## May 22, 2013

### Philosophy Talks in Oxford

#### Posted by Simon Willerton

**Guest post by Bruce Bartlett**

On Monday, David Corfield and Kobi Kremnitzer gave philosophy talks in a snazzy new building at Oxford:

- Kobi Kremnitzer, What is geometry?, 2-4pm.
- David Corfield, What might philosophy make of homotopy type theory?, 4.30-6.30pm.

The talks shared homotopy type theory as a common theme. The name “Per Martin-Löf” was mentioned a lot, which was good for me since I had always thought Martin and Löf were two separate people:

Notes are available above, but I will try to give some brief impressions.

### In the News

#### Posted by David Corfield

Applications of category theory are described by Julie Rehmeyer in ScienceNews under the banner

One of the most abstract fields in math finds application in the ‘real’ world.

Now, how about applications in the real world?

## May 17, 2013

### Semantics of Proofs in Paris

#### Posted by John Baez

There’s going to be a “thematic trimester” in Paris starting next spring:

- Semantics of proofs and certified mathematics, Institut Henri Poincaré, April 22nd - July 11th, 2014, organized by Pierre-Louis Curien, Hugo Herbelin, Paul-André Melliès.

If you like applications of category theory to logic and computer science, there should be a lot for you here!

## May 16, 2013

### The Propositional Fracture Theorem

#### Posted by Mike Shulman

Suppose $X$ is a topological space and $U\subseteq X$ is an open subset, with closed complement $K = X\setminus U$. Then $U$ and $K$ are, of course, topological spaces in their own right, and we have $X = U\sqcup K$ as a set. What additional information beyond the topologies of $U$ and $K$ is necessary to enable us to recover the topology of $X$ on their disjoint union?

## May 14, 2013

### Bounded Gaps Between Primes

#### Posted by Tom Leinster

*Guest post by Emily Riehl*

Whether we grow up to become category theorists or applied mathematicians, one thing that I suspect unites us all is that we were once enchanted by prime numbers. It comes as no surprise then that a seminar given yesterday afternoon at Harvard by Yitang Zhang of the University of New Hampshire reporting on his new paper “Bounded gaps between primes” attracted a diverse audience. I don’t believe the paper is publicly available yet, but word on the street is that the referees at the *Annals* say it all checks out.

What follows is a summary of his presentation. Any errors should be ascribed to the ignorance of the transcriber (a category theorist, not an analytic number theorist) rather than to the author or his talk, which was lovely.