass of water, it gradually leans over further until you reach the point where it suddenly falls over. Another familiar example is pushing on a light switch until it ‘flips’ and the light turns on.

In the Earth’s climate, a number of tipping points could cause abrupt climate change:

(Click to enlarge.) They include:

• Loss of Arctic sea ice.
• Melting of the Greenland ice sheet.
• Melting of the West Antarctic ice sheet.
• Permafrost and tundra loss, leading to the release of methane.
• Boreal forest dieback.
• Amazon rainforest dieback
• West African monsoon shift.
• Indian monsoon chaotic multistability.
• Change in El Niño amplitude or frequency.
• Change in formation of Atlantic deep water.
• Change in the formation of Antarctic bottom water.

You can read about them here:

• T. M. Lenton, H. Held, E. Kriegler, J. W. Hall, W. Lucht, S. Rahmstorf, and H. J. Schellnhuber, Tipping elements in the Earth’s climate system, Proceedings of the National Academy of Sciences 105 (2008), 1786–1793.

Mathematicians are getting interested in how to predict when we’ll hit a tipping point:

• Peter Ashwin, Sebastian Wieczorek and Renato Vitolo, Tipping points in open systems: bifurcation, noise-induced and rate-dependent examples in the climate system, Phil. Trans. Roy. Soc. A 370 (2012), 1166–1184.

Abstract: Tipping points associated with bifurcations (B-tipping) or induced by noise (N-tipping) are recognized mechanisms that may potentially lead to sudden climate change. We focus here a novel class of tipping points, where a sufficiently rapid change to an input or parameter of a system may cause the system to “tip” or move away from a branch of attractors. Such rate-dependent tipping, or R-tipping, need not be associated with either bifurcations or noise. We present an example of all three types of tipping in a simple global energy balance model of the climate system, illustrating the possibility of dangerous rates of change even in the absence of noise and of bifurcations in the underlying quasi-static system.

We can test out these theories using actual data:

• J. Thompson and J. Sieber, Predicting climate tipping points as a noisy bifurcation: a review, International Journal of Chaos and Bifurcation 21 (2011), 399–423.

Abstract: There is currently much interest in examining climatic tipping points, to see if it is feasible to predict them in advance. Using techniques from bifurcation theory, recent work looks for a slowing down of the intrinsic transient responses, which is predicted to occur before an instability is encountered. This is done, for example, by determining the short-term auto-correlation coefficient ARC in a sliding window of the time series: this stability coefficient should increase to unity at tipping. Such studies have been made both on climatic computer models and on real paleoclimate data preceding ancient tipping events. The latter employ re-constituted time-series provided by ice cores, sediments, etc, and seek to establish whether the actual tipping could have been accurately predicted in advance. One such example is the end of the Younger Dryas event, about 11,500 years ago, when the Arctic warmed by 7 C in 50 years. A second gives an excellent prediction for the end of ’greenhouse’ Earth about 34 million years ago when the climate tipped from a tropical state into an icehouse state, using data from tropical Pacific sediment cores. This prediction science is very young, but some encouraging results are already being obtained. Future analyses will clearly need to embrace both real data from improved monitoring instruments, and simulation data generated from increasingly sophisticated predictive models.

The next paper is interesting because it studies tipping points experimentally by manipulating a lake. Doing this lets us study another important question: when can you push a system back to its original state after it’s already tipped?

• S. R. Carpenter, J. J. Cole, M. L. Pace, R. Batt, W. A. Brock, T. Cline, J. Coloso, J. R. Hodgson, J. F. Kitchell, D. A. Seekell, L. Smith, and B. Weidel, Early warnings of regime shifts: a whole-ecosystem experiment, Nature 332 (2011), 1079–1082.

Abstract: Catastrophic ecological regime shifts may be announced in advance by statistical early-warning signals such as slowing return rates from perturbation and rising variance. The theoretical background for these indicators is rich but real-world tests are rare, especially for whole ecosystems. We tested the hypothesis that these statistics would be early-warning signals for an experimentally induced regime shift in an aquatic food web. We gradually added top predators to a lake over three years to destabilize its food web. An adjacent lake was monitored simultaneously as a reference ecosystem. Warning signals of a regime shift were evident in the manipulated lake during reorganization of the food web more than a year before the food web transition was complete, corroborating theory for leading indicators of ecological regime shifts.

