Category Theory, Knot Polynomials, and Projective Geometry.

Registration for the Summer Intensive is now open.

The Summer Intensive will be held from the beginning of July to the end of August.

It will consist of 2 courses per month of 3 hours during six weeks on Category Theory, Knot Polynomials, and/or Projective Geometry.

It is open to anyone and does not presuppose a previous technical background. Texts and articles are introduced in the intensive.

An Open internet forum will run concurrently with the course to both assist with any questions and to make room for a discussion between participants.

The aim is to introduce those working through Lacanian theory to a constructive approach to the fundamental concepts.

Cost for all six sessions: $750. (= six credit hours for those participating in the Sclinic)

- Cartel was held in 2012.
- Date: Begins June 29, 2013 11:00 am / Course Change in effect: Part I_ Aristotle's Physics

**Summer Immersion 2014: Algebra, Logic, & Topology****Tuition:**$300.**First Meeting:**11:00-1:30 Saturday July 12, 2014; then three more Saturdays till Aug. 2.**Requirements**: Open to the Public. The immersion is for all levels and requires no previous background in logic or mathematics.Class limited to first six applications (reception of tuition required to confirm registration).**Descriptive:**The immersion will concentrate on developing a translation between Algebra, Logic, and Topology. It proceeds in the manner of an atelier in the sense that the participant will need paper, color pencils-pen, scissors to construct topological objects and images that conform to the writing of Logic and Algebra.The immersion is not a lecture, but is a collaborative effort in presenting constructions that responds to a problem posed during the course.The immersion is developed in the context of the recent 'Constructing Oedipus' course, especially the problem of symmetries and dualities in space. This much said, the immersion will not develop the translation into the psychoanalytic vocabulary, but will concentrate solely on the Algebra, Logic, and Topology.**Text:**The immersion will use as its reference*Groups and Their Graphs*by Israel Grossman and WIlhem Magnus; American Mathematical Association, 1964.Pre-immersion assignment: it is advised to read

*Groups and Their Graphs*chpts. 1–4 with a focus on writing a presentation of a triangle in space (2 and 3 dimensions).**Plan of Immersion****I - July 12:**Call for presentations and constructions of the Group of a triangle in space. Call for the presentation of the multiplication table of the Group for the triangle. Call for the presentation of the axioms of a Group.Discussion of problems/results: symmetries, rotations, identities, etc.Assignment for July 19: Read Chpts. 5, 7,10. Focus: writing the presentation of a tetrahedron in space

**II - July 19:**Call for presentations of the graph of the group of a triangle. Call for presentations and constructions of the Group of a tetrahedron in space (3 dimensions and 4). Call for the graph of the group of a tetrahedron.Assignment for July 26: Read 11,12, 13.

**III - July 26:**Call for presentations and constructions of the Normal Sub-group, Galois Groups, and Quarternions.Assignment for August 2: Read Chpt. 14 on the Group of Links and handout of immersion on Groups of Knots and Logic. Focus on the Group of the Knot, Link, and Lock – with the translation in to Logic.

**IV - Aug. 2**: Call for constructions and/or presentations of the Group of the Knot, Link, or Lock.Call for a translation of the Algebraic (Group) notation into a Logic of the Knot.Concluding summaries from the participants (if they have one) and proposals for future work.- The course constructs graphs, surfaces, then knots in a category, while showing the implications of Gödel's Incompleteness Theorems.
- Introduction To A Theory Of Knots

The 2009 Summer Intensive aims to introduce a theory of knots without vulgarizing. This much said, no previous mathematical or technical competence is required to participate, just a certain amount of perseverance, colored pens, and paper.

INSTRUCTOR

Robert Groome and invited guests.

PLACE & TIME

It will take place on every Saturday from 12:00-2:30 from June 6th to July 18th in Santa Monica, CA.

COST

Participation costs: $750.

COURSE ADMISSION

Open. Limited to 5 participants. Pre-registration suggested. To enroll contact – Place@topoi.net – for code and access to class via the website.

COURSE SUMMARY

1. Introduction to the theory of Links, Locks, and Knots: Problems, Theorems, and Conjectures.

2. The Object of Knot Theory: Duality, Symmetry, and Projection

3. Methods of Knot Theory: Codes, Graphs, Groups, and Polynomials

4. Reformulation of the Classical Theory of Knots: Lock Theory

5. Generalized Lock Theory

6. Modern Analytic Constructions: Lacan, Soury, Vappereau, and Bertheux.

7. Open questions and final presentations

TEXTS

Adams, The Knot Book, 1994.

P.G. Tait, On Knots, 1876-85.

R. Groome, Return to On Knots: New Elements For An Analytic Construction, 2009.