# Category: Mathematics

## Stephen Hawking says he’s solved a black hole mystery, but physicists await the proof

*(latimes.com)*

Physicist Stephen Hawking made a splash this week when he announced that he had solved a vexing conundrum that had puzzled generations of leading physicists -- including the 73-year-old scientific superstar himself -- for the better part of a half-century.

## Algebraic Number Theory | UCLA Extension

### Only Me

Like a kid anxiously awaiting Christmas morning, I spent some time refreshing UCLA Extension’s web page over the weekend in hopes of seeing the announcement of Mike Miller’s Fall math course with no results.

I checked again a half hour ago and their site was down!

### My salivating hit a fever pitch!

Refreshing, refreshing, refreshing… and now it’s live again with:

Mike Miller is teaching Algebraic Number Theory in the Fall!

Register quickly before it fills up. And let the pool for the guesses about which textbook he’ll recommend begin!

## Algebraic Number Theory

MATH X 450.8 | 3.00 units

In no field of mathematics is there such an irresistible fascination as in the theory of numbers. This course, the first in a two-quarter sequence, is an introductory, yet rigorous, survey of algebraic number theory, which evolved historically through attempts to prove Fermat’s Last Theorem. Beginning with a quick review of primality and unique factorization for ordinary integers, the course extends these notions to more exotic domains: quadratic, cubic, cyclotomic, and general number fields. This development is then applied to the representation of integers as sums of squares and, more generally, to classic Diophantine equations. Topics to be discussed include: Euclidean, principal ideal, and Noetherian domains; integral bases; binary quadratic forms; algebraic field extensions; and several remarkable theorems/conjectures of Ramanujan.

UCLA: 5137 Math Sciences

Tuesday, 7-10pm,

September 22 – December 8

11 meetings total

(no mtg 11/17)

See you all in just a few weeks!

## A Note For the Reticent

### Exercise Your Brain

As many may know or have already heard, Dr. Mike Miller, a retired mathematician from RAND and long-time math professor at UCLA, has been offering incredibly inexpensive upper level undergraduate and graduate level math courses for 30+ years through UCLA Extension.

Whether you’re a professional mathematician, engineer, physicist, physician, or simply a hobbyist interested in mathematics you’ll be sure to get something interesting out of this course, not to mention the camaraderie of 20-30 other “regulars” with widely varying backgrounds (actors to surgeons and evolutionary theorists to engineers) who’ve been taking almost everything Mike has offered over the years. Once most new students have taken one class, they’re incredibly prone to want to take them all (and yes, he’s THAT good — we’re sure you’ll be addicted too.)

### “Beginners” Welcome!

Even if it’s been years since you last took calculus or linear algebra, Mike (and usually the rest of the class) will help you get quickly back up to speed to delve into what is often a very deep subject. Though there are a handful who will want to learn the subject for specific applications, naturally, it’s simply a beautiful and elegant subject for those who just want to meander their way through higher mathematics for the fun of it (this will probably comprise the largest majority of the class by the way.)

Whether you’ve been away from serious math for decades or use it every day or even if you’ve never gone past calculus, this is bound to be the most entertaining thing you can do with your Tuesday nights in the fall. If you’re not sure what you’re getting into (or are scared a bit by the course description), **I highly encourage to come and join us for at least the first class before you pass up on the opportunity** – there’s no need to preregister or prepay if you’re unsure. I’ll mention that the greater majority of new students to Mike’s classes join the ever-growing group of regulars who take almost everything he teaches subsequently.

For the reticent, I’ll mention that one of the first courses I took from Mike was Algebraic Topology which generally requires a few semesters of Abstract Algebra and a semester of Topology as prerequisites. I’d taken neither of these prerequisites, but due to Mike’s excellent lecture style and desire to make everything comprehensible to the broadest number of students, I was able to do exceedingly well in the course. Also keep in mind that you can register to take the class for a grade, pass/fail, or even no grade at all to suit your needs/lifestyle.

## Textbook: Introductory Algebraic Number Theory

*Update (8/19/15)* Per my email conversation with Dr. Miller, despite that neither the Extension website nor the bookstore have a book listed for the class yet, he’s going to be recommending *Introductory Algebraic Number Theory* by Saban Alaca and Kenneth S. Williams (Cambridge University Press, 2003, ISBN: 978-0521183048).