IdeaLab program

If you’re seriously interested in this stuff, and you recently got a PhD, you should apply to IdeaLab 2013, which is a program happening at ICERM from the 15th to the 19th of July, 2013. Here’s the deal:

The Idea-Lab invites 20 early career researchers (postdoctoral candidates and assistant professors) to ICERM for a week during the summer. The program will start with brief participant presentations on their research interests in order to build a common understanding of the breadth and depth of expertise. Throughout the week, organizers or visiting researchers will give comprehensive overviews of their research topics. Organizers will create smaller teams of participants who will discuss, in depth, these research questions, obstacles, and possible solutions. At the end of the week, the teams will prepare presentations on the problems at hand and ideas for solutions. These will be shared with a broad audience including invited program officers from funding agencies.

Two Research Project Topics:

• Tipping Points in Climate Systems (MPE2013 program)

• Towards Efficient Homomorphic Encryption

IdeaLab Funding Includes:

• Travel support

• Six nights accommodations

• Meal allowance

The Application Process:

IdeaLab applicants should be at an early stage of their post-PhD career. Applications for the 2013 IdeaLab are being accepted through

Application materials will be reviewed beginning March 15, 2013.

I’m Looking For Good Math Grad Students

11 December, 2012

I am looking for hardworking math grad students who:

1) know some category theory and ideally a bit of 2-category theory,

2) know some mathematical physics, stochastic processes and/or Bayesian network theory, and

3) want to apply these ideas to subjects like chemistry, biology, ecology and climate science.

If this is you, please email me and/or apply to the math Ph.D. program at U.C. Riverside. To apply, follow the directions here. For more information, go here. The deadline is January 5th.

We have very little money for foreign students, so this advertisement is mainly for students from the US and especially California. If you want to work with me, mention my name in your application.

I can’t promise to work with you, of course, until you’re accepted and I get to know you and decide we can work well together! Luckily there are other good professors in the department doing other interesting things.

I urge would-be students to come to my seminar, which meets once a week, and also my special sessions where we work on projects, which currently also occur once a week. I’ll pick students from among people who do these things. Right now there are 6 candidates. I can’t take this many new students every year, so I’ll pick the ones who show the most initiative and promise.

I’m working on network theory and information theory, and I’m also getting started on climate physics, especially glacial cycles. You can decide if these topics interest you by clicking on the links. I’m not taking students who want to do thesis work on my old interests (quantum gravity and n-categories).

The U.C.R. math building looks 2-dimensional in this shot, but I promise you’ll get a well-rounded education if you work with me.

Graduate Program in Biostatistics

7 November, 2012

Are you an undergrad who likes math and biology and wants a good grad program? This one sounds really interesting. The ad I bumped into is focused on minority applicants, maybe because U.C. Riverside is packed with students whose skin ain’t pale. But I’d say biostatistics is a good career even if you have the misfortune of needing high-SPF sunscreen:    

The Department of Biostatistics, which administers PhD training at the Harvard School of Public Health, seeks outstanding minority applicants for its graduate programs in Biostatistics.

Biostatistics is an excellent career choice for students interested in mathematics applied to real world problems. The current data explosion is contributing to the rising stature of, and demand for biostatisticians, as noted in the New York Times:

I keep saying that the sexy job in the next 10 years will be statisticians … and I’m not kidding.

To date, Biostatistics has not been successful in attracting qualified minority students, particularly African Americans. Students best suited for careers in Biostatistics are those with strong mathematical abilities, combined with interests in health and biology. Unfortunately, statistics is not widely taught at the undergraduate level, and many potentially excellent candidates simply do not learn about the possibility of a valuable and fulfilling career in Biostatistics. Many minority students who could thrive in a Biostatistics program choose instead to enter medical school. Public health in general, and Biostatistics in particular, are not even considered as options. We would like your help in identifying qualified students before they make their choices regarding graduate school or other career paths.

All doctoral students accepted in our department are guaranteed full tuition and stipend support throughout their program, as long as they are making satisfactory progress towards the PhD degree. Every effort is made to meet the individual needs of each student, and to insure the successful completion of graduate work.

The web site for prospective students is here.

Please note the deadline for submitting applications to the MA and PhD programs for entry in the fall of 2013 is December 15, 2012.

We look forward to answering any questions you may have. Questions about our graduate programs can be directed to Jelena Follweiller, at

Bioremediation and Ecological Restoration Job

23 October, 2011

The University of Texas – Pan American (UTPA) Department of Biology is trying to fill an Assistant Professor Faculty position in Bioremediation and Ecological Restoration, which will start in Fall 2012 pending budget approval. They’re looking for someone whose area of research is bioremediation and/or ecological restoration, and they’re especially interested in candidates whose research focuses on environmental issues relevant to the Lower Rio Grande Valley.

For more details, go here.