Spencer Stirling

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Informal meeting 1: May 19 2-4pm INSCC 445 (probably)

We will discuss and plan the talk for May 28 which will concern
various concepts about Monoidal Categories (see below for
the references).

**TALK 1: BASICS OF CATEGORY THEORY (Ren Pankovich) May 21 2-4pm**

MacLane - Categories for the Working Mathematician, Chapter 1

Kassel - Quantum Groups, Chapter XI.1 - XI.2

**TALK 2: BASICS OF CATEGORY THEORY (Ren Pankovich) May 26 2-4pm**

MacLane - Categories for the Working Mathematician, Chapter 1

Kassel - Quantum Groups, Chapter XI.1 - XI.2

**TALK 3: MONICS, EPIS, NULLS, AND ZEROS (Ren Pankovich) May 26 2-4pm**

MacLane - Categories for the Working Mathematician, Chapter 1

Kassel - Quantum Groups, Chapter XI.1 - XI.2

**TALK 4: NATURAL TRANSFORMATIONS (Ren Pankovich) June 2 2-4pm**

MacLane - Categories for the Working Mathematician, Chapter 1

Kassel - Quantum Groups, Chapter XI.1 - XI.2

**TALK 5: MONOIDAL CATEGORIES (Aaron Ballard) June 4 2-4pm**

MacLane - Categories for the Working Mathematician, Chapter VII.1 - VII.3

Kassel - Quantum Groups, chapter XI.2 - XI.7

Joyal and Street - Braided Monoidal Categories section 1

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.1-4.2

**TALK 6: EXERCISES IN MONOIDAL CATEGORIES (Aaron Ballard) June 9 2-4pm**

MacLane - Categories for the Working Mathematician, Chapter VII.1 - VII.3

Kassel - Quantum Groups, chapter XI.2 - XI.7

Joyal and Street - Braided Monoidal Categories section 1

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.1-4.2

**TALK 7: COHERENCE IN MONOIDAL CATEGORIES (Aaron Ballard) June 11 2-4pm**

MacLane - Categories for the Working Mathematician, Chapter VII.1 - VII.3

Kassel - Quantum Groups, chapter XI.2 - XI.7

Joyal and Street - Braided Monoidal Categories section 1

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.1-4.2

**TALK 8: COHERENCE IN MONOIDAL CATEGORIES II (Aaron Ballard) June 16 2-4pm**

MacLane - Categories for the Working Mathematician, Chapter VII.1 - VII.3

Kassel - Quantum Groups, chapter XI.2 - XI.7

Joyal and Street - Braided Monoidal Categories section 1

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.1-4.2

**TALK 9: COHERENCE IN MONOIDAL CATEGORIES III (Aaron Ballard) June 18 2-4pm**

MacLane - Categories for the Working Mathematician, Chapter VII.1 - VII.3

Kassel - Quantum Groups, chapter XI.2 - XI.7

Joyal and Street - Braided Monoidal Categories section 1

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.1-4.2

**TALK 10: BRAIDED MONOIDAL CATEGORIES (Yuting Hu) June 23 2-4pm**

Turaev - Quantum Invariants of Knots and 3 Manifolds Section I.1.2

Bakalov and Kirillov - Lectures on Tensor Categories and Modular Functor Chapter 1

Kassel - Quantum Groups, chapter XIII

Joyal and Street - Braided Monoidal Categories section 2

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.3

**TALK 11: BRAIDED MONOIDAL CATEGORIES (Yuting Hu) June 25 2-4pm**

Turaev - Quantum Invariants of Knots and 3 Manifolds Section I.1.2

Bakalov and Kirillov - Lectures on Tensor Categories and Modular Functor Chapter 1

Kassel - Quantum Groups, chapter XIII

Joyal and Street - Braided Monoidal Categories section 2

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.3

**TALK 12: THEOREMS IN BRAIDINGS (Yuting Hu) June 30 2-4pm**

Turaev - Quantum Invariants of Knots and 3 Manifolds Section I.1.2

Bakalov and Kirillov - Lectures on Tensor Categories and Modular Functor Chapter 1

Kassel - Quantum Groups, chapter XIII

Joyal and Street - Braided Monoidal Categories section 2

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.3

**TALK 13: THEOREMS IN BRAIDINGS (Yuting Hu) July 2 2-4pm**

Turaev - Quantum Invariants of Knots and 3 Manifolds Section I.1.2

Bakalov and Kirillov - Lectures on Tensor Categories and Modular Functor Chapter 1

Kassel - Quantum Groups, chapter XIII

Joyal and Street - Braided Monoidal Categories section 2

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.3

**TALK 14: CENTER CONSTRUCTION (Yuting Hu) July 9 2-4pm**

Turaev - Quantum Invariants of Knots and 3 Manifolds Section I.1.2

Bakalov and Kirillov - Lectures on Tensor Categories and Modular Functor Chapter 1

Kassel - Quantum Groups, chapter XIII

Joyal and Street - Braided Monoidal Categories section 2

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.3

**TALK 15: CENTER CONSTRUCTION (Yuting Hu) July 14 2-4pm**

Turaev - Quantum Invariants of Knots and 3 Manifolds Section I.1.2

Bakalov and Kirillov - Lectures on Tensor Categories and Modular Functor Chapter 1

Kassel - Quantum Groups, chapter XIII

Joyal and Street - Braided Monoidal Categories section 2

Stirling - Abelian Chern-Simons with toral gauge group, modular tensor categories, and group categories, chapter 4.3

**TALK 16: TENSOR STRUCTURES (Robert Roundy) July 16 2-4pm**

Kassel - Quantum Groups, chapter II

**TALK 17: TENSOR STRUCTURES (Robert Roundy) July 21 2-4pm**

Kassel - Quantum Groups, chapter II

**TALK 18: TENSOR STRUCTURES (Robert Roundy) July 23 2-4pm**

Kassel - Quantum Groups, chapter II

**TALK 19: UNIVERSALITY OF TENSOR STRUCTURES (Robert Roundy) July 28 2-4pm**

Kassel - Quantum Groups, chapter II

**TALK 20: PRODUCTS AND COPRODUCTS (Robert Roundy) July 30 2-4pm**

Kassel - Quantum Groups, chapter II

**TALK 21: RIGIDITY FOR VECTOR SPACES (Robert Roundy) August 4 2-4pm**

Kassel - Quantum Groups, chapter II

**TALK 22: RIGIDITY AND GRAPHICAL CALCULUS (Robert Roundy) August 6 2-4pm**

Kassel - Quantum Groups, chapter XIV

FALL CONTINUATION

**TALK 23: REVIEW OF SUMMER (Ren Pankovich) September 9 2-4pm**

**TALK 24: BALANCING (Ren Pankovich) September 16 2-4pm**

Kassel - Quantum Groups, chapter XIV.3

Joyal and Street - Braided Tensor Categories section 6

**TALK 25: BALANCING (Ren Pankovich) September 23 2-4pm**

Kassel - Quantum Groups, chapter XIV.3

Joyal and Street - Braided Tensor Categories section 6

**TALK 26: LEFT/RIGHT RIGIDITY ISOMORPHISMS (Ren Pankovich) October 7 2-4pm**

Stirling and Wu - Braided Categorical Quantum Mechanics I

Kassel - Quantum Groups, chapter XIV.3

Joyal and Street - Braided Tensor Categories section 6

**TALK 27: INTRO TO SEMISIMPLICITY (Robert Roundy) October 28 2-4pm**

MacLane - Categories for the Working Mathematician Chapter III and Chapter VIII.2

**TALK 28: BIPRODUCTS (Robert Roundy) November 4 2-4pm**

MacLane - Categories for the Working Mathematician Chapter III and Chapter VIII.2

**TALK 29: ABELIAN CATEGORIES (Robert Roundy) November 18 2-4pm**

MacLane - Categories for the Working Mathematician Chapter III and Chapter VIII.2

**TALK 30: MODULAR TENSOR CATEGORIES (Aaron Ballard) December 2 2-4pm**

Turaev

**TALK 31: MODULAR TENSOR CATEGORIES II (Aaron Ballard) December 9 2-4pm**

Bakalov and Kirillov

SPRING 2010 CONTINUATION

**TALK 32: QUANTUM 6J SYMBOLS (Spencer Stirling) January 21 2-3:30pm**

Turaev Chapter VI

**TALK 33: QUANTUM 6J SYMBOLS II (Spencer Stirling) January 26 2-3:30pm**

Turaev Chapter VI

**TALK 34: Z2 LATTICE GAUGE THEORY (Robert Roundy) February 9, 2010 2-3:30pm**

Levin and Wen - arXiv:cond-mat/0404617v2 (2004)

**TALK 35: LATTICE GAUGE THEORY PART II (Robert Roundy) February 16, 2010 2-3:30pm**

Levin and Wen - arXiv:cond-mat/0404617v2 (2004)

**TALK 36: INTRO TO STRING NETS (Robert Roundy) February 23, 2010 2-3:30pm**

Levin and Wen - arXiv:cond-mat/0404617v2 (2004)

**TALK 37: HAMILTONIANS FOR STRING NETS (Ren Pankovich) March 2, 2010 2-3:30pm**

Levin and Wen - arXiv:cond-mat/0404617v2 (2004)

**TALK 38: QUASIPARTICLE EXCITATIONS IN STRING NETS (Yuting Hu) March 9, 2010 2-3:30pm**

Levin and Wen - arXiv:cond-mat/0404617v2 (2004)

**TALK 39: QUASIPARTICLE EXCITATIONS IN STRING NETS II (Yuting Hu) March 11, 2010 2-3:30pm**

Levin and Wen - arXiv:cond-mat/0404617v2 (2004)

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