Graduate Geometry Seminar



Welcome to the homepage of the UCSB Graduate Geometry Seminar. The purpose of this seminar is to provide a structured forum for graduate students to discuss their interests in differential geometry and related fields.



Spring Quarter 2017

We collaboratively read Lectures on Mechanics by Jerrold E. Marsden. (flyer)

  1. Introduction
  2. A Crash Course in Geometric Mechanics
  3. Tangent and Cotangent Bundle Reduction
  4. Relative Equilibria
  5. The Energy-Momentum Method
  6. Geometric Phases
  7. Stabilization and Control
  8. Discrete Reduction
  9. Mechanical Integrators
  10. Hamiltonian Bifurcation

Each participant is responsible for mastering a different section of the weekly reading, as determined at the end of the previous meeting.




Winter Quarter 2017

A conference-style seminar with each speaker presenting a chapter of A Mathematical Introduction to Conformal Field Theory, by Martin Schottenloher.



Saturday Jan 14, 9am
Conformal Transformations and Killing Fields

Joey Chahine
10
The Conformal Group

Alexandra Miller*
11
Central Extensions of Groups

Colleen Delaney
12
Central Extensions of Lie ALgebras and Bargmann's Theorem

Brianna Grado-White*
Seth Koren*
1
The Virasoro Algebra

Alex Kinsella*
Sunday Jan 15, 9am
Representation Theory of the Virasoro Algebra

Zach Blumenstein
10
String Theory as a Conformal Field Theory

Eric Mefford*
11
Axioms of Relativistic Quantum Field Theory

Matt Brown*
12
Foundations of Two-Dimensional Conformal Quantum Field Theory

Matt Brown*
1
Vertex Algebras

Wade Bloomquist
2
Mathematical Aspects of the Verlinde Formula

Casey Blacker

*Department of Physics




Fall Quarter 2015

This quarter we will work through Methods of Classical Mechanics, by V.I. Arnold.



Oct 3
Newtonian Mechanics

Milind Shyani*
Oct 10
Variational Principles

Kyle Mylonakis
Oct 17
Lagrangian Mechanics on Manifolds

Joey Chahine
Oct 24
Oscillations

Brianna Grado-White*
Seth Koren*
Oct 31
Rigid Bodies

Liam Dalton
Nov 7
Symplectic Manifolds

Yihan Li
Nov 14
Canonical Formalism

Matthew Brown*
Nov 21
Introduction to Perturbation Theory

Megan Leoni*
Nov 28
The Hydrodynamics of an Ideal Fluid

Chaitanya Murthy*
Dec 5
Contact Structures

Casey Blacker

*Department of Physics




Fall Quarter 2014

We are reading Characteristic Classes, by John Milnor and James Stasheff.


We meet 10am Saturday in Room 6635, Floor 6 of South Hall.

Oct 11
Introduction and Review

Ebrahim Ebrahim
Oct 18
Stiefel-Whitney Classes

Wade Bloomquist
Oct 25
Grassmann Manifolds and Universal Bundles

Alex Rasmussen
Nov 1
The Cohomology Ring H*(Gn ; Z2 )

Casey Blacker
Nov 8
Oriented Bundles and the Euler Class

Zhongmin Jin
Nov 15
The Thom Isomorphism Theorem

Yihan Li
Nov 22
Obstructions

Changliang Wang
Nov 29
Chern Classes

Ebrahim Ebrahim
Dec 6
Pontrjagin Classes

Casey Blacker
Dec 13
Chern Classes and Pontrjagin Numbers

Xingshan Cui