## I’m a sucker for references to math and pastry

## The Math That Connects Pluto to DNA — NOVA Next | PBS

*(NOVA Next | PBS)*

How a mathematical breakthrough from the 1960s now powers everything from spacecraft to cell phones.

## Game Theory’s Tit-for-Tat is Just a Mathematically Complete Version of Religion’s Golden Rule

## Why Information Grows: The Evolution of Order, from Atoms to Economies

From the book description:

“What is economic growth? And why, historically, has it occurred in only a few places? Previous efforts to answer these questions have focused on institutions, geography, finances, and psychology. But according to MIT’s antidisciplinarian César Hidalgo, understanding the nature of economic growth demands transcending the social sciences and including the natural sciences of information, networks, and complexity. To understand the growth of economies, Hidalgo argues, we first need to understand the growth of order.

At first glance, the universe seems hostile to order. Thermodynamics dictates that over time, order–or information–will disappear. Whispers vanish in the wind just like the beauty of swirling cigarette smoke collapses into disorderly clouds. But thermodynamics also has loopholes that promote the growth of information in pockets. Our cities are pockets where information grows, but they are not all the same. For every Silicon Valley, Tokyo, and Paris, there are dozens of places with economies that accomplish little more than pulling rocks off the ground. So, why does the US economy outstrip Brazil’s, and Brazil’s that of Chad? Why did the technology corridor along Boston’s Route 128 languish while Silicon Valley blossomed? In each case, the key is how people, firms, and the networks they form make use of information.

Seen from Hidalgo’s vantage, economies become distributed computers, made of networks of people, and the problem of economic development becomes the problem of making these computers more powerful. By uncovering the mechanisms that enable the growth of information in nature and society, Why Information Grows lays bear the origins of physical order and economic growth. Situated at the nexus of information theory, physics, sociology, and economics, this book propounds a new theory of how economies can do, not just more, but more interesting things.”

## How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics | Category Theory

*How to Bake Pi: An Edible Exploration of the Mathematics of Mathematics*.

It just came out in the U.S. market on May 5, 2015, so it’s very new in the market. My guess is that even those who aren’t intimidated will get a lot out of it as well. A brief description of the book follows:

“What is math? How exactly does it work? And what do three siblings trying to share a cake have to do with it? In How to Bake Pi, math professor Eugenia Cheng provides an accessible introduction to the logic and beauty of mathematics, powered, unexpectedly, by insights from the kitchen: we learn, for example, how the béchamel in a lasagna can be a lot like the number 5, and why making a good custard proves that math is easy but life is hard. Of course, it’s not all cooking; we’ll also run the New York and Chicago marathons, pay visits to Cinderella and Lewis Carroll, and even get to the bottom of a tomato’s identity as a vegetable. This is not the math of our high school classes: mathematics, Cheng shows us, is less about numbers and formulas and more about how we know, believe, and understand anything, including whether our brother took too much cake.

At the heart of How to Bake Pi is Cheng’s work on category theory—a cutting-edge “mathematics of mathematics.” Cheng combines her theory work with her enthusiasm for cooking both to shed new light on the fundamentals of mathematics and to give readers a tour of a vast territory no popular book on math has explored before. Lively, funny, and clear, How to Bake Pi will dazzle the initiated while amusing and enlightening even the most hardened math-phobe.”

Dr. Cheng recently appeared on NPR’s Science Friday with Ira Flatow to discuss her book. You can listen to the interview below. Most of the interview is about her new book. Specific discussion of category theory begins about 14 minutes into the conversation.

Dr. Eugenia Cheng can be followed on Twitter @DrEugeniaCheng. References to her new book as well as some of her syllabi and writings on category theory have been added to our Category Theory resources pages for download/reading.

## The Category Theory Site Is Now Live

## Platform Choice

I’ve made a few posts here [1] [2] about a summer study group for category theory. In an effort to facilitate the growing number of people from various timezones and differing platforms (many have come to us from Google+, Tumblr, Twitter, GoodReads, and friends from Dr. Miller’s class in a private Google Group), I’ve decided it may be easiest to set up something completely separate from all of these so our notes, resources, and any other group contributions can live on to benefit others in the future. Thus I’ve built Category Theory: Summer Study Group 2015 on WordPress. It will live as a sub-domain of my personal site until I get around to buying a permanent home for it (any suggestions for permanent domain names are welcome).

## Registration

We’ve actually had a few people already find the new site and register before I’ve announced it, but for those who haven’t done so yet, please go to our participant registration page and enter your preferred username and email address. We’ll email you a temporary password which you can change when you login for the first time. Those who want to use their pre-existing WordPress credentials are welcome to do so.

Once you’ve registered, be sure to update your profile (at least include your name) so that others will know a little bit more about you. If you’d like you can also link your WordPress.com account [or sign up for one and then link it] so that you can add a photo and additional details. To login later, there’s a link hidden in the main menu under “Participants.”

You can also add your details to the form at the bottom of the Participants page to let others know a bit more about you and where you can be reached. Naturally this is optional as I know some have privacy issues. In the notes, **please leave your location/timezone** so that we can better coordinate schedules/meetings.

## Category Theory Blog

Your username/password will allow you to post content directly to the study group’s blog. This can be contributed notes, questions, resources, code, photos, thoughts, etc. related to category theory and related areas of mathematics we’ll be looking at. Initially your posts will be moderated (primarily only to prevent spam), and over time your status will be elevated to allow immediate posting and editing. If you have any questions or need administrative help, I’m easy to find and happy to help if you get into trouble. Most of the interface will hopefully be easy to understand.

For those with questions, please try to read posts as you’re able and feel free to comment with hints and/or solutions. I’ve created “categories” with the chapter titles from the text we’re using to facilitate sorting/searching. Depending on the need, we can granularize this further as we proceed. There is also the ability to tag posts with additional metadata or upload photos as well.

As appropriate, I’ll take material out of the blog/posts stream and place it into freestanding pages for easier reference in the future. As an example, I’ve already found some material on YouTube and MIT’s Open Course Ware site (Spivak posted his 2013 class using our same text, though it unfortunately doesn’t include video or audio) that may be relevant to many.

For those interested, WordPress supports most basic LaTeX, though I doubt it supports any of the bigger category theory diagramming packages, so feel free to draw out pictures/diagrams, photograph them, and upload them for others to see if necessary.

As an advocate of the open web and owning one’s own data, I highly recommend everyone publish/post their content here as well as to their favorite site/platform of choice as they see fit.

## Textbook

In emails and chatter around the web, I haven’t heard any major objections to the proposed textbook so far, so unless there are, I’m assuming that it should serve most of us well. Hopefully everyone has a copy by now (remember there are free versions available) and has begun reading the introductory material. Those requiring a bit more mathematical rigor and challenge can supplement with additional texts as I’m sure I and many others will. If you’re posting questions to the site about problems/questions from other texts, please either state them explicitly or tag them with the author’s last name as well as the problem/exercise number. (I’ll try to make them all canonical on the back end as we progress, so don’t worry too much if you’re not sure how or what to tag them with.)

## Conference Call Tool

At the moment, most people have been fairly open to the three big platforms, though a few on either Linux or Chromebooks don’t have access to be able to install/operate anything but Google Hangouts, so I’m presently proposing that we adopt it for our group. Nearly everyone in the group already has a gmail account, so I don’t expect it to be an undue burden. If you haven’t used it before, please download/install any plugins you may require for your platform in advance of our first “call.”

## Meeting Times

I’ve only heard back from a small handful of people on availability so far, but it doesn’t look like it will be difficult to find an appropriate time. If you haven’t already done so, please fill out the “survey,” so we can determine a good call time for next week. If necessary, we can do additional times to help serve everyone’s needs. We don’t want to leave out any who sincerely want to participate.

## Office Hours

As most of the participants are spread over the United States, Europe, and Asia, I’m suggesting that everyone carve out a standing block of time (we can call them “office hours”) that they can use to be available (via Google Hangouts or otherwise) to help out others having difficulty or who have questions. Since there isn’t a “professor” I’m hoping that we can all serve each other as unofficial teaching assistants to get through the process, and having standing office hours may be the easiest way to catch others for help in addition to the web site itself.

## Questions? Comments? Snide Remarks?

If you have any questions, or I’ve managed to miss something, please don’t hesitate to make a comment below. I’m hoping to get enough responses by Friday/Saturday this week to post our first meeting time for next week.

## Commutative Diagrams in LaTeX

## Overview

With my studies in category theory trundling along, I thought I’d take moment to share some general resources for typesetting commutative diagrams in . I’ll outline below some of the better resources and recommendations I’ve found, most by much more dedicated and serious users than I. Following that I’ll list a few resources, articles, and writings on some of the more common packages that I’ve seen mentioned.

Naturally, just reading through some of the 20+ page user guides to some of these packages can be quite daunting, much less wading through the sheer number that exist. Hopefully this one-stop-shop meta-overview will help others save some time trying to figure out what they’re looking for.

### Feruglio Summary

Gabriel Valiente Feruglio has a nice overview article naming all the primary packages with some compare/contrast information. One will notice it was from 1994, however, and misses a few of the more modern packages including TikZ. His list includes: AMS; Barr (diagxy); Borceux; Gurari; Reynolds; Rose (XY-pic); Smith (Arrow); Spivak; Svensson (kuvio); Taylor (diagrams); and Van Zandt (PSTricks). He lists them alphabetically and gives brief overviews of some of the functionality of each.

Feruglio, Gabriel Valiente. *Typesetting Commutative Diagrams.* TUGboat, Volume 15 (1994), No. 4

### Milne Summary

J.S. Milne has a fantastic one-page quick overview description of several available packages with some very good practical advise to users depending on the level of their needs. He also provides a nice list of eight of the most commonly used packages including: array (LaTeX); amscd (AMS); DCpic (Quaresma); diagrams (Taylor); kuvio (Svensson); tikz (Tantau); xymatrix (Rose); and diagxy (Barr). It’s far less formal than Feruglio, but is also much more modern. I also found it a bit more helpful for trying to narrow down one or more packages with which to play around.

Milne, J.S. *Guide to Commutative Diagram Packages*.

### Spivak Pseudo-recommendations

David Spivak, the author of *Category Theory for the Sciences*, seems to prefer XY-pic, diagXY, and TikZ based on his website from which he links to guides to each of these.

## Resources for some of the “Bigger” Packages

Based on the recommendations given in several of the resources above, I’ve narrowed the field a bit to some of the better sounding packages. I’ve provided links to the packages with some of the literature supporting them.

### Diagxy: Michael Barr

- CTAN Package
- Brief four page introduction
- Barr, Michael.
*A new diagram package*. (Version 2011-06-18)

### XY-pic: Kristoffer Rose & Ross Moore

- CTAN Package
- XY-pic User Guide
- Blaga, Paul A.
*Commutative Diagrams with XY-pic I. Kernel Functions and Arrows*. The PracTEX Journal, Draft of November 16, 2006.

### Diagrams: Paul Taylor

### TikZ-CD: Florêncio Neves

- CTAN Package
- TikZ-CD Package Documentation:
*{tikzcd} Commutative diagrams with TikZ*. Version 0.9e; October 30, 2014. - Lenders, Felix.
*Commutative Diagrams using TikZ*. April 12, 2012.

#### Is there a particular package you recommend? Feel free to add your thoughts, comments, and additional resources in the comments below.

## Category Theory Summer Study Group 2015

## Syllabus

Initial details for putting the group together can be found at http://boffosocko.com/2015/05/21/category-theory-anyone/.

Below is a handful of suggestions and thoughts relating to the study group in terms of platforms to assist us in communicating as well as a general outline for the summer. I’m only “leading” this in the sense that I put my foot forward first, but I expect and sincerely hope that others will be active leaders and participants as well, so please take the following only as a suggestion, and feel free to add additional thoughts and commentary you feel might help the group.

## Primary resources:

### General Communication

Since many within the group are already members of the Google Group “Advanced Physics & Math – Los Angeles.” I suggest we use the email list here as a base of communication. I believe the group is still “private” but am happy to invite the handful of participants who aren’t already members. Those actively participating are encouraged to change their settings so that they receive emails from the group either as they’re posted, or in batches once a day. Those subscribed only once a week or less frequently are likely to miss out on questions, comments, and other matters.

Alternately we might also use the GoodReads.com discussion group within the “Mathematics Students” group. I believe only about three of us so far may already be goodreads members, so this may require more effort for others to join.

If anyone has an alternate platform suggestion for communicating and maintaining resources, I’m happy to entertain it.

I wouldn’t be opposed to setting up a multi-user WordPress site that we could all access and post/cross-post to. Doing this could also allow for use of as well, which may be useful down the line. This would also have the benefit of being open to the public and potentially assisting future students. It also has built-in functionality of notifying everyone of individual posts and updates as they’re entered.

### Meetings

I’ll propose a general weekly meeting online via Google Hangouts on a day and time to be determined. It looks like the majority of respondents are in the Pacific timezone, so perhaps we could shoot for something around 7pm for an hour or so if we do something during weekdays so that East coasters can join without us running too late. If we decide to do something during the weekend, we obviously have a good bit more flexibility.

If we could have everyone start by indicating which days/times absolutely won’t work for them and follow up with their three to four preferred days/times, then we might be able to build a consensus for getting together.

Alternate videoconference options could include Skype, ooVoo, or others, in some part because I know that most participants are already part of the Google ecosystem and know that one or more potential participants is using Google Chromebooks and thus may not be able to use other platforms. Is anyone not able to use Google Hangouts? If we opt for something else, we want something that is ubiquitous for platform, allows screen sharing, and preferably the ability to record the sessions for those who aren’t present.

Ideally the videoconference meetings will be geared toward an inverted classroom style of work in which it would be supposed that everyone has read the week’s material and made an attempt at a number of problems. We can then bring forward any general or specific conceptual problems people may be having and then work as a group toward solving any problems that anyone in the group may be having difficulty with.

I’ll also suggest that even if we can’t all make a specific date and time, that we might get together in smaller groups to help each other out. Perhaps everyone could post one or two regular hours during the week as open “office hours” so that smaller groups can discuss problems and help each other out so that we can continue to all make progress as a group.

## Primary Textbook

**Spivak, David I. Category Theory for the Sciences. (The MIT Press, 2014)**

Given the diversity of people in the group and their backgrounds, I’ll suggest Spivak’s text which has a gentle beginning and is geared more toward scientists and non-professional mathematicians, though it seems to come up to speed fairly quickly without requiring a large number of prerequisites. It also has the benefit of being free as noted below.

The textbook can be purchased directly through most book retailers. Those looking for cheaper alternatives might find these two versions useful. The HTML version should be exactly in line with the printed one, while the “old version” may not be exactly the same.

- Old version:
*arxiv.org/abs/1302.6946* - HTML version:
*mitpress.mit.edu/books/category-theory-sciences*

Following this, I might suggest we use something like Awody’s text or Leinster’s which are slightly more technical, but still fairly introductory. Those who’d like a more advanced text can certainly supplement by reading portions of those texts as we work our way through the material in Spivak. If all of the group wants a more advanced text, we can certainly do it, but I’d prefer not to scare away any who don’t have a more sophisticated background.

## Additional References

- Adámek, Jirí & Herrlich, Horst & Strecker, George E.
*Abstract and Concrete Categories, The Joy of Cats.*(Wiley, 2000) & (Dover, 2009) & (Free downloadable version from authors, 2004) - Awody, Steve.
*Category Theory**(Oxford Logic Guides, #52)*. (Oxford University Press, 2nd Edition, 2010) - Lawvere, F. William & Schanuel, Stephen H.
*Conceptual Mathematics: A First Introduction to Categories*. (Cambridge University Press, 2nd Edition, 2009) - Leinster, Tom.
*Basic Category Theory**(Cambridge Studies in Advanced Mathematics, #143).*(Cambridge University Press, 2014) - Mac Lane, Saunders.
*Categories for the Working Mathematician**(Graduate Texts in Mathematics, #5).*(Springer, 2nd Edition, 1998)

## Proposed Schedule

The following schedule takes us from now through the end of the summer and covers the entirety of the book. Hopefully everyone will be able to participate through the end, though some may have additional pressures as the beginning of the Fall sees the start of other courses. Without much prior experience in the field myself, I’ve generally broken things up to cover about 35 pages a week, though some have slightly more or less. Many, like me, may feel like the text really doesn’t begin until week three or four as the early chapters provide an introduction and cover basic concepts like sets and functions which I have a feeling most have at least some experience with. I’ve read through chapter two fairly quickly already myself. This first easy two week stretch will also give everyone the ability to settle in as well as allow others to continue to join the group before we make significant headway.

If anyone has more experience in the subject and wishes to comment on which sections we may all have more conceptual issues with, please let us know so we can adjust the schedule as necessary. I suppose we may modify the schedule as needed going forward, though like many of you, I’d like to try to cover as much as we can before the end of the summer.

*Week One: May 24 (24 pages)*

Administrative tasks

- Purchase Textbook
- Decide on best day/time for meeting
- Decide on platform for meetings: Google Hangouts /Skype /ooVoo /Other

- 1 A brief history of category theory
- 1.2 Intention of this book
- 1.3 What is requested from the student
- 1.4 Category theory references
- 2 The Category of Sets 9
- 2.1 Sets and functions
- 2.2 Commutative diagrams

*Week Two: May 31 (50 pages)*

- 2.3 Ologs
- 3 Fundamental Considerations in Set 41
- 3.1 Products and coproducts
- 3.2 Finite limits in Set

*Week Three: June 7 (40 pages)*

- 3.3 Finite colimits in Set
- 3.4 Other notions in Set

*Week Four: June 14 (31 pages)*

- 4 Categories and Functors, Without Admitting It 115
- 4.1 Monoids
- 4.2 Groups

*Week Five: June 21 (38 pages)*

- 4.3 Graphs
- 4.4 Orders

*Week Six: June 28 (19 pages)*

- 4.5 Databases: schemas and instances

*Week Seven: July 5 (36 pages)*

- 5 Basic Category Theory 203
- 5.1 Categories and functors

*Week Eight: July 12 (28 pages)*

- 5.2 Common categories and functors from pure math

*Week Nine: July 19 (48 pages)*

- 5.3 Natural transformations
- 5.4 Categories and schemas are equivalent, Cat » Sch

*Week Ten: July 26 (45 pages)*

- 6 Fundamental Considerations of Categories
- 6.1 Limits and colimits

*Week Eleven: August 2 (15 pages)*

- 6.2 Other notions in Cat

*Week Twelve: August 9 (26 pages)*

- 7 Categories at Work 375
- 7.1 Adjoint functors

*Week Thirteen: August 16 (32 pages)*

- 7.2 Categories of functors

*Week Fourteen: August 23 (19 pages)*

- 7.3 Monads

*Week Fifteen: August 30 (23 pages)*

- 7.4 Operads

## Additional resources

## Requested/Required Responses from participants:

### Preferred platform(s) for communications:

#### Email and/or online discussions

Platform | Can use | Can’t use | Prefer Not to Use |

Google Group | |||

WordPress Site | |||

GoodReads Group | |||

Other: |

#### Videoconferences

Platform | Can use | Can’t use | Prefer Not to Use |

Google Hangouts | |||

Skype | |||

ooVoo | |||

Other |

Dates and times you absolutely CAN’T make for meetings (please include your local time zone):

Weekdays:

Weekends:

Dates and times you prefer (please include your local time zone):

Weekdays:

Weekends:

One or two time periods during the week you could generally/reliably be available for “office hours”:

Any other thoughts on the material above:

- Textbooks
- Schedule
- Additional resources for the group
- Other

If you’d like to join us, please fill out the contact information and details below based on the material above:

## 8th Annual North American School of Information Theory (NASIT)

*(nasit15.ucsd.edu)*

Application deadline: June 7, 2015

The School of Information Theory will bring together over 100 graduate students, postdoctoral scholars, and leading researchers for four action-packed days of learning, stimulating discussions, professional networking and fun activities, all on the beautiful campus of the University of California, San Diego (UCSD) and in the nearby beach town of La Jolla.

- Tutorials by some of the best known researchers in information theory and related fields
- Poster presentations by student participants with feedback and discussion
- Panel discussion on “IT: Academia vs. Industry Perspectives”
- Social events and fun activities

## BIRS Workshop: Advances and Challenges in Protein-RNA: Recognition, Regulation and Prediction (15w5063)

*(Banff International Research Station | birs.ca)*

BIRS 5 day worksop, arriving in Banff, Alberta Sunday, June 7 and departing Friday, June 12, 2015

In the years since the first assembly of the human genome, the complex and vital role of RNA and RNA binding proteins in regulation of the genome expression has expanded through the discovery of RNA-binding proteins and large classes of non-coding RNA that control many developmental decisions as part of protein- RNA complexes. Our molecular level understanding of RNA regulation has dramatically improved as many new structures of RNA–protein complexes have been determined and new sophisticated experimental technologies and dedicated computational modeling have emerged to investigate these interactions at the whole-genome level. Further deep insight on the molecular mechanisms that underline genome expression regulation is critical for understanding fundamental biology and disease progression towards the discovery of new approaches to interfere with disease progression.

The proposed workshop will bring together experts in RNA biology with structural biologists that focus on RNA-protein complexes, as well as computational biologists who seek to model and develop predictive tools based on the confluence of these experimental advances. The workshop intends to foster new collaborations between experimental and computational biologists and catalyze the development of new and improved technologies (such as single cell binding methods) that merge experimental analysis with novel mathematical and computational techniques to better understand the rules of protein-RNA recognition and RNA-based biological regulation.

The organizers of the workshop are both leaders in the field of protein-RNA recognition and interactions: Yael Mandel-Gutfreund has been working in the field of protein-Nucleic Acids interactions since 1994. Her main research interest is protein-RNA recognition and regulation. She has developed several tools and web servers for predicting RNA binding proteins and RNA binding motifs. Yael is the head to the computational molecular laboratory at the Technion and the president of the Israeli society of Bioinformatics and Computational Biology. Gabriele Varani has been working in the field of RNA structure and protein-RNA interactions since 1987. His main research interest is the structural basis for protein-RNA recognition and the prediction and design of RNA-binding proteins. He determined some of the first few structures of protein-RNA complexes and developed computational tools to analyze and predict the specificity of RNA -binding proteins. His group applies these tools to design RNA-binding proteins with new specificity to control gene expression. Our invitation to participate in the workshop has been met with great enthusiasm by the researchers. More than 20 principle investigators have already confirmed their interest in attending. Six of the confirmed participants are female scientists including the organizer Yael Mandel-Gutfreund as well as Traci Hall, Lynne Maquat, Elena Conti, Susan Jones, Drena Dobbs. We also have invited and confirmed the participation of young and promising researchers including Markus Landthaler, Gene Yeo, Jernej Ule, Uwe Ohler and others. Our confirmed participants come from many different countries: US, Canada, UK, Scotland, Germany, Spain, Switzerland, Poland and Israel. Two confirmed participants as well as the organizer have attended the BIRS workshops in the past.

A key objective of the workshop is to bring together researchers with experimental, mathematical and computational background to share results and discuss the main advances and challenges in the prediction, analysis and control of RNA-protein recognition and RNA-based regulation of gene expression. Towards this aim, we plan to adopt the format of previous BIRS meetings in which invited participants (including selected students) will present relatively short presentations of 20 minutes plus 10 minutes of active discussions. This format will leave aside ample time for informal discussions to foster exchanges between participants. To stress the collaborative, multidisciplinary nature of the workshop, we plan to dedicate each of the workshop sessions to a specific topic that will comprise presentations of structural, experimental and computational approaches, rather than create session focused on a particular approach. Each session we will include at least one lecture from a young scientist/postdoctoral fellow/student to be chosen among attendees by the organizers.

Suggested preliminary schedule:

- Day 1: Modeling and high throughput approaches to genome-wide analysis of protein-RNA interactions
- Day 2: Predicting and designing new RNA binding proteins
- Day 3: Generating and modeling RNA-based regulatory networks
- Day 4: Principles of RNA regulation by RNA binding proteins
- Day 5: Conclusion round table discussion on the present and future challenges of the field

## The Information Universe Conference

I’ll let their site speak for itself below, but they already have an interesting line up of speakers including:

### Keynote speakers

- Erik Verlinde, Professor Theoretical Physics, University of Amsterdam, Netherlands
- Alex Szalay, Alumni Centennial Professor of Astronomy, The Johns Hopkins University, USA
- Gerard ‘t Hooft, Professor Theoretical Physics, University of Utrecht, Netherlands
- Gregory Chaitin, Professor Mathematics and Computer Science, Federal University of Rio de Janeiro, Brasil
- Charley Lineweaver, Professor Astronomy and Astrophysics, Australian National University, Australia
- Lude Franke, Professor System Genetics, University Medical Center Groningen, Netherlands

### Conference synopsis from their homepage:

Additional details about the conference including the participants, program, venue, and registration can also be found at their website.

## Category Theory Anyone?

I’m putting together a study group for an introduction to category theory. Who wants to join me?

Usually in the Fall and Winter, I’m concentrating on studying some semblance of abstract mathematics with a group of 20-30 kamikaze amateurs under the apt tutelage of Dr. Michael Miller through UCLA Extension. Since he doesn’t offer any classes in the Spring or Summer and we haven’t managed to talk Terence Tao into offering something interesting *à la* Leonard Susskind, we’re all at a loss for what to do with some of our time.

A small cohort of regulars from Miller’s class has recently taken up plowing through Howard Georgi’s *Lie Algebras and Particle Physics*. Though this seems very diverting to me given our work on Lie groups and algebras in the Fall and Winter, I don’t see any direct or exciting applications to anything more immediate.

## Why Not Try Category Theory?

Since the death of Grothendieck I have seen a growing number of references to the area of category theory from a variety of different fronts.

Most notably, for the past year I’ve been more closely following John Baez’s Azimuth Blog which has frequent posts relating to category theory with applications I can directly use in various areas. Unfortunately I couldn’t attend his recent workshop at NIMBioS on Information and Entropy in Biological Systems, which apparently means I missed meeting Tom Leinster who recently released the textbook *Basic Category Theory* (Cambridge University Press, 2014). [I was already never going to forgive myself after I missed the workshop, but this fact now seems to be additional salt in the wound.]

The straw that broke the proverbial camel’s back was my serendipitously stumbling across Ilyas Khan‘s excellent post “Category Theory – the bedrock of mathematics?” while doing a Google image search for something entirely unrelated to anything remotely similar to mathematics. His discussion and the breadth of links to interesting and intriguing papers and articles within it and several colleagues thanking me for posting about it have finally forced my hand. (I also find myself wishing that he would write on a more formal basis more frequently.)

So over the past week or so, I’ve done some basic subject area searching, and I’ve picked up David I. Spivak’s book *Category Theory for the Sciences* (The MIT Press, 2014) to begin plowing through it.

## Anyone Care to Join Me?

Since doing abstract math is always more fun with companions, and I know there are several out there who might be interested in some of the areas which category theory touches on, why don’t you join in? Over the coming months of Summer, let’s plot a course through the subject. I’ll suggest Spivak’s book first as it seems to be one of the most basic as well as the broadest out there in terms of applications. (There are also free copies of versions available through arXiv and MIT.) It doesn’t have a huge list of prerequisites either, so a broader category of people might be able to join in as well.

We can have occasional weekly or bi-weekly “meetings” via internet using something like Google Hangouts, Skype, or ooVoo to discuss problems and help each other out as necessary. Ideally those who join will spend at least 3 hours a week, if not more reading the text and working through problems. Following Spivak, we might try dipping into Leinster, Awody, or Mac Lane.

From the author of *Category Theory for the Sciences*:

### References

Awody, Steve. *Category Theory (Oxford Logic Guides, #52)*. (Oxford University Press, 2nd Edition, 2010)

Lawvere, F. William & Schanuel, Stephen H. *Conceptual Mathematics: A First Introduction to Categories*. (Cambridge University Press, 2nd Edition, 2009)

Leinster, Tom. *Basic Category Theory (Cambridge Studies in Advanced Mathematics, #143).* (Cambridge University Press, 2014)

Mac Lane, Saunders. *Categories for the Working Mathematician (Graduate Texts in Mathematics, #5).* (Springer, 2nd Edition, 1998)

Spivak, David I. *Category Theory for the Sciences*. (The MIT Press, 2014)

If you’d like to join us, please leave a comment below and be sure to include your email address in the comment form so we can touch base regarding details.