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What John did from 2012 to 2015

edited October 2015 in Strategy

I'm applying for a salary increase. The University of California has an elaborate bureaucratic procedure for doing this. Part of what you need to do is write a 2-page "self statement" about your activities. Since a lot of this is connected to Azimuth, I thought I'd post a copy here.

It involves a lot of bragging, and I apologize for that. But it explains a bit of what the Azimuth Project has been doing... which might help us think about what to do next.

I also feel like posting it just to get it out of my mind and move on to the next task.

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1.
edited October 2015

In the Fall of 2012, I returned to U.C. Riverside after a two-year leave working at the Centre for Quantum Technologies, which is affiliated with the National University of Singapore. My research since then has been inspired by this question: what can mathematicians do about climate change? There are many possible answers, but my research illustrates a few.

The Mathematics of Climate. To inform myself and others about the mathematics of climate change, I am helping run an international online collaboration called the Azimuth Project. The others involved tend to be academic mathematicians, physicists and climate scientists together with statisticians and computer programmers from outside academia. Our biggest project has been to redo and check a paper that used network theory methods to predict El Niños. We made the computer code publicly available and explained it on the Azimuth Blog. I discussed this work in a plenary talk at NIPS 2014, the premier conference on neural networks and machine learning. Over 1000 experts on these subjects attended the talk.

As part of the educational mission of the Azimuth Project, I have given different versions of a talk on "The Mathematics of Planet Earth'' at the 55th Annual Congress of the South African Mathematical Society, the 2013 British Mathematical Colloquium, the University of Cambridge, the University of Birmingham, the University of Warwick, the Open University, and the Perimeter Institute. More locally, I gave this talk as the annual Serge Lang Lecture at U.C. Berkeley, and at the University of Southern California and Moreno Valley College. I also gave two talks on climate change at the Balsillie School of International Affairs, which is affiliated with Waterloo University in Canada.

In addition, I published a paper on "Monte Carlo Methods in Climate Science'' with David Tweed of the Azimuth Project, and gave a talk on "The Azimuth Project: an Open-Access Educational Resource'' at the Fall 2012 meeting of the American Geophysical Union.

Information and Entropy. I am fascinated by the potential of thermodynamics and information theory to shed light on seemingly disparate aspects of complex systems. In April 2015, together with the ecologist John Harte of U. C. Berkeley and the evolutionary game theorist Marc Harper, I organized a workshop on Information and Entropy in Biological Systems at the National Institute for Mathematical and Biological Synthesis.

I am a cooperating faculty in the physics department, and am working on these topics with Blake Pollard, a graduate student there. So far we have written two papers together on topics related to entropy, and he has written a third with my help. In 2014 and 2015 he visited me at the Centre for Quantum Technologies, where I continue to work during the summers. I have also written a paper on the concept of "relative entropy" with Tobias Fritz, a physicist at the Perimeter Institute. The overall goal of this project is to develop a rigorous foundation for the thermodynamics of "open systems": that is, systems that interact with their environment.

Network Theory. Currently my main line of research focuses on "network theory": the study of complex systems made of interacting parts. This is important in understand biological systems, ecosystems, but also human-engineered systems such as power grids. My novel contribution is applying category theory - often considered to be the purest of pure mathematics - to these very practical subjects.

In March 2014, I gave a series of four lectures on network theory at the Computer Science Department at the University of Oxford. At the end of May in that year, I helped run a workshop on Categorical Methods at the Crossroads at the computer science conference center in Germany called Schloss Dagstuhl. I ran this with Samson Abramsky and Fabio Gadducci in computer science and Viktor Winschel in economics. Many of the researchers at this workshop were involved in network theory in one way or another. In May 2015, I helped organize a workshop on Categorical Foundations of Network Theory at the Institute for Scientific Interchange in Turin, Italy. Here several researchers presented their visions for how to use category theory to study complex networks, and we came to a good understanding of how research should move forward.

My most important papers in this topic are "Categories in Control'', which applies category theory to a branch of engineering called control theory, "A Compositional Framework for Passive Linear Networks'', which applies it to electrical engineering, and "A Compositional Framework for Markov Processes'', which applies it to random processes. All three were written with graduate students here at U. C. Riverside, and the last also with Brendan Fong, a student I am advising at the University of Oxford. I have also written two papers on chemical reaction networks, one with Fong.

Teaching. I take teaching very seriously. I generally have excellent teaching evaluations for both undergraduate and graduate courses. I run a seminar on my research and have weekly meetings with my graduate students, and I involve them in my research, writing joint-authored papers with them to help "show them the ropes". I also wrote a paper with an undergraduate student, Karine Bagdasaryan, in which together with another mathematician we made progress on an unsolved 100-year-old problem in geometry called the Lebesgue Universal Covering Problem. We recently published this in the Journal of Computational Geometry.

Comment Source:In the Fall of 2012, I returned to U.C. Riverside after a two-year leave working at the Centre for Quantum Technologies, which is affiliated with the National University of Singapore. My research since then has been inspired by this question: _what can mathematicians do about climate change?_ There are many possible answers, but my research illustrates a few. **The Mathematics of Climate.** To inform myself and others about the mathematics of climate change, I am helping run an international online collaboration called the [Azimuth Project](http://www.azimuthproject.org/azimuth/show/HomePage). The others involved tend to be academic mathematicians, physicists and climate scientists together with statisticians and computer programmers from outside academia. Our biggest project has been to redo and check a paper that used network theory methods to predict El Ni&ntilde;os. We made the computer code publicly available and explained it on the [Azimuth Blog](https://johncarlosbaez.wordpress.com/2014/06/20/el-nino-project-part-1/). I discussed this work in a plenary talk at NIPS 2014, the premier conference on neural networks and machine learning. Over 1000 experts on these subjects attended the talk. As part of the educational mission of the Azimuth Project, I have given different versions of a talk on "The Mathematics of Planet Earth'' at the 55th Annual Congress of the South African Mathematical Society, the 2013 British Mathematical Colloquium, the University of Cambridge, the University of Birmingham, the University of Warwick, the Open University, and the Perimeter Institute. More locally, I gave this talk as the annual Serge Lang Lecture at U.C. Berkeley, and at the University of Southern California and Moreno Valley College. I also gave two talks on climate change at the Balsillie School of International Affairs, which is affiliated with Waterloo University in Canada. In addition, I published a paper on "Monte Carlo Methods in Climate Science'' with David Tweed of the Azimuth Project, and gave a talk on "The Azimuth Project: an Open-Access Educational Resource'' at the Fall 2012 meeting of the American Geophysical Union. **Information and Entropy.** I am fascinated by the potential of thermodynamics and information theory to shed light on seemingly disparate aspects of complex systems. In April 2015, together with the ecologist John Harte of U. C. Berkeley and the evolutionary game theorist Marc Harper, I organized a workshop on [Information and Entropy in Biological Systems](http://www.nimbios.org/wordpress-training/entropy/schedule/) at the National Institute for Mathematical and Biological Synthesis. I am a cooperating faculty in the physics department, and am working on these topics with Blake Pollard, a graduate student there. So far we have written two papers together on topics related to entropy, and he has written a third with my help. In 2014 and 2015 he visited me at the Centre for Quantum Technologies, where I continue to work during the summers. I have also written a paper on the concept of "relative entropy" with Tobias Fritz, a physicist at the Perimeter Institute. The overall goal of this project is to develop a rigorous foundation for the thermodynamics of "open systems": that is, systems that interact with their environment. **Network Theory.** Currently my main line of research focuses on "network theory": the study of complex systems made of interacting parts. This is important in understand biological systems, ecosystems, but also human-engineered systems such as power grids. My novel contribution is applying category theory - often considered to be the purest of pure mathematics - to these very practical subjects. In March 2014, I gave a series of four lectures on network theory at the Computer Science Department at the University of Oxford. At the end of May in that year, I helped run a workshop on [Categorical Methods at the Crossroads](http://www.dagstuhl.de/de/programm/kalender/semhp/?semnr=14182) at the computer science conference center in Germany called Schloss Dagstuhl. I ran this with Samson Abramsky and Fabio Gadducci in computer science and Viktor Winschel in economics. Many of the researchers at this workshop were involved in network theory in one way or another. In May 2015, I helped organize a workshop on [Categorical Foundations of Network Theory](http://math.ucr.edu/home/baez/networks_isi/) at the Institute for Scientific Interchange in Turin, Italy. Here several researchers presented their visions for how to use category theory to study complex networks, and we came to a good understanding of how research should move forward. My most important papers in this topic are "Categories in Control'', which applies category theory to a branch of engineering called control theory, "A Compositional Framework for Passive Linear Networks'', which applies it to electrical engineering, and "A Compositional Framework for Markov Processes'', which applies it to random processes. All three were written with graduate students here at U. C. Riverside, and the last also with Brendan Fong, a student I am advising at the University of Oxford. I have also written two papers on chemical reaction networks, one with Fong. **Teaching.** I take teaching very seriously. I generally have excellent teaching evaluations for both undergraduate and graduate courses. I run a seminar on my research and have weekly meetings with my graduate students, and I involve them in my research, writing joint-authored papers with them to help "show them the ropes". I also wrote a paper with an undergraduate student, Karine Bagdasaryan, in which together with another mathematician we made progress on an unsolved 100-year-old problem in geometry called the Lebesgue Universal Covering Problem. We recently published this in the _Journal of Computational Geometry_.