Student Working seminar in Algebra & Geometry

- Category Theory & De Rham Cohomology -

- Fall 2016 -

TIME: Tuesday 4:00 - 5:30 pm.

ROOM: 628.

ORGANIZERS: Taylor Brysiewicz, Timo de Wolff, Kevin Kordek, and Ola Sobieska.
Email: tbrysiewicz(at)math.tamu.edu, dewolff(at)math.tamu.edu, kordek(at)math.tamu.edu, sobieska(at)math.tamu.edu

GOALS:
STRUCTURE:

REFERENCES:


CATEGORY THEORY SCHEDULE
Date Facilitator Reading Assignment Topic
8/30/16 N/A N/A Organizational meeting
9/6/16 Pablo Sanchez Ocal CWM I. 1-4 Definition of category, functor, natural transformations, etc
9/13/16 Konrad Wrobel CWM I. 5-8 Monics, epis, zeros, foundations, large categories, hom-sets, etc
9/20/16 Alex Ruys de Perez CWM II. 1-4 Duality, contravariance/opposites, products of categories, functor categories, etc
9/27/16 Adam Deaton CWM II. 5-8 The category of all categories, comma categories, graphs/free categories, quotient categories, etc
10/4/16 Christian Williams CWM III. 1-4 Universal arrow, Yoneda lemma, coproducts/colimits, products and limits, etc
10/11/16 Dr. Eric Rowell N/A Rigid, balanced, monoidal categories



DE RHAM COHOMOLOGY SCHEDULE
Date Facilitator Reading Assignment Topic
10/18/16 Nida Obatake TBA Differential Forms and Manifolds. Integration. Stoke's Theorem.
10/25/16 Dustin McPhate TBA The De Rham Complex and De Rham Cohomology. Examples and formal properties.
11/1/16 Fulvio Gesmundo BT I.2, I.4, I.5. L 17 (Theorem 17.20 on), 18. Examples and Tools. Mayer Vietoris, Kunneth Theorem, De Rham Theorem, etc.
11/8/16 David Buzinski BT I.5 Poincare Duality for Compact Orientable Manifolds. Examples.
11/15/16 Kash Bari BT I.6 More Poincare Duality (more geometric viewpoint)
11/22/16 Dr. Paulo Lima-Filho N/A Characteristic Classes for Real and Complex Vector Bundles