**The New York City**

**Category Theory Seminar**

**
Department of Computer Science**

Department of Mathematics

The Graduate Center of The City University of New York

365 Fifth Avenue (at 34th Street) map

(Diagonally across from the Empire State Building)

New York, NY 10016-4309

Wednesdays 7:00 - 8:30 PM.

Room 6417 .

Contact N. Yanofsky to
schedule a speaker

or to add a name to the
seminar mailing list.

**Spring 2017 **

The New York Category Theory Seminar and the New York Haskell Meetup is sponsoring a

**Topos Theory Reading Group**

We will be reading **
**## Sheaves in Geometry and Logic: A First Introduction to Topos Theory

by Saunders MacLane, Ieke Moerdijk

The list for announcements and scheduling regarding this group is also at the hott-nyc google group:

https://groups.google.com/forum/#!forum/hott-nyc

We meet the first and third Wednesdays of each month from 7:00 to 8:30 PM in Room 6417. The meetings are run by Gershom Bazerman.

Speaker: ** David Ellerman
University of California at Riverside**

Date and Time: ** Wednesday January 18, 2017, 7:00 - 8:30 PM., Room 6417.**

Title:** From Abstract Objects in Mathematics to
Indefinite ''Blobs'' in Quantum Mechanics
**** Abstract: **** Given an equivalence relation ~ on a set U, an abstraction operator @ takes two equivalent entities to the same abstract thing: u~u' iff @(u)=@(u'). In mathematics there two different notions of 'abstraction' at work. The #1 version is just the equivalence class, e.g., a homotopy type is just the equivalence class of homotopic spaces. The #2 version is a more abstract object that is, for example, definite on what is common to all the spaces homotopic to each other but is indefinite on where they differ.
**

We show how to mathematically model the two versions starting just with a subset S of U and then focus on the less familiar #2 interpretation where S is viewed not as a set of distinct elements but as a more abstract entity 'S-ness' that is definite on what is common between the elements of S and indefinite on how they differ.
The point is that the #2 case dovetails precisely with the quantum mechanics notion of a superposition of distinct eigenstates of some observable which is a state definite only on what is common to the superposed eigenstates and is objectively or onticly indefinite between them. The process in general of classifying by some attribute to make the #2 indefinite state more definite then emerges as the process of measurement in QM.

** Speaker: **** Raymond Puzio.** **
**

Date and Time: ** Wednesday February 1, 2017, 7:00 - 8:30 PM., Room 6417.**

Title:** Topos Theory Reading Group --- Slice Categories. **

Speaker: ** Gershom Bazerman.**

Date and Time: ** Wednesday March 8, 2017, 7:00 - 8:30 PM., Room 6417.**

Title:** Topos Theory Reading Group --- Lattice and Heyting algebra objects in a topos. **

Speaker: ** Mikael Vejdemo-Johansson, College of Staten Island.**

Date and Time: ** Wednesday March 29, 2017, 7:00 - 8:30 PM., Room 6417.**

Title:** Persistent homology and the persistence topos. **

Abstract: ** Persistent homology is a fundamental technique in topological data analysis, summarizing the variations in homology groups in a parametrized topological space as the parameter sweeps through all valid values. Since the first definition of persistent homology in 2000, several algebraic frameworks have been proposed to capture the underlying ideas of persistent homology. For each new framework, the scope of data analyses possible has increased.
**

Joint with Primoz Skraba and Joao Pita Costa, we have developed a topos-based foundation for persistent homology, where the underlying Heyting algebra P captures the *shape* of the persistent homology theory, and persistent homology emerges as the internal theory of (semi)simplicial homology within the set theory determined by the topos of sheaves over P.

In this talk, I will give an introduction to persistent homology, and demonstrate how the theory fits with a topos-based foundation.

** Speaker: **** Raymond Puzio.** **
**

Date and Time: ** Wednesday April 5, 2017, 7:00 - 8:30 PM., Room 6417.**

Title:** Topos Theory Reading Group --- Lawvere-Tierney topologies. **

Speaker: ** Noson Yanofsky, Brooklyn College and The GC.**

Date and Time: ** Wednesday May 10, 2017, 7:00 - 8:30 PM., Room 6417.**

Title:** Theoretical Computer Science for the Working Category Theorist. **

Abstract: ** We will describe certain
categories of computable functions and categories of models of computations such as Turing machines,
circuits, and register machines. There will be functors between these various categories.
Surprisingly, many of the results of computability theory, complexity theory, and Kolmogorov complexity theory are simple consequences of
functoriality and composition. Most of this talk will be understandable if you only know the definition of a category and a functor.
**

** Speaker: **** Emily Riehl, Johns Hopkins University.** **
**

Date and Time: ** Wednesday May 17, 2017, 5:00 - 6:30 PM. NOTE SPECIAL TIME, Room TBA.**

Title:** Towards a synthetic theory of (∞,1)-categories. **

Abstract: **
This talk will discuss joint work in progress with Michael Shulman that aims to develop a synthetic theory of (∞,1)-categories in
homotopy type theory. This work is motivated by a particular model of homotopy type theory in the category of simplicial spaces,
which is an example of an ∞-cosmos, a "universe" in which one can develop a the basic category theory of infinite-dimensional
categories "synthetically" (i.e. in ignorance that the objects being discussed are simplicial spaces) as opposed to "analytically"
(as is the strategy of similar work by Joyal and Lurie).
**

Previous Semesters:

Other Category Theory Seminars